Solution:
Given:
[tex]2x^5+5x^4-9x+5[/tex]A coefficient is a number multiplied by a variable.
Hence,
[tex]The\text{ coefficient of }x^5\text{ is 2}[/tex]Therefore, the coefficient is 2.
Which inequality below is represented by the following graph: A. y < -2x² + 10z - 8 B. y 2x² + 10x – 8
Explanation
We are required to determine the inequality that satisfies the given graph.
This is achieved thus:
We can deduce from the graph that the curve drawn is not a broken line. Therefore, it cannot be strictly greater than or strictly less than.
We know that only "true" region is shaded. By testing the origin, we can deduce that the correct inequality is:
[tex]y\geqslant-2x^2+10x-8[/tex]Hence, the answer is:
Option D
Write an equation of a line in a slope intercept form that has a slope of 3/7 and y intercept of -23
If the slope is 3/7 and the y-intercept is -23, let's replace them in the formula.
y = mx + b
m is the slope and b is the y-intercept.
Then:
[tex]\begin{gathered} y=\frac{3}{7}x+\text{ \lparen}-23) \\ y=\frac{3}{7}x\text{ - }23 \end{gathered}[/tex]Assume that a researcher randomly selects 14 newborn babies and counts the number of girls, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the questions using the table.
Find the probability of selecting 5 or fewer girls.
A probability distribution is one that lists all of the outcomes of an experiment or a variable together with their respective probabilities. The total probability must equal 0.0424 because it includes all of the possible outcomes.
How do you calculate probability?probability distribution for 5 fewer girls is
(0.001+0.006+0.022+0.061+0.122) divided by 5
is equal to 0.0424
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution.Theoretical Probability is one of three main categories of probability. Scientific Probability. Probability axiomatically.To learn more about probability refer to:
https://brainly.com/question/251701
#SPJ1
Let f= {(5,5),(8,-8),(-8,5)}. Find (a) f(5) and (b) f(-8).
The given function f(x) is
[tex]f(x)=\lbrace(5,5),(8,-8),(-8,5)\rbrace[/tex]We need to find
a) f(5)
It means finding the value of the y-coordinate in the ordered pair that has x-coordinate = 5
Look at the function
At x = 5, y = 5 (1st orderd pair), then
f(5) = 5
b) f(-8)
It means finding the value of the y-coordinate in the ordered pair that has x-coordinate = -8
Look at the function
At x = -8, y = 5, (last ordered pair), then
f(-8) = 5
12x(4+16)-78×3 =
O A) 6
O B) 54
O C) 159
OD) 486
Answer:
The answer for 12x(4+16)-78×3= is 6
The exact Value of the sine, cosine, and tangent about of the angle
Answer:
Below are the exact values of sine, cosine, and tangent of the given angle -11π/12.
[tex]sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}[/tex][tex]cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4}[/tex][tex]tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}=2-\sqrt{3}[/tex]Explanation:
We can use the following trigonometric identities to solve the exact value of the given angle.
[tex]\begin{gathered} sin(x+y)=sin\text{ }x\text{ }cos\text{ }y+cos\text{ }x\text{ }sin\text{ }y \\ cos(x+y)=cos\text{ }x\text{ }cos\text{ }y-sin\text{ }x\text{ }sin\text{ }y \end{gathered}[/tex]For sine function, we have:
[tex]\begin{gathered} sin(-\frac{11\pi}{12})=sin(\frac{\pi}{4}-\frac{7\pi}{6}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=sin\text{ }\frac{\pi}{4}cos(-\frac{7\pi}{6})+cos\text{ }\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}[/tex]Simplify.
[tex]\begin{gathered} sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})+\frac{\sqrt{2}}{2}(\frac{1}{2}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}+\frac{\sqrt{2}}{4} \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}+\sqrt{2}}{4} \\ sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4} \end{gathered}[/tex]For cosine function, we have:
[tex]\begin{gathered} cos(-\frac{11\pi}{12})=cos(\frac{\pi}{4}-\frac{7\pi}{6}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=cos\frac{\pi}{4}cos(-\frac{7\pi}{6})-sin\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}[/tex]Simplify.
[tex]\begin{gathered} cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})-(\frac{\sqrt{2}}{2})(\frac{1}{2}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}-\frac{\sqrt{2}}{4} \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}-\sqrt{2}}{4} \\ cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4} \end{gathered}[/tex]Lastly, for tangent function, it is the ratio between sine and cosine function.
[tex]tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}[/tex]Applying the division rule, we get the reciprocal of the denominator and multiply it to the numerator. The equation becomes:
[tex]tan(-\frac{11\pi}{12})=sin(-\frac{11\pi}{12})\times\frac{1}{cos(-\frac{11\pi}{12})}[/tex]Now, let's replace the sine and cosine value that we have calculated above.
[tex]tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}\times\frac{4}{-\sqrt{6}-\sqrt{2}}[/tex]Since 4 is a common factor on both numerator and denominator, we can cancel it out. The equation then becomes,
[tex]tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}[/tex]To further simplify the function, let's remove the radicals in the denominator by rationalization.
[tex]\begin{gathered} tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}\times\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}+\sqrt{2}} \\ tan(-\frac{11\pi}{12})=\frac{6-\sqrt{12}-\sqrt{12}+2}{6-\sqrt{12}+\sqrt{12}-2} \end{gathered}[/tex][tex]\begin{gathered} tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{12}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{4\times3}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-(2\times2\sqrt{3})}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-4\sqrt{3}}{4} \\ Factor\text{ }4\text{ }in\text{ }the\text{ }numerator. \\ tan(-\frac{11\pi}{12})=\frac{4(2-\sqrt{3})}{4} \\ Cancel\text{ }4. \\ tan(-\frac{11\pi}{12})=2-\sqrt{3} \end{gathered}[/tex]How to graph using this info and create a function ?
The instantaneous rate of change at x = 2 is 0
at x = 3 is negative
0 <= x <= 4 is 0
a function has an instantaneous rate of change of 0 at a maximum or minimum
the instantaneous rate of change at x = 3 being negative means it goes down after the maximum or minimum meaning it is a maximum
the average rate of change on the interval is 0, so the function goes up and then down
these all sound like a parabola
y = -2(x - 2)^2 + 10 is a parabola that fits the requirements
The vertices of a rectangle are R(-5, -5), S(-1, -5), T(-1, 1), and U(-5, 1). After translation, R' is the point (-9, 1). Find the translation rule and
coordinates of U'.
2 of 27
Answer:
Transformation rule: (x, y) → (x - 4, y + 6),Coordinates of U' = ( - 9, 7).==============
Compare the coordinates of R and R' to find the transformation rule:
R(- 5, - 5) → R'(- 9, 1)Change in x:
-9 - (-5) = - 4Change in y:
1 - (-5) = 6The rule is:
(x, y) → (x - 4, y + 6)Apply this rule to U to find the coordinates of U':
U(-5, 1) → U'(-5 - 4, 1 + 6) = U'(-9, 7)Answer quick! Due today!Please help with explanation each graph shown is a translation of the graph of f(x)=x^2 write the function in vertex form
For a graph with f(x)=x^2, the vertex of the parabola is at the origin.
In the given graph, the parabola is shifted 3 units to the left and 1 unit down.
The general vertex form of a parabola is,
[tex]f(x)=a(x-h)^2+k[/tex]Here, h is the horizontal shift and k is the vertical shift.
Since the graph is only translated and not shrinked or expanded , a=1.
Since the graph is shifted horizonatlly to the left, h is negative.
So, h=-3.
Since the graph is shifted vertically down, k is negative.
So, k=-1.
So, the equation for the given graph becomes,
[tex]\begin{gathered} f(x)=(x-(-3)^2-1 \\ f(x)=(x+3)^2-1_{} \end{gathered}[/tex]Therefore, the function in vertex form is,
[tex]f(x)=(x+3)^2-1[/tex]pounds. To be able to ride in a car together, how muchcan you weigh? Write and solve an inequality.(1 point)Ox-60221; at most 60 pounds
Let x represent your weight, then we can set the following inequality:
[tex]x+60\leq221.[/tex]Solving the inequality for x, we get:
[tex]\begin{gathered} x+60-60\leq221-60, \\ x=161. \end{gathered}[/tex]Therefore, at most, you can weigh 161 pounds.
Answer: [tex]x+60\leq221,\text{ at most 161 pounds.}[/tex]Use the table to find the product of the two polynomials. Write your answers in descending orde.
Given:
Given the polynomial
[tex](4x^2-4x)(x^2-4)[/tex]Required: The product of the polynomials
Explanation:
Fill the table by taking the product of the values written in the left and up of each column.
The product of the polynomials is the sum of each entry in the column. Thus,
[tex](4x^2-4x)(x^2-4)=4x^4-4x^3-16x^2+16x[/tex]Final Answer:
[tex](4x^2-4x)(x^2-4)=4x^4-4x^3-16x^2+16x[/tex]3. Sharon is using a calculator to find out
how many hours she has spent on a
certain job. She divides, and her display
reads:
4.666666666
Assuming her calculations are correct,
how many hours did she spend on the
job?
A. 4 1/6
B. 4 2/3
C. 4 6/7
D. 46
Answer:
4 6/7
Step-by-step explanation:
(Not really sure you should go with whatever answer you're sure of)
or 4 1/6
Answer:
B. 4 2/3
it's right, I took this last year.
meic had m CDs. He gave 3 CDs to a friend. How many CDs does meic have now?
AS per the concept of algebraic expression, There are m - 3 CDs meic have now.
Algebraic expression:
Algebraic expression refers the idea of expressing numbers using letters or alphabets without specifying their actual values.
Given,
Meic had m CDs. He gave 3 CDs to a friend.
Here we need to find the number of CDs does meic have now.
Here we know that the number of CDs Meic have is M.
Ad he gave 3 of his CDs to his friend.
Which means that 3 number of CDs in the total number is reduced.
So, the total number of CDs is calculated as,
=> number of CDs - 3
Therefore, the number f CDs does Meic had is m - 3.
To know more about Algebraic expression here.
https://brainly.com/question/953809
#SPJ1
Which of the following equations has the same graph as 2x + 3y = 12?
Select all that apply.
A. y-2=-2/3(x-3)
B. x+3/2y=6
c. -2x-3y = - 12
D. y-2=-2/3x+4
E. y=-2/3x+4
Answer:
A, B, C, E
Step-by-step explanation:
You want to know the equations on the list that have the same graph as 2x+3y=12.
Comparing equationsEquations are most easily compared when they are written in the same form. Here, there is a mix of "standard form", "slope-intercept form", and "point-slope form." We can convert all of these to slope-intercept form to make the comparison.
EquationsReference equation
2x +3y = 12 ⇒ 3y = -2x +12 ⇒ y = -2/3x +4
A.y -2 = -2/3(x -3) ⇒ y = -2/3x +2 +2 ⇒ y = -2/3x +4 . . . equivalent
B.x +3/2y = 6 ⇒ 3/2y = -x +6 ⇒ y = -2/3x +4 . . . equivalent
This is the original equation divided by 2.
C.-2x -3y = -12 ⇒ -2x +12 = 3y ⇒ y = 2/3x +4 . . . equivalent
This is the original equation multiplied by -1.
D.y -2 = -2/3x +4 ⇒ y = -2/3x +6 . . . not equivalent
E.y = -2/3x +4 . . . equivalent
Draw the figure and its rotation as described. Identify the coordinates of the image. J(−4, 1), K(−2, 1), L(−4,−3) 90° clockwise about vertex L.
The new coordinates of the image after rotation are L′(−4,1), J′(0,−3), and K′ (0,−5).
Step 1:
The first thing we have to do is to graph the figure. We will color it red. The graph is shown below:
Step 2:
We know that the distance between L and J is 4 units upward. If we rotate it 90° clockwise, the direction will become right. Therefore,
J′ is 4 units to the right of L. We can see that the distance between
J and K is 2 units to the right. If we rotate it 90° clockwise, the direction will become downwards. Therefore, K′ is 2 units down of L′.
Then, connect L and K′ to complete the figure. The new coordinates are L′(−4,1), J′(0,−3), and K′ (0,−5). We will graph it and color it blue.
Hence the answer is the new coordinates of the image after rotation are L′(−4,1), J′(0,−3), and K′ (0,−5).
To learn more about coordinates click here https://brainly.com/question/17206319
#SPJ1
Jodi buys nine pens at $1.10 per pen. Which of the following represents the change she would receive if she purchased the pens using a $20 bill?
A $20 – (9)($1.10)
B ($20 – 9)($1.10)
C $20 + (9)($1.10)
D ($20 – $1.10)(9)
E $20 – 9 – $1.10
The expression (A) $20 – (9)($1.10) will correctly represents the given situation.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression that represents the given situation will be:
The total bill is 20$.The number of pens purchased is 9.Each pen cost $1.10.Then, the expression will be:
20 - 9(1.10)Therefore, the expression (A) $20 – (9)($1.10) will correctly represents the given situation.
Know more about expressions here:
https://brainly.com/question/28934492
#SPJ1
Trying to pass math class
Answer:
55
Step-by-step explanation:
All the triangles are right angled triangles.
So, one of the angle is 90°.
There is a property of angle of triangles.
Exterior angle = Sum of opposite interior angles
145 = m∠1 + 90
m∠1 = 145 - 90
m∠1 = 55
Simplify
[tex]( \sqrt{3}) \: ( {}^{5} \sqrt{3} )[/tex]
a :
[tex]3 \frac{1}{10} [/tex]
B:
[tex]3 \frac{3}{5} [/tex]
C:
[tex]3 \frac{9}{10} [/tex]
D:
[tex]3 \frac{7}{10} [/tex]
Find number if 5/3 of it is 15
Answer:
25
Step-by-step explanation:
15/3 = 5
5*5 = 25
Easy as pie
how do you find the distance between the point shown?
We can find the distance between the points shown by adding the distance between each point and the y-axis which is the fourth option.
We are given the points:-
A (-8, -4) and,
B (2, -4)
We have to find the distance between the points AB.
We know that,
Distance between points AB = Distance between A and y -axis + Distance between y -axis and B
Hence, according to the cartesian plane given, we can write,
We can find the distance between the points shown by adding the distance between each point and the y-axis which is the fourth option.
To learn more about distance, here:-
https://brainly.com/question/15172156
#SPJ1
If you have a 77.2% and you got 34% on a test and it’s worth 60% of your grade, what would you grade be now?
Answer:
If you have a 77.2% and you got 34% on a test and it’s worth 60% of your grade, your percentage grade would be 63.2%.
The limousine that you hired costs $400 plus $45 for each hour of service. If your total cost for the limousine is $670, how many hours did you have the vehicle?
Answer: 6 hours
Step-by-step explanation:
670-400
270
270/45
6 hours
15. A scale model of the Shanghai Tower is 3 inches tall. The actual tower is 2,073 feet tall. What is the scale?
en español porfis
The scale is of 8,292 ft. 1 ft in the scale is equal to 8292 ft of the actual.
Given, a scale model of the Shanghai Tower is 3 inches tall.
The actual tower is 2,073 feet tall.
We have to find the scale.
Now, as 1 ft = 12 inch
1 inch = 1/12 ft
3 inches = 3/12 ft
3 inches = 1/4 ft
So, 1/4 ft of scale = 2,073 ft of actual
1 ft of scale = 8,292 ft of actual
So, 1 ft in the scale is equal to 8,292 ft of the actual.
Hence, 1 ft in the scale is equal to 8,292 ft of the actual.
Learn more about Unitary Method here https://brainly.com/question/28627316
#SPJ9
What is the slope of the line that passes through the points (12, -13) and (-18, 11)? Round your answer to the nearest tenth.
The slope of the line is 0.8.
What is slope of the line?
The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x.
slope of the line = (y2-y1)/x2-x1
Here, the points are (12,-13) and (-18,11)
x1=12,y1=-13, x2=-18, y2=11
m (slope of line) = 11+13/(-18-12)
=24/-30
=-4/5
=0.8
To know more about slope of line, visit;
https://brainly.com/question/5600317
#SPJ1
One year, the population of a city was 253,000. Several years later it was 288,420. Find the percent increase.
The percentage increase is 14%
Given,
In the question;
The population of a city was 253,000.
and, Several years later it was 288,420.
To find the percent increase.
Now, According to the question;
Based on the given conditions,
Formulate:
The population of a city was 253,000.
Several years later = 288,420
(288420 - 253000) ÷ 253000
[tex]\frac{288420 - 253000}{253000}[/tex]
Calculate
= 35420/ 253000
= 7/50
Convert to percentage
7/50
Multiply a number to both the numerator and the denominator
7/50 x 2/2
= 14/100
= 14%
Hence, The percentage increase is 14%
Learn more about Percentage at:
https://brainly.com/question/15423393
#SPJ1
The robotics team needs new uniforms. The students plan to sell plush toy lions(The school mascot) for 5$ each. The students find three companies on-line that sell stuffed mascots. Company a sell 18 lions for $51.84. company B sells 12 lions for 34.32. company c charges 42.75 for 15 lions. which company has the best buy
Answer:
Company B would be the best place to get their supply from. First, I multiplied all of the quantities by 5 (33.72*5)(44.48*5)(42.6*5) and got my sums. Then, I subtracted the price to be earned from selling the plush toys by the price of the bundle. Lastly, I compared the amounts earned by using each.
A. $26.28 B. $35.52 C. $32.4
Company B is the best place to buy from.
0Over ten years, the population of fish in a lake increases by 3%. After the increase, there are 10,094 fish. Whichexpressions are equivalent to the number of fish ten years before? Select all that apply.9,80010,39710,094 : 1.0310,094 (100+310010,094 - 3%Brun
The fish population has been increasing over 10 years giving a total of 10094 as a result. We are asked to find the initial population of fish.
So we write the expression for popukation increase:
[tex]N(t)=N_{0\, }(1+0.03)^t[/tex]where No is the initial population, and what we want to find, while N(t) is the current population (10094) and the exponent (t) is the equivalent to ten year units (so we use "1"). The rate is 3% per ten years, and this in decimal form is 0.03.
We solve for No in the equation by dividing bby 1.03, which gives us:
No= 10094 / 1.03 = 9800
Therefore, one has to select the option 10094 divided by 1.03, (typed as 10094 : 1.03), and also the numerical answer 9800 (first option)
Help asap, The graph compares the total cost of buying movie tickets for members and nonmembers of a movie club
A negative correlation is the relationship where an increase in one of the variable say x lead to a decrease in the other variable say y
In the question given, the variables are the number of workers in the x- axis and the hours of complete job in the y axis
Therefore option C is the only option where increase in the number of workers led to decrease in the hours of complete job
Hence the correct answer is option C
Employee at an antique store are hired at a wedge of $15 per hours, and they got a $9.75 raise each year. naomi make $20.25 per hours working at the store. how long has she worked there
Number of years she worked at the store is 0.5385 years ( 0.6 years approx. ).
What is rate of change ?A rate of change is a measurement of the ratio of one quantity to another. Rate of Change: 1608042=802=401; Change in Y = Change in X; Change in Distance; Change in Time. It develops either at a 40 or 401 rpm rate. This shows that an automobile is traveling at a 40 mph speed.
CalculationRate of early age of employee = $15 per hour
raise price per year = $9.75
Naomi wage per hour = $20.25
then gain extra wage = 20.25 - 15
= $5.25
number of years she worked = 5.25 / 9.75
= 0.5385 years ( 0.6 years approx)
learn more about rate of change here :
brainly.com/question/12786410
#SPJ4
PLS HELP Which of the following quantities are directly proportional?
the number of pumps used to fill a tank and the time needed to fill that tank
Number of pipes to fill a tank and the time required to fill the same tank is directly proportional.
Given,
Direct proportion;
When the ratio x:y is constant, two values, x and y, are said to be directly proportional to one another. If we spend $50 on two pens, as an example. For four pens, it will cost us 100 $When the ratio x:y1 is
Here
Option d Number of pipes to fill a tank and the time required to fill the same tank is directly proportional. Because in a fixed time interval, as the speed of a vehicle increases, the distance travelled by it also increases in the same ratio.
Learn more about direct proportion here;
https://brainly.com/question/28730073
#SPJ1
The given question is incomplete. Completed question is given below;
Which of the following is in direct proportion?
(a) One side of a cuboid and its volume.
(b) Speed of a vehicle and the distance travelled in a
fixed time interval.
(c) Change in weight and height among individuals.
(d) Number of pipes to fill a tank and the time required
to fill the same tank.