The range of values of x which satisifies both of the inequalities is:
(-3, 2)
What range of values of x satisfies both inequalities?Here we have two inequalities:
3 + x < 5
8 + x > 5
And we want to see which range of values of x satisfie both of these inequalities.
If we isolate x on both inequalities, we will get:
3 + x < 5
x < 5 - 3
x < 2
And the other one is:
8 + x > 5
x > 5 - 8
x > -3
Then we havethe compound inequality:
x < 2
x > -3
Then the range of values that satisfies both inequalities is (-3, 2)
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ANAGNOS: Possible. I should warn you, she is much given to tantrums.
ANNIE: Means something is inside. Well, so am I, if I believe all I hear. Maybe you should warn them.
ANAGNOS [FROWNS]: Annie. I wrote them no word of your history. You will find yourself among strangers now, who know nothing of it.
ANNIE: Well, we’ll keep them in a state of blessed ignorance.
Which statement best describes Annie’s attitude toward her upcoming assignment in this excerpt?
The statement that best describes Annie’s attitude toward her upcoming assignment in this excerpt is "she is studious and eager to share her knowledge"
What is the main message of Annie?Annie is all about maintaining optimism and hope throughout life's journey, no matter the circumstances.
The young orphan Annie has led a difficult life in the cruel matriarch Miss Agatha Hannigan's anything-but-cheerful orphanage. With a shattered necklace, she stealthily leaves her orphanage and goes in search of her parents, who she hopes would adopt her.
She may be the offspring of a Marleyan and an Eldian liaison, and her parents abandoned her when she was a baby. But after being transported to the Internment Zone, a guy took her up and started to train her as a warrior so that he could live better in Marley.
Therefore, Annie is studious and eager to share her knowledge.
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Samuel buys 3 bottles of juice that each have an original price of 2.80. He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%. How much does samuel pay 3 bottles of juice?
Samuel pay 5.81 for the 3 bottles of juice.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Samuel buys 3 bottles of juice that each have an original price of 2.80.
And, He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%.
Here, The original cost of 3 bottles of juice = 3 × 2.80
= 8.40
Now, He uses a coupon for 35% off.
Hence, The off price = 35% of 8.40
= 35/100 × 8.40
= 2.94
So, The amount of 3 bottles of juice = 8.40 - 2.94
= 5.46
And, He is changed sales tax at a rate of 6.5%.
Thus, The sales tax on bottles = 6.5% of 5.46
= 6.5/100 × 5.46
= 0.35
Thus, The actual amount of 3 bottles of juice = 5.46 + 0.35
= 5.81
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DE is
midsegment of AABC. Find the value of x
B
X
The length of x in the triangle is 8 units.
How to find the side of a triangle with mid segment?A midsegment is the line segment connecting the midpoints of two sides of a triangle.
The midsegment theorem states that a line segment connecting the midpoints of any two sides of a triangle is parallel to the third side of a triangle and is half of it
Therefore, DE is the mid segment of the triangle ABC. The value of x can be found as follows:
Using the mid segment principle,
BE = EC
BD = DA
Therefore,
x = 8 units
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At a large museum, there are 60 people in each tour group. Use this information to fill in the table. Then plot the ordered pairs given by the table. Number of tour groups Number of people y60120180240300360420480540600660x12345678910110
At a large museum, there are 60 people in each tour group. so that the ordered pairs are 1 - 60 peoples, 2 - 120 peoples, 3 - 180 peoples, 4 - 240 peoples, 5 - 300 peoples, 6 - 360 peoples etc.
What is the ordered pairs?An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
In order to understand a point visually, it can be helpful to position it on the Cartesian plane.
An ordered pair's numerical values may be fractions or integers.
Given that, at a large museum, there are 60 people in each tour group.
In 1 group there are 60 peoples.
In 2 group there are 2 * 60 = 120 peoples.
In 3 group there are 3 * 60 = 180 peoples.
like this the correct ordered pairs are 1 - 60 peoples, 2 - 120 peoples, 3 - 180 peoples, 4 - 240 peoples, 5 - 300 peoples, 6 - 360 peoples etc.
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What is the domain of f(x)=^3radx+2-2
The domain of the function is the set of all real numbers
How to determine the domain of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=^3radx+2-2
Express properly
So, we have the following representation
f(x) = ∛(x + 2) - 2
The above function is a cubic function
A cubic function has no restriction on its input value
This implies that the domain is the set of all real numbers
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5. Ken will flip a fair coin and then randomly choose one of three colored cards. The
possible outcomes are shown below.
Heads
Red
Blue
Green
Red
Blue
Green
What is the probability that tails will turn up and that he will choose a red card?
Tails
The probability that tails will turn up and that he will choose a red card is 1/6.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The probability of choosing a tail is 0.5.
The probability of choosing ref card is 1/3.
Therefore, the probability will be:
= 1/2 × 1/3
= 1/6
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what is the solution to the equation 7.5z-2=8.5.
Answer:
z=1.4
Step-by-step explanation:
honestly, I'm not that smart so i just looked it up.
but Im pretty sure thats the right answer.
annalise works out with a treadmill program that varies the amount of time she runs and walks she has the treadmill set to a walking speed of 15 minutes per mile and a running speed of 9 minutes per mile. The amount of time running and walking can be different for every workout, but she always does a total of 6 miles. (a) suppose that one day, Annalise only walks. How much time would she spend on the treadmill. show your work or explain your answer. (c) write three other combinations for running and walking rimes would she spend on the treadmill. (d) on the graph below, plot the running and walking combinations you determined in parts a, b, and c.
The graph would be a line, where the x-axis represents the distance in miles running, and the y-axis represents the time spent on the treadmill. The points on the graph would be (0,90), (2,78), (4,66), (3,72).
How to solve the problem?(a) If Annalise only walks on the treadmill, she would spend 15 minutes per mile walking. Since she does a total of 6 miles, she would spend 15 minutes/mile * 6 miles = 90 minutes on the treadmill.
(c) Here are three other combinations for running and walking times on the treadmill:
2 miles running and 4 miles walking: 2 miles * 9 minutes/mile running + 4 miles * 15 minutes/mile walking = 18 minutes + 60 minutes = 78 minutes
4 miles running and 2 miles walking: 4 miles * 9 minutes/mile running + 2 miles * 15 minutes/mile walking = 36 minutes + 30 minutes = 66 minutes
3 miles running and 3 miles walking: 3 miles * 9 minutes/mile running + 3 miles * 15 minutes/mile walking = 27 minutes + 45 minutes = 72 minutes
(d) The graph would be a line, where the x-axis represents the distance in miles running, and the y-axis represents the time spent on the treadmill. The points on the graph would be (0,90), (2,78), (4,66), (3,72).
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a survey among tenants of shared apartments asked each tenant what percentage of the cleaning around the apartment he or she does. the survey found that aggregating the percentages for each apartment produces an average of much more than 100%. this result may be due to what bias?
The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.
The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.
In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.
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When parking a car in a downtown parking lot, drivers pay according to the number of hours or fraction thereof. The probability distribution of the number of hours cars are parked has been estimated as follows:
A. Mean=
B. Standard Deviation=
The cost of parking is 5 dollars per hour. Calculate the mean and standard deviation of the amount of revenue each car generates.
A. Mean=
B. Standard Deviation
col1 X 1 2 3 4 5 6 7 8
col2 P(X) 0. 229 0. 113 0. 114 0. 076 0. 052 0. 027 0. 031
0. 358
The mean is 24.2 and the standard deviation is 8.7.
MeanThe mean amount of revenue each car generates can be calculated by multiplying the mean number of hours parked by the cost per hour. To find the mean number of hours parked, we need to multiply each possible number of hours by its probability and add them up.
E(X) = (1 * 0.229) + (2 * 0.113) + (3 * 0.114) + (4 * 0.076) + (5 * 0.052) + (6 * 0.027) + (7 * 0.031) = 4.84 hours
So, the mean revenue is 4.84 * 5 = 24.2 dollars
Standard DeviationThe standard deviation of the revenue can be calculated by finding the standard deviation of the number of hours parked and then multiplying by the cost per hour.
SD(X) = sqrt( (1^2 * 0.229) + (2^2 * 0.113) + (3^2 * 0.114) + (4^2 * 0.076) + (5^2 * 0.052) + (6^2 * 0.027) + (7^2 * 0.031) - (4.84)^2) = 1.74 hours
So, the standard deviation of the revenue is 1.74 * 5 = 8.7 dollars.
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Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply
Answer:
x=5/2 and x=0
Step-by-step explanation:
To solve this equation, we first need to get all the terms on one side of the equation by subtracting 3x from both sides:
4x^2 - 7x - 3x = 24
Simplifying, we get:
4x^2 - 10x = 24
Now, we can factor out the GCF (Greatest common factor) on the left side of the equation:
2x(2x-5) = 24
Now we can divide both sides of the equation by 2x(2x-5) to get the solutions for x:
x = 5/2 , x = 0
So the solutions of the equation 4x^2 - 7x = 3x + 24 are x=5/2 and x=0
A farmer's conveyor belt carries bales of hay from the ground to the barn loft. The conveyor belt moves at 100 ft/min.
Q1:How many Second does it take for a bale of hay to go from the ground to the barn loft?
Q2:Which part of a right triangle does the conveyor belt represent?
Q3:You know the speed. What other information do you need to find time?
Q4:How are minutes and seconds related?
Answer for the conveyer belt moves at 100ft/min from bales of hay to barn loft is given by :
1. Seconds taken by conveyer belt is 60 seconds.
2. Hypotenuse represents the conveyer belt in right triangle.
3. Distance is other information to calculate time.
4. 1 minute = 60 seconds.
Rate at which conveyer belts moves = 100ft/min
⇒1 minute = 100ft
⇒60seconds = 100 ft
1. Seconds taken by bale of hay to move from ground to barn loft is 60 seconds.
2. Conveyer felt represent the hypotenuse of the right triangle.
Feet represents the height , and minutes (time) represents the base.
3. Speed is given to us , to calculate time we should have distance.
4. Relation between minutes and seconds is given by:
1 minute = 60 seconds.
Therefore, for the given conveyer belt moves with 100ft/min answer of the following question are:
1. Seconds taken by moving bale of hay to barn loft is 60 seconds.
2. Conveyer belt represent hypotenuse.
3. To calculate time we need distance apart from speed.
4. One minute is equal to sixty seconds.
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Choose all that are correct. Refer to image.
The apothem of a regular pentagon exists [tex]$4.6797 \mathrm{~cm}$[/tex], and the perimeter exists [tex]$34 \mathrm{~cm}$[/tex]. The area equals [tex]$79.55 \mathrm{~cm}^2$[/tex].
What is meant by regular pentagon?It is a regular pentagon if all of its sides and angles are equal in size. It is not normal if not. Each angle inside the regular pentagon is 108°, while each angle outside is 72°. There are 5 equal sides in an equilateral pentagon.
Five congruent sides (sides of identical length), five congruent inner angles (each measuring 108°), and five congruent outer angles of 72° are necessary for a regular pentagon to exist.
If a polygon's sides and angles are equal, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a regular quadrilateral is a square.
Therefore, the correct answer is option c) The apothem of a regular pentagon is [tex]$4.6797 \mathrm{~cm}$[/tex], and the perimeter is [tex]$34 \mathrm{~cm}$[/tex]. The area equals [tex]$79.55 \mathrm{~cm}^2$[/tex].
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Sophia is a student at Windsfall High School.These histograms give information about the number of hours
spent volunteering by each of the students in Sophia's homeroom and by each of the students in the tenth-
grade class at her school.
Number of Students
10
Sophia's Homeroom
0-9 10-19 20-29 30 or
more
Hours Spent Volunteering
Number of Students
70
222882
60
50
10
Tenth-Grade Class at
Windsfall High School
0-9 10-19 20-28 30 or
more
Hours Spent Volunteering
Compare the medians of the data in the histograms.
The median of the number of hours spent volunteering by each student in Sophia's homeroom is more than the median
of the number of hours spent volunteering by each student in the tenth-grade class
O The median of the number of hours spent volunteering by each student in Sophia's homeroom is less than the median of
the number of hours spent volunteering by each student in the tenth-grade class
The median of the number of hours spent volunteering by each student in Sophia's homeroom is same as the median of
the number of hours spent volunteering by each student in the tenth-grade class
O No sufficient data to compare median
The correct option regarding the median of each data-set is given as follows:
The median of the number of hours spent volunteering by each student in Sophia's homeroom is less than the median of the number of hours spent volunteering by each student in the tenth-grade class.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
For Sophia's Homeroom, the total number of students is given as follows:
4 + 9 + 3 + 7 = 23.
Hence the median is the 12th element, which is on the interval 10-19.
For the Tenth Grade class, the total number of students is given as follows:
42 + 38 + 65 + 40 = 185.
Hence the median is the element at the position (185 + 1)/2 = 93, which is on the interval 20-29.
Hence the median is the 12th element, which is on the interval 10-19.
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Bryan is eight years younger than two times his friend Nancy's age. The sum of their ages is greater than sixteen. What is the youngest age Nancy can be? Give your answer as a whole number. The youngest age Nancy can be is_____Year old [help ASAP]
Hi There!
Your Answer could be 8 don't trust me i might be wrong
Solve for z…. Z - 1/5=7/10
Please help :(
(8^x/5) (8^x/4)=8^4
The value of x in (8^x/5) (8^x/4)=8^4 is 80/9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given;
The equation;(8^x/5) (8^x/4)=8^4
LHS=(8^x/5) (8^x/4)
=(8^x/5) (8^x/4)
=8^(x/5+x/4)
=8^((4x+5x)/20)
=8^(9x/20)
Now, by comparing LHS to RHS
We will get;
9x/20=4
9x=80
x=80/9
Therefore the answer of the equation will be 80/9
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what is the average (arithmetic mean) number of runs per game scored by the new york yankees last season ? (1) last season, the new york yankees played 160 games (2) last season, the new york yankees scored four runs per game in exactly 1/5 of their games, five runs per game in exactly 3/4 of their games, and nine runs per game in exactly 1/20th of their games.
Answer:
5
Step-by-step explanation:
(1) last season, the new york yankees played 160 games
(2) last season, the new york yankees scored
4 runs per game in exactly 1/5 of their games, 1/5*160 =32 games
5 runs per game in exactly 3/4 of their games, 3/4*160 =120 games
9 runs per game in exactly 1/20th of their games 1/20*160 = 8 games
total runs 4*32+ 5*120 + 9 *8 = 128+600+72 =800
total games 160
average: 800/160 =5
Pleasee Help !!!!
Given: ∆KLM, KL = LM m∠K = 17°, R = 1. 08 Find: KM
triangle is inside a circle with a midpoint O
From the triangle KLM inside the circle, the value of KM is calculated. And, the value is 1.2079.
A triangle is a polygon made up of three vertices, three angles, and three sides. First, draw a circle with a midpoint represented by O. Then, draw a triangle KLM inside a circle. Now, construct the line segments KO, MO, and LO because they form the circle's radius.
Given that KL = LM. Since two sides of the triangle KLM is equal, it is an isosceles triangle. Also, ∠K=∠M=17°. The total angle of this triangle is 180°. Then, ∠L=180°-17°-17°=146°.
Half the angle L is 73°. Then, ∠KLO=∠MLO=73°.
Consider triangle KLO, this triangle is also isosceles because KO = LO. Then, ∠KLO=∠OKL=73°.
Now, ∠KOL is calculated as follows from the triangle KLO,
[tex]\begin{aligned}\angle KOL&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]
Similarly, consider triangle MLO, this triangle is also isosceles because LO=MO. Then, ∠MLO=∠OML=73°.
Now, ∠LOM is calculated as follows from the triangle MLO,
[tex]\begin{aligned}\angle LOM&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]
Then,
[tex]\begin{aligned}\angle KOM&=\angle KOL+\angle LOM\\&=34^{\circ}+34^{\circ}\\&=68^{\circ}\end{aligned}[/tex]
Using, the cosine law of the triangle KOM, we get,
[tex]\begin{aligned}(KM)^2&=1.08^2+1.08^2-2(1.08)(1.08)\cos 68^{\circ}\\&=2.3328-2.3328(\cos 68^{\circ})\\&=2.3328(1-\cos 68^{\circ})\\&=2.3328(0.6254)\\&=1.4589\\KM&=\sqrt{1.4589}\\&=1.2079\end{aligned}[/tex]
Therefore, the required answer is 1.2079.
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i don’t understand what i’m doing and i need help
Answer: 77 degrees
Step-by-step explanation:
Ratio of the angles = 5 : 7 : 9 = 5x : 7x : 9x
5x + 7x + 9x = 21x
180 = 21x
x = 180/21
Largest angle = 9x,
= 9 * 180/21
= 540/7
540/7 = 77.14285...
Which is rounded to 77 degrees :>
Explain why the value of 0.6 is greater than the value of 0.39.
A 0.39 is greater than 0.6 because 9 hundredths is greater than 6 tenths.
B 0.39 is less than 0.6 because 3 tenths is less than 6 tenths.
C 0.6 is greater than 0.39 because 6 tenths is greater than 9 hundredths.
D 0.6 is less than 0.39 because 6 tenths is less than 9 hundredths.
The value of 0.6 is greater than the value of 0.39 because; C 0.6 is greater than 0.39 because 6 tenths is greater than 9 hundredths.
How to evaluate decimal number digits?When we are talking about decimals, the left hand side before the decimal are referred to as whole numbers while the first digit after the decimal represents the tenths place, the next digit after the tenths place represents the hundredths place, the next digit after the hundredths place represents the thousandths place and so on.
Now, we are given two decimals 0.6 and 0.39.
We see clearly that 0.6 has a greater tenths digit than the hundredths digit in 0.39. This is seen as;
0.6 = 6/10 while 0.39 = 39/100
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Which of the following graphs has a slope of negative three halves and a y-intercept of 3?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
The line y = -3/2(x) + 3 has a slope of negative three halves and a y-intercept of 3.
The correct option is C.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
We have a graph that has a slope of negative three halves and a y-intercept of 3.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂),
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁).
A). Line passing through the points (0, 2) and (3, 0).
y - 2 = 2/3(x)
y = 2/3(x) + 2.
This is not a required line.
B). Line passing through the points (0, 2) and (2, -1).
y - 2 = -3/2(x)
y = -3/2(x) + 2.
This is not a required line.
C). Line passing through the points (0, 3) and (2, 0).
y - 3 = -3/2(x)
y = -3/2(x) + 3.
This is a required line.
D). Line passing through the points (0, 3) and (3, 1).
y - 3 = -2/3(x)
y = -2/3(x) + 3.
This is not a required line.
Therefore, y = -3/2(x) + 3 is a required line.
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Answer:
The line y = -3/2(x) + 3 has a slope of negative three halves and a y-intercept of 3.
The correct option is C.
Step-by-step explanation:
Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g.
The only option that is true for the function g is; Option D: g(3) = 18
How to interpret the domain and range of a function?The function, g, has;
Domain; -1 ≤ x ≤ 4
Range: 0 ≤ g(x) ≤ 18
g(-1) = 2 and g(2) = 8
Then the following properties must hold to be true;
The value(s) of x must be between -1 and 4
The values of g(x) must be between 0 and 18.
We consider the options and state why they are true or otherwise.
Option A: g(5) = 12
When x = 5, g(5) = 12. This contradicts property 1 stated above and as such it is not true.
Option B: g(1) = -2
When x = 1, g(x) = -2. This contradicts property 2 stated above and as such, it is not true.
Option C: g(2) = 4
When x = 2, g(2) = 4. However by property 4 stated above, g(2)=9. Therefore, we can say that it is not true.
Option D: g(3) = 18
When x =3 means that its domain lies between -1 and 4 and its range lies between 0 and 18.
Therefore, Option D is true.
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The missing options are;
A) g(5)=12
B) g(1) = -2
C) g(2) = 4
D) g(3) = 18
3. The graph of a polynomial function f is shown. Select all the true statements about
the polynomial.
-4 -3 +2
YA
12
9
6
3
1
2 B
-6
-9
-12
-15
A. The degree of the polynomial is even.
B. The degree of the polynomial is odd.
C. The leading coefficient is positive.
D. The leading coefficient is negative.
E. The constant term of the polynomial is positive.
F. The constant term of the polynomial is negative.
4
After inspecting the graph, when x=0 y is 6 so the constant is +6 which is Positive
What is polynomial function ?
A polynomial characteristic is a function that includes handiest non-bad integer powers or simplest tremendous integer exponents of a variable in an equation like the quadratic equation, cubic equation, and so forth. for example, 2x+5 is a polynomial that has exponent same to one.
Given ,
The graph is a polynomial function.
This is an odd degree polynomial since end behavior is +infinitely when x is positive and -infinity when x is negative
For an even degree polynomial en behavior will be positive regardless of the sign as a negative number raised to an even power is always positive
The leading coefficient is positive other wise the function would be flipped around the x axis
Inspect the graph. when x=0 y is 6 so the constant is +6 which is Positive
Hence , After inspecting the graph, when x=0 y is 6 so the constant is +6 which is Positive
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when
�
=
1
p=1p, equals, 1 and
�
=
7
q=7q, equals, 7
The resultant answer of the given equation 7 – 5p + 3q is 23.
What are equations?A math formula is a formula that uses the equal sign to represent the equivalence of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
by inserting the provided values, we must determine the value of the given equation.
The result is obtained by changing the values of p and q in the above equation.
Thus, if p = 1 and q = 7.
So, we get the equation: 7 – 5p + 3q
Calculate as follows:
7 – 5(1) + 3(7)
7 – 5 + 21
28 – 5
23
Therefore, the resultant answer of the given equation 7 – 5p + 3q is 23.
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Correct question:
Evaluate 7-5{p}+3q7−5p+3q7, minus, 5, p, plus, 3, q when p=1p=1p, equals, 1 and q=7q=7q, equal, 7.
1/2+1/3w=1/6
Please help it’s urgent
Answer:
See below
Step-by-step explanation:
1/2 + 1/3 w = 1/6 subtract 1/2 from both sides of the equation
1/3 w = - 2/6 multiply both sides by 3
w = -1
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This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of -1 in the y-direction. Therefore, we have:
t=(3,−1)
How to find translation vector?To find the translation vector that maps quadrilateral ABCD to quadrilateral $A"B"C"D"$, we can subtract the coordinates of corresponding vertices. Let $\mathbf{t}$ be the translation vector. Then:
[tex]$$ \begin{align*}\\\mathbf{A}" - \mathbf{A} &= \langle -3 - t_x, -3 - t_y \rangle - \langle -3, -2 \rangle \\\&= \langle -3 - t_x + 3, -3 - t_y + 3 \rangle \\\&= \langle -t_x, -t_y \rangle\end{align*} $$[/tex]
Similarly, we have:
[tex]$$ \begin{align*}\mathbf{B}" - \mathbf{B} &= \langle 0 - t_x, -1 - t_y \rangle - \langle 0, -2 \rangle \\\&= \langle -t_x, 1 - t_y \rangle \\\\\\mathbf{C}" - \mathbf{C} &= \langle 1 - t_x, -3 - t_y \rangle - \langle 1, 0 \rangle \\\&= \langle -t_x, -3 - t_y \rangle\end{align*}[/tex]Since [tex]$\mathbf{D}"$[/tex] is not given, we cannot use it to solve for the components of [tex]$\mathbf{t}$[/tex]. However, note that the x-coordinate of [tex]$\mathbf{A}"$[/tex] is -3, which is 3 less than the x-coordinate of [tex]$\mathbf{A}$[/tex]. This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of 3 in the x-direction. Similarly, the y-coordinate of [tex]$\mathbf{B}"$[/tex] is -1, which is 1 more than the y-coordinate of [tex]$\mathbf{B}$[/tex]. This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of -1 in the y-direction. Therefore, we have:
t=(3,−1)
which means that the correct answer is [tex]$\boxed{\langle 3, -1 \rangle}$[/tex]
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What is the value of 4.3x10^5
Broderick has $420 in his checking account. He made 6 deposits of 35. 50 each. He needs to write 6 checks for 310. 75 each
Broderick needs $610.00 in his account to cover his checks.
We know that the balance Boderick has is $420.
First, we will calculate the total amount of the 6 deposits made by Broderick each of $35.50 deposit as follows -
$35.50 x 6 = $213.00
Hence, the total amount of the 6 deposits made by Broderick is $213.00
Next, we will calculate the total amount of the 4 checks he needs to write-
$310.75 x 4 = $1243.00
Hence, the total amount of the 4 checks that Broderick needs to write is $1243.00
Now we will find the final balance of Broderick's account after all the deposits and check withdrawals. We can do this by adding the total amount of the deposits to his initial balance and subtracting the total amount of the checks as follows-
$420.00 + $213.00 - $1243.00 = -$610.00
Thus, Broderick needs $610.00 in his account to cover his checks.
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The complete question is -
Broderick had $420 in his checking account. He made 6 deposits of $35.50 each. He needs to write 4 checks for $310.75 each. How much money does Boderick need to add to his account to cover his checks? Show your work.
a personnel director for a corporation has hired ten new engineers. if three (distinctly different) positions are open at a cleveland plant, in how many ways can she fill the positions?
There are 720 ways that personnel director for a corporation fills the positions
What is permutation?It is the ordered arrangement of members belonging to a set with no repeats.
To solve this problem the formula and the permutation procedure we must use is:
nPr = n! / (n-r)!
Where:
nPr = permutationn = total number of objectsr = number of selected objects! = factorial of the numberInformation about the problem:
n = 10r = 3Applying the permutation formula we have:
nPr = n! / (n-r)!
10P3 = 10! / (10-3)!
10P3 = 10! / 7!
10P3 = 10*9*8*7! / 7!
10P3 = 10*9*8
10P3= 720
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