the given equation is,
[tex]y=x^3+2x+5[/tex]and
[tex]z=x^2+7x+1[/tex]now the expression is,
2y + z
put the values,
[tex]2(x^3+2x+5)+x^2+7x+1[/tex][tex]\begin{gathered} 2x^3+4x+10+x^2+7x+1 \\ 2x^3+x^2+11x+11 \end{gathered}[/tex]thus, the correct answer is option C
Given{x=7y-9 2x-14y= -18I think the solution is b? Am I correct?
there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)
Explanation:Given:
x = 7y - 9 . . .(1)
2x - 14y = -18 . . . (2)
To find:
the solution of the system of equations
To determine the value of x and y, we will apply the substitution method:
we will substitute for x in equation (2):
2(7y - 9) - 14y = -18
2(7y) + 2(-9) - 14y = -18
14y - 18 - 14y = -18
14y - 14y - 18 = -18
0 - 18 = -18
-18 = -18
The left-hand side of the equation is equal to the right side of the equation.
when this happens, it is called infinitely many solutions.
Hence, there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)
twice a number is increased by one-third the same number. the result is 28.Find the number?
To begin solving this question, let us represent the unknown number by x.
First
We are told that twice a number is increased by one-third the same number
so, we can represent this as
[tex]2\times x+\frac{1}{3}x[/tex][tex]2x+\frac{1}{3}x[/tex]Next, we are told that the result is 28, thus
[tex]2x+\frac{1}{3}x=28[/tex]The final step will be to simplify the expression
[tex]\frac{7x}{3}=28[/tex]Cross multiply to get x
[tex]\begin{gathered} 7x=3\times28 \\ x=\frac{3\times28}{7} \\ x=3\times4 \\ x=12 \end{gathered}[/tex]Hence, the number is 12
A car rental agency charges a fixed fee plus a daily rate. The function f (x) = 30x + 10 expresses the total cost of renting a car for x days. Suppose the agency doubles the fixed fee and increases the daily rate by $5. Which function represents these changes? A. f(x) = 60 (x + 5) + 10 B.f(x) = 60x + 15 C. f(x) = 30 (x + 5) + 20 D. f (x) = 35x + 20
In the given equation:
f(x) = 30x+ 10, where x is the number of days
We can see that at the beggining, when x = 0, then f (0) = 30 · 0+ 10 = 10
Then, renting a car costs at least $10, so $10 is the fixed fee
Each day that passes $30 is being multiplicated, then it cost $300 per day.
Then, the equation is expressed by
f(x)= daily rate · x + fixed fee
If the agency doubles the fixed fee, it would be that 2 · $10 = $20
If the agency increases the daily rate by $5, in addition, then $30 + $5 = $35 woul be the cost each day.
Then, with these new costs we reaplce our equation
f(x)= daily rate · x + fixed fee
f(x)= 35 · x + 20
Answer: D. f (x) = 35x + 20Pythagorean Theorem• Create a real-world problem involving three lengths that form a right triangle• Give the measurement of the “legs”, then solve for the missing hypotenuse
Solution
Problem
A ladder is leaning on a wall that is 6 feet tall. The distance from the bottom of the ladder to the wall is 8 feet wide.
Solution
Therefore, using the Pythagorean Theorem, 6^2 + 8^2 = 36 + 64 = 100. The square root of 100 is 10. The triangle's hypotenuse or the ladder's length is 5 feet.
Tracy's Termite Control has a net worth of $750,000. The assets total $980,235. Find the amount of the liabilities.$1,730,235$730,235$229,765$230,235None of these choices are correct.
Tracy's Termite Control has a net worth of $750,000.
The assets total $980,235.
Recall that the assets are the sum of liabilities and equity.
[tex]Assets=Liabilities+Equity[/tex]For the given case,
Assets = $980,235
Equity = $750,000
Let us substitute these values into the above formula and solve for liabilities
[tex]\begin{gathered} Assets=Liabilities+Equity \\ 980,235=Liabilities+750,000 \\ Liabilities=980,235-750,000 \\ Liabilities=\$230,235 \end{gathered}[/tex]Therefore, the amount of the liabilities is $230,235
The 4th option is the correct answer.
5) 3 people exercising on an oval. It takes Tony 2 minutes to complete a cycle by bicycle, Malcolm 4 minutes by running and Julie 6 minutes by walking. If they start together at a same point how long does it take them to meet each other again?
Answer: 12 minutes
Step-by-step explanation:
Julie needs 6 minutes, when she completes one, she will be at the bgining, Malcolm at half, and Tony with her, therefore you will need to double it.
very confused on this , if possible please explain step by step
The resultant of the subtraction of the equation 8x³ + 2x² - 5x -6 from the equation 9x³ + 3x² - 6x + 4 is x³ + x² - x + 10.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
The group's total number of items decreases or becomes lower when we subtract from it.
As per the given equations,
9x³ + 3x² - 6x + 4 and 8x³ + 2x² - 5x -6
The subtraction of both equations will be,
⇒ [9x³ + 3x² - 6x + 4] - [8x³ + 2x² - 5x -6 ]
⇒ 9x³ + 3x² - 6x + 4 - 8x³ - 2x² + 5x + 6
⇒ 9x³ - 8x³ + 3x² - 2x² - 6x + 5x + 4 + 6
⇒ x³ + x² - x + 10.
Hence "The resultant of the subtraction of the equation 8x³ + 2x² - 5x -6 from the equation 9x³ + 3x² - 6x + 4 is x³ + x² - x + 10".
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A monk crossbred plants, which can have purple or white flowers, and obtained 518 plants with white flowers and 229 plants with purple flowers. Find the
empirical probability that a plant had each type of flower.
The probability a plant had white flowers is. (Round to the nearest hundredth as needed.)
Probability that a plant had each type of flower. 0.36 and 0.64
What is Probability?
Probability is a branch of mathematics that quantifies the Probability of an event occurring or the Probability of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.
Number of white flower plants = 660
Number of purple flower plants = 368
To discover the empirical Probability that a plant had each sort of flower.
Formula
empirical Probability is found by rehashing an test and watching the outcomes.
P(event) = (the number of time the occasion happens) ÷ (add up to number of trial)
Here, Total number of plants = (660+368) = 1028
Now, Probability of white flower plant = = 0.64
And,
Probability of purple flower plant = = 0.36
Hence, The empirical Probability of white flower is 0.64 and the empirical Probability of purple flower is 0.36
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Based on statistics from a worldwide health organization, in 2005 there were22.6 million people worldwide living with a certain disease, and 1.9 million deaths from the disease. By 2015,the number of people living with the disease had grown to 38.9 million deaths were reported. Find the percent change for each statistic, and write any conclusion you can draw.
Percent change of people living with the disease = 72.1%
Percent change of number of death = 5.2%
Explanation:The Number of people living with the disease increased from 22.6 million in 2005 to 38.9 million in 2015
To get the percentage, we will apply the formula:
[tex]percent\text{ change = }\frac{New\text{ value - Old value}}{Old\text{ value}}\times\text{ 100\%}[/tex][tex]\begin{gathered} new\text{ value = 38.9 million, old value = 22.6 million} \\ percent\text{ change = }\frac{38.9\text{ - 22.6}}{22.6}\text{ }\times100 \\ percent\text{ change = 0.721 }\times\text{ 100\% = 72.1\%} \end{gathered}[/tex]The number of death increased from 1.9 million to 2 million from 2005 to 2015:
[tex]\begin{gathered} new\text{ value = 2 million, old value = 1.9 million} \\ The\text{ percent change = }\frac{2-1.9}{1.9}\times100\text{ \%} \\ The\text{ percent change = 0.052 }\times\text{ 100\% = 5.2\%} \end{gathered}[/tex]Conclusion:
The number of people living with the disease increased drastically within 10 years.
But the percent change in the number of death isn't as high as the number of people living with the disease. It means the disease is highly infectious but has a low death rate
Which subtraction expression does the number line model show? A number line with arrowed movements. Start at 0 on the right and move 4 units to the left. From that number, move 9 more units to the left. End at negative 13. –13 + 4 –4 – 13 –4 – 9 –4 + 9ne with arrowed movements. Start at 0 on the right and move 4 units to the left. From that number, move 9 more units to the left. End at negative 13.
The subtraction expression which the given number line model (see attachment) show is: C. -4 - 9
What is a number line?In Mathematics, a number line is a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Note: Each interval on this number line represents -1 unit.
Next, we would add the given numbers together as follows:
Number = -4 + (-9)
Number = -4 - 9
Number = -13.
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Complete Question:
Which subtraction expression does the number line model show?
-13 + 4
-4 - 13
-4 -9
-4 + 9
Who is Caleb? What is his job? Hpw p;d ois;O?
Answer:
oiutwecldvi ufa
Step-by-step explanation:
Polynomial equation
Using the Factor Theorem, the polynomial function with the desired characteristics is given by:
f(x) = -x(x² + 9)(x - 1)(x - 2).
Factor TheoremThe Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule presented as follows.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative), determining the end behavior of the function.
For this function, we have:
Two complex roots, hence a factor of (x² + 9).A root at x = 0, hence f(x) = ax(x² + 9).The two other roots are free, hence I am going to attribute x = 1 and x = 2, hence the equation is:
f(x) = ax(x² + 9)(x - 1)(x - 2).
The end behavior is that the function increases to the left and decays to the right, meaning that the leading coefficient is negative, hence a possible function is given by:
f(x) = -x(x² + 9)(x - 1)(x - 2).
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Expand and simplify(3x+4)(2x + 3)
Answer:
6x²+17x+12
Step-by-step explanation:
open the bracket
3x(2x+3) 4(2x+3)
6x²+9x+8x+12
6x²+17x+12
hope it helps
please mark brainliest
Answer:
6x^2 + 17x + 12
Step-by-step explanation:
first (distribute):
(3x+4)(2x+3)
3x(2x+3) + 4(2x + 3)
then (distribute) again:
3x(2x+3) = 6x^2 + 9x
4(2x + 3) = 8x + 12
then (combine terms):
6x^2 + 9x + 8x + 12
6x^2 + 17x + 12
hi, i need aloy of help
Answer:
XY ≈ 14.32
Step-by-step explanation:
XY² = XZ² + ZY²
XY² = 6² +13²
XY² = 36 + 169
XY² = 205
XY = [tex]\sqrt{205\\[/tex]
XY ≈ 14.32
At the movie theatre, child admission is 5.40 and adult admission is 8.90On Monday, three times as many adult tickets as child tickets were sold, for a total sales of \$706.20 How many child tickets were sold that day?
Solution
Step 1
Let the number of adult tickets = 3m
The number of child tickets = m
Step 2
[tex]\begin{gathered} Total\text{ cost of adult tickets = 26.7m} \\ Total\text{ cost of child tickets = 5.4m} \end{gathered}[/tex]Step 3:
Total sales = $706.20
[tex]\begin{gathered} 26.7m\text{ + 5.4m = 706.2} \\ 32.1m\text{ = 706.2} \\ m\text{ = }\frac{706.2}{32.1} \\ \text{m = 22} \end{gathered}[/tex]Number of child tickets that were sold that day = 22
Why do y’all not explain like please I went on brainly for a reason
Hello, may I please have some help on this practice question? Thank you.
Data:
• p1 = ,the proportion of Republican voters in the first state
,• p2 =, the proportion of Republican voters in the second state
,• P1 = ,the proportion of Republican voters in the sample from the first state
,• P1 = ,the proportion of Republican voters in the sample from the second state
,• n = ,sample
Procedure
0. Finding the mean proportions
[tex]p_1-p_2=0.52-0.47=0.05[/tex]2. Finding the standard deviation of the difference
[tex]\sigma=\sqrt[]{\frac{0.52\cdot(1-0.52)}{100}+\frac{0.47\cdot(1-0.47)}{100}}=0.0706[/tex]To have a greater percentage of republicans in the second state than in the first, the difference should be less than zero. Thus, the value of the difference of the proportion corresponds to zero.
[tex]Z=\frac{0-0.05}{0.0706}=-0.7080[/tex]Using the Standard Normal Table, the value of Z previously calculated corresponds to 0.2394.
Therefore, the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state is 0.24.
Answer: C) 0.24
Use the sequence below to complete each task. -2, 8, -32,... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 10th term (a,0)
hello
we're required to write an equation to represent the sequence
-2, 8, -32
first of all, let's identify the first term
first term = -2
common ratio = ?
c
A physics class has 40 students. Of these, 18 students are physics majors and 17 students are female. Of the physics majors, seven are female. Find the probability that a randomly selected student is female or a physics major.
Answer:
Probability (Physics Major or Female) = 28/40 = 0.7
Step-by-step explanation:
The probability of being a female is 17/40
The probability of being a physics major is 18/40
The number of students counted twice is 7/40
Probability (Physics Major or Female) = 17/40 + 18/40 - 7/40
Probability (Physics Major or Female) = 28/40 = 0.7
In 1991 the average family income was about 39000, and in 2011 it was about 66820.
Let
x
=
0
represent 1991,
x
=
1
represent 1992, and so on. Find values for
a
and
b
(rounded to one decimal place if necessary) so that
f
(
x
)
=
a
x
+
b
models the data
a
=
b
=
What was the average family income in 2006?
$
The average family income in 2006 is $59865.
What is the income?Based on the information illustrated, the required model is given as:
y = ax + b
y = average family income
x = years since 1991
The slope based on the information given is b = 39000.
Therefore, the family income in 2006 will be:
= (1391 × 15) + 39000
= 59865
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f(n)=(x + 1)(x - 5)| has three solutions. What is the value of f(n)? How would you describe the location of this solution?
The equation given is a quadratic equation that has roots -1 and 5.
Roots of Quadratic EquationTo solve this problem, we have to find the roots of the quadratic equation and we can simply multiply through and then calculate the roots.
[tex](x+1)(x-5) = x^2 -5x + x - 5\\f(n) = x^2 -4x - 5[/tex]
Let's solve this quadratic equation above.
Using factorization method, we can find the factors of the quadratic equation and simplify.
[tex]x^2 - 4x -5 = 0\\(x+1)(x-5) = 0\\x + 1 = 0\\or \\x - 5 = 0\\x = -1 or x = 5[/tex]
The roots to the equation (x + 1)(x - 5) = 0 are - 1 and 5.
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type the correct answer in the Box spell all words correctly which type of coordinates does Andrews. Take Andrew studying mathematics and studying about the (blank (coordinate system in this system the coordinates of the of a point are dependent on the distance of the point from the origin and the angle of the start of the points substance at the origin
Where the coordinates of a points pedepend on the distance to the origin of the coordinate system and also depend on the angle, the coordinate system is a POLAR coordinate system.
1. Suppose a designer has a palette of 6 colors to work with, and wants to design a flag
with 5 vertical stripes, all of different colors.
How many possible flags can be created?
2. Evaluate the expression P(9,3), equivalently 9P3
Part a: The total possible flags can be created using 6 colours is 720.
Part b: ⁹P₃ = 60480.
What is defined as the permutation?When the order of the arrangements matters, a permutation is a mathematical method that calculates the number of possible arrangements in a set. A common mathematical problem involves selecting only a few items from the a set of items in a specific order.For the given question;
Part a: A designer has total 6 palette of colors.
A flag has to made with 5 vertical stripes, all of different colors.
The, this could be done by using permutation.
= 6!
= 6×5×4×3×2×1
= 720
Thus, the total possible flags can be created is 720.
Part b: The value of the expression P(9,3), equivalently ⁹P₃.
⁹P₃ = 9!/3!
⁹P₃ = (9×8×7×6×5×4×3!)3!
⁹P₃ = 9×8×7×6×5×4
⁹P₃ = 60480.
Thus, the equivalent value of the expression is ⁹P₃ = 60480.
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If a car moves along a perfectly straight road at a velocity of 24 m/s, how far will the car go in 35 minutes?
Answer:
distance = rate x time
Step-by-step explanation:
distance = ?
rate = 24 m/s
time = (35 x 60) = 2100 s
thus,
distance = 24 x 2100 = 50400 m
2, 4, 5, 6, 6, 7
What is the mean of the list of numbers above?
Answer: 5
Step-by-step explanation: add up the numbers to get 30 then divide by 6 (the amount of numbers) to get 5
Answer: 5
Step-by-step explanation:
the mean is the average. add the numbers together then divide by how many addends you have.
2 + 4 + 5 + 6 + 6 + 7 = 30
30/6 = 5
:)
a commuter travels 67 km in 32 min .what is it's speed in kilometer per hour?
125.625 kilometers per hour
Explanations:Note:
60 minutes = 1 hour
32 minutes = 32/60 hours
The speed is the distance traveled in 1 hour
Distance = 67 km
Time = 32/60 hours
Speed = Distance / time
[tex]\begin{gathered} Speed\text{ = 67 }\div\text{ }\frac{32}{60} \\ \text{Speed = 67 }\times\text{ }\frac{60}{32} \\ \text{Speed = }\frac{4020}{32} \\ \text{Speed = }125.625\text{ km per hour} \end{gathered}[/tex]if you walk 2 1/4 miles in 3/4 hours how far can you walk in 2 1/2 hours
FIrst calculate the speed, as follow:
speed = distance/time
distance = 2 1/4 mi = 2.25 mi
time = 3/4 h = 0.75 h
speed = 2.25 mi/0.75 h = 3 mi/h
next, for the distance traveled in 2 1/2 hours, use:
distance = speed x time
time = 21/2 h = 2.5 h
distance = (3 mi/h) x (2.5 h)
distance = 7.5 mi =7 1/2 mi
Hence, you can walk 7 1/2 miles in 2 1/2 hours
a business has total revenues of $55,000 and total expenses of $63,000. what is the net income or net loss? a. $11800b.-$11800c. $8000d.-$8000
Recall that:
[tex]NetIncome=Revenues-Expenses.[/tex]Since the business has a total revenue of $55,000 and total expenses of $63,000, therefore the net income is:
[tex]\begin{gathered} NetIncome=\text{ \$}55,000-\text{ \$}63,000 \\ =-\text{ \$}8000. \end{gathered}[/tex]Answer: Option D.
Brand A granola is 25% nuts and dried fruit and brand B granola is 20% nuts and dried fruit. How much of sweet item A and sweet item B should be mixed to form a 10-lb batch of sweetsthat is 22% nuts and dried fruit?The batch of sweets should contain of Brand A granola and of Brand B granola.
The batch of sweet should contain 4 lb of Brand A granola
The batch of sweet should contain 6 lb of Brand B granola
Explanations:Total amount of sweet items = 10 lb
Let the amount of brand A granola be x
Amount of brand B granola = 10 - x
Amount of nuts and dried fruits in the total sweet items = 22% of 10
Amount of nuts and dried fruits in the total sweet items = 0.22 x 10
Amount of nuts and dried fruits in the total sweet items = 2.2lb
Amount of nuts and dried fruits in brand A granola = 25% of x
Amount of nuts and dried fruits in brand A granola = 0.25x
Amount of nuts and dried fruits in brand B granola = 20% of (10-x)
Amount of nuts and dried fruits in brand B granola = 0.2(10 - x)
Amount of nuts and dried fruits in brand A granola + Amount of nuts and dried fruits in brand B granola = Amount of nuts and dried fruits in the total sweet items
0.25x + 0.2(10 - x) = 2.2
0.25x + 2 - 0.2x = 2.2
Collect like terms
0.25x - 0.2x = 2.2 - 2
0.05x = 0.2
x = 0.2 / 0.05
x = 4 lb
The batch of sweet should contain 4 lb of Brand A granola
Amount of brand B granola = 10 - x
Amount of brand B granola = 10 - 4
Amount of brand B granola = 6 lb
The batch of sweet should contain 6 lb of Brand B granola
i need help with this problem. im not sure if b is the correct answer. please help
From the graph, we can't see any clear asymptote. Also, the arrow at the right tip of the graph tells us that it continues indefinitely, i.e., both the number of years and the population increases indefinitely.
Now, notice that the population increases as the number of years increases.
Therefore, the only true statement is:
As the number of years increases without bound, the population increases without bound.