Answer:
f(10) = -300
Step-by-step explanation:
f(x) = -3x^2
f(10) = -3(10)^2
f(10) = -3(100)
f(10) = -300
Multiply the rational expressions and express the product in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.\frac{\left(2x^2+9x-35\right)}{\left(x^2+10x+21\right)}\cdot \frac{\left(3x^2+2x-21\right)}{\left(3x^2+14x-49\right)}The numerator is AnswerThe denominator is Answer
Given:
The expression is,
[tex]\frac{(2x^2+9x-35)}{(x^2+10x+21)}\times\frac{(3x^2+2x-21)}{(3x^2+14x-49)}[/tex]Simplify the expression,
[tex]\begin{gathered} \frac{(2x^2+9x-35)}{(x^2+10x+21)}\times\frac{(3x^2+2x-21)}{(3x^2+14x-49)} \\ =\frac{2x^2-5x+14x-35}{x^2+3x+7x+21}\times\frac{3x^2-7x+9x-21}{3x^2-7x+21x-49} \\ =\frac{x(2x^{}-5)+7(2x-5)}{x(x^{}+3)+7(x+3)}\times\frac{x(3x^{}-7)+3(3x-7)}{x(3x^{}-7)+7(3x-7)} \\ =\frac{(2x-5)(x+7)}{(x+3)(x+7)}\times\frac{(3x-7)(x+3)}{(3x-7)(x+7)} \\ \text{Cancel the common factor } \\ =\frac{2x-5}{x+3}\times\frac{x+3}{x+7} \\ =\frac{2x-5}{x+7} \end{gathered}[/tex]Answer:
Numerator is 2x - 5.
Denominator is x + 7.
A local bakery has determined the probability distribution for the number of cheesecake that they sell in a given date that X = number of cheesecake sold on organismly selected day
Having the probability distribution in the range from 0 to 20, the sum of all probabilities should give 1. This will be useful to estimate the missing value (P(x = 15)).
Let's establish the sum of probabilities:
[tex]P(x=0)+P(x=5)+P(x=10)+P(x=15)+P(x=20)=1[/tex]Now, we can replace values and solve for P(x = 15):
[tex]0.11+0.3+0.21+P(x=15)+0.1=1[/tex][tex]0.72+P(x=15)=1[/tex][tex]\begin{gathered} P(x=15)=1-0.72 \\ P(x=15)=0.28 \end{gathered}[/tex]The probability of selling 15 cheesecakes on a given day is 0.28 (28%)
Now, to estimate the probability of selling at least 10 cheesecakes can be calculated by summing the probabilities of selling 10, 15, or 20. In this case, we include the 10 because it says at least. Then:
[tex]P(x\ge10)=P(x=10)+P(x=15)+P(x=20)[/tex]Replacing values:
[tex]P(x\ge10)=0.21+0.28+0.1[/tex][tex]P(x\ge10)=0.59[/tex]The probability of selling at least 10 is 0.59 (59%))
18-?=32
Find the ?
Thank you so much for the help
Answer:
-14
Step-by-step explanation:
[tex]18-?=32 \\ \\ -?=14 \\ \\ ?=-14[/tex]
Please help. Albert invested money into the stock market, and the table represents his earnings. What type of function could be used to model his bank account as a function of time? Justify your answer.
Answer:
You have the right answer
Step-by-step explanation:
Could please get help with this math. I need help weather each of the triangles can be the HL congruence property?
In order to use the HL congruence property, the triangles must have the hypotenuses and one pair of corresponding legs with the same length.
(a)
These are right triangles and have only one pair of legs with the same length, therefore the answer is NO.
(b)
These right triangles have one pair of legs with the same length and a common hypotenuse, therefore the answer is YES.
(c)
These triangles are not right triangles, therefore the answer is NO.
(d)
These right triangles have one pair of legs with the same length and the hypotenuses also have the same length, therefore the answer is YES.
Graphing Technology RequiredA study investigated the relationship between the amount of daily food waste measured in pounds and the number of people in a household. The data in the table displays the results of the study.Use graphing technology to create the line of best fit for the data in the table.What is the equation of the line of best fit for this data? Round numbers to two decimal places.
In the next graph, the data points and the line of the best fits are shown.
The equation of the line of best fit is:
[tex]y=1.22x-0.09[/tex]
F(x) = x^2 -4x + 6
Find the value of f( - 4)
Write the answer as an integer or a decimal number.
Answer:
38
Step-by-step explanation:
[tex]f(-4)=(-4)^2-4(-4)+6 \\ \\ =16+16+6 \\ \\ =38[/tex]
f(-4) = (-4)^2 -4(-4) +6
f(-4 = 16+16+6
f(-4) = 38)
integrate 1∫^-1 (2-x/3) dx
Answer:
Step-by-step explanation:
[tex]\int~x^{-1}(2-x/3) dx \\\int\frac{2-x/3}{x} dx\\=\int\frac{2}{x} dx-\int~x^{-2/3}~dx\\=2 ln ~x-\frac{x^(-2/3+1)}{-2/3+1} +c\\=lnx^2-3x^{1/3}+c[/tex]
PLEASE HELP IM SICK AND I DONT UNDERSTAND.DO IN 30 MINS!!!!!!
Answer:
x = 7Step-by-step explanation:
The given angles are corresponding angles and as such have same measure.
Set equation and solve for x:
14x + 12 = 16x - 216x - 14x = 12 + 22x = 14x = 7OGRAPHS AND FUNCTIONSFinding slopes of lines parallel and perpendicular to a line given.
We have the next line:
[tex]-5x\text{ - 7y = -8}[/tex]Solve the equation using the slope-intercept form:
[tex]y\text{ = mx + b}[/tex]Where m is the slope and b is the y-intercept:
Solving the equation:
-5x - y7 = -8
Add 5x on both sides
-5x + 5x - y7 = -8 + 5x
-7y = -8 +5x
Divide by 7 into both sides:
-7y/7 = (-8 +5x)/7
-y = (-8 +5x)/7
Multiply by -1 to calcel the negative sign:
(-1)(-y) =(-1)* (-8 +5x)/7
y = (8 -5x)/7
y = -5x/7 + 8/7
Now, we need to find the slope of a line perendicular to this line.
"Two lines are perpendicular if and only if their slopes are negative" reciprocals"
So the slope, in this case, is -5x/7
To find the perpendicular line use:
-5x/7 * m = -1
Solve the equation m:
m = (-1)/(-5x/7)
m = 7/5x
So m = 7/5x is the slope of the perpendicular line.
To find the parallel line use:
"Two lines are parallel lines if they do not intersect. The slopes of the"
lines are the same."
So m = -5x/7
10tY -10 10 -10 Match the function with the graph. a =Inx+3 --in C. b. =n- 3 d y=-n(x+ 3) -1 AL-
The function that matches the graph above is -ln(x+3). The answer is option d.
As we can see, the ln(x) has a transformation since it was multiplied by -1 (changing its direction), and is shifted three units to the left, represented by (x+3). We have to remember that the ln(x) function passes through the point (1, 0), and shifted three units to left makes the function passes through the point (-2, 0) (this is the x-intercept).
Select all the correct answers.
A triangular frame has two side lengths measuring 18 inches and 12 inches. Which values are possible lengths for the third side?
20 in
32 in
28 in
6 in
24 in
30 in
As per the Pythagoras theorem, the possible length of the third side are 30 or 32.
Pythagoras theorem:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Given,
A triangular frame has two side lengths measuring 18 inches and 12 inches.
Here we need to find the possible length of the third sides.
WE know that, the third side of a must be greater than the sum of the other two sides.
So, we have to add the given sides then w get get the value,
=> 18 + 12
=> 30.
So, therefore, the third side must be greater than 30.
From the given options the possible values of the third side are 30 and 32.
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Answer:24 in. 28in. 20in.
Step-by-step explanation:
George drives a delivery route thatcovers 320 miles each day. He works8 hours each day. How many miles doesGeorge drive each hour?
Gorge drives 40 miles each hour
Explanation:Distance covered per day = 320 miles
Number of hours George works per day = 8 hours
Distance covered by George per hour = 320/8
Distance covered by George per hour = 40 miles
Gorge drives 40 miles each hour
The diameter of the Sun is 1,400,000 km. The diameter of Earth is 1.28 x10 km. How many times greater is the
diameter of the Sun than the diameter of Earth? Scientific notation
Answer:
[tex]1.09375 \times 10^5[/tex]
Step-by-step explanation:
[tex]1400000=1.4 \times 10^6 \\ \\ \frac{1.4 \times 10^6}{1.28 \times 10}=1.09375 \times 10^5[/tex]
Calculate the length of the bolded arc. Round your answer to the nearest hundredth (two decimal places). No units are needed.
The length of arc is given as:
[tex]\begin{gathered} \text{length of arc = }\frac{\theta}{360}_{}\times2\times\pi\times r \\ r\text{ is the radius of the circle} \\ \\ \theta=165^0 \\ r=11ft \end{gathered}[/tex]Therefore, we can solve for the length of the arc:
[tex]\begin{gathered} \text{length of arc =}\frac{165}{360}\times2\times\pi\times11=10.0833\pi \\ \text{length of arc=31.6777ft}^2 \\ \\ To\text{ the nearest hundredth:} \\ \text{length of arc = 31.68ft}^2 \end{gathered}[/tex]If the population of Alaska in 2000 was
622,000 and 733,000 in 2020, assuming
exponential growth, what would the
population be in 2050?
[?] people
Using mathematical operations, the population of Alaska in 2050 will be 8,99,500.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.A mathematical action is called an operation. Mathematical operations include addition, subtraction, multiplication, division, and finding the root.So, the population in 2050:
Population increases from 2000 to 2020:733,000 - 622,000 = 1,11,000Population change in 20 years = 1,11,000In 10 years = 1,11,000/2 = 55,500So, poulation in 5050:
2020 (20 years) ⇒ 2040 (00 years) ⇒2050= 733,000 + 1,11,000 + 55,500= 8,99,500Therefore, using mathematical operations, the population of Alaska in 2050 will be 8,99,500.
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Answer: 937,723
Step-by-step explanation:
What is 3804 divided by 7?
Answer: 3
Step-by-step explanation:
how to solve 4d without a graphing tool and basically graph the whole equation
The given system of equations is:
[tex]\begin{gathered} x^2+y-3=0 \\ x^2-y+1=0 \end{gathered}[/tex]Add the two equations to eliminate the variable y:
[tex]\begin{gathered} 2x^2-2=0 \\ 2x^2=2 \\ x^2=1 \\ \text{ Therefore,} \\ x=\pm1 \end{gathered}[/tex]Substite x = 1 into the first equation:
[tex]\begin{gathered} (-1)^2+y-3=0 \\ 1+y-3=0 \\ y=3-1=2 \end{gathered}[/tex]Subtitute x=-1 into the second equation:
[tex]\begin{gathered} (1)^2+y-3=0 \\ 1+y-3=0 \\ y=3-1=2 \end{gathered}[/tex]Therefore, the points (-1, 2) and (1, 2) are solutions of the system.
The graph of the system is:
what is the answer to -4=r-6solve for r
-4 = r-6
Add 6 to both sides of the equation:
-4+6 = r-6+6
2 = r
r=2
Peter is building a fence. If each section is 4 1/2 feet long, how many sections will there be in the finished fence shown?
Using proportions, the number of sections that will be in the finished fence is of:
8.5 sections = 8 and 1/2 (as a mixed number).
What is a proportion?A proportion is a fraction of a total amount, and arithmetic operations such as multiplication or division are used to find the equivalent amounts.
In the context of this problem, we have that the relevant lengths are given as follows:
Each section is of 4.5 feet long.The total length of the fence is of 38.25 feet.Hence, applying a rule of three, as the total length is proportional to the length of each section, the number of sections is given by the division of the total length of the fence by the length of each section, as follows:
Number of sections = 38.25/4.5 = 8.5 sections = 8 and 1/2 (as a mixed number).
What is the missing information?The total length of the fence is missing, and it is of 38.25 feet.
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An ion has a charge of +7. How far is it from being neutral? a. -0.07b. -7c. 7d. 70e. 0.7
If the ion has a charge of +7, in irder to get to neutral (charge zero), one needs to subtract 7 charges from it. Therefore it is -7 far from being neutral.
Then the correct answer is option "b" in the list.
A population of values has a normal distribution with μ=126.7 and σ=78.3. You intend to draw a random sample of size n=242.
In a population of values having a normal distribution with (μ = 126.7) and (σ = 78.3), and we intend to draw a random sample of size (n = 242),
(i) The probability that a single randomly selected value is greater is than 119.2 is 0.54
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2 is 0.932
As per the question statement, a population of values has a normal distribution with (μ = 126.7) and (σ = 78.3) and we intend to draw a random sample of size (n = 242).
We are required to calculate:
(i) The probability that a single randomly selected value is greater is than 119.2
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2
Let us assume that, a random variable "X" follows normal distribution with mean (μ = 126.7), standard deviation (σ = 78.3) and a sample size of (n = 242).
(i) The probability that a single randomly selected value is greater is than 119.2 is,
P (X > 119.2) = [1 - P(X < 119.2)]
= [1 - P{(X - μ)/σ < (119.2 - 126.7)/78.3}]
= [1 - P{Z < (-0.096)}]
= (1 - 0.462)...[Using Excel Function "NORMSDIST (-0.096)]
= 0.538
≈ 0.54
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2 is.
P(X bar > 119.2) = [1 - P( < 119.2)]
= [1 - P{(X bar - μ)/(σ/√n) < (119.2 - 126.7)/(78.3/√242)}]
= [1 - P{(X bar - μ)/(σ/√n) < (119.2 - 126.7)/5.033}]
= [1 - P{Z < (-1.49)}]
= (1 - 0.068)...[Using Excel Function "NORMSDIST (-1.49)]
= 0.932
Probability: Probability is the branch of mathematics concerning numerical descriptions about the extent to which an event is likely to occur, or how likely it is that, a proposition is true, and is measured by the ratio of the favorable cases to the whole number of cases possible.Sample: In statistics, quality assurance, and survey methodology, sampling is a logical selection of a subset (a statistical sample) of individuals from within a larger statistical population to estimate characteristics of the whole population.To learn more about Samples and Probability, click on the link below.
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Four hundred ninety two in standard form
Answer: 43x10
Step-by-step explanation:
The sum of the first five terms of an arithmetic sequence is 20 and the sixth term is 25. What is the first term of the sequence and the common difference?
S5 = 20
A6 = 25
A1=
d=
The general formula for arithmetic sequence is:
An = A1 + (n - 1)d
25 = A1 + 6d - d (1)
And the formula for arithmetic sum:
Sn = n(A1 + An)/2
20 = 5(A1 + 25 - d)/2
8 = A1 + 25 - d (2)
We have a system of two equations with two variables.
25 = A1 + 5d
8 = A1 + 25 - d
For both equations, we can solve for d and then equal both equations as follows:
5 - A1/5 = d (1)
A1 + 17 = d (2)
A1 + 17 = 5 - A1/5
A1 = -10.
Now we just replace the value of A1 in equation 1:
d = 7
Please help asap due today
Solve y^3 = −125.
y = −5
y = ±5
y = −25
y = ±25
Answer:
A. y = −5
Step-by-step explanation:
Yw :)
Help please show your work please
Therefore Bill will be able to stay 8 days in his vacation.
Given:
Money Bill saved = $3500
Expenditure for plane tickets = $816
Expenditure per day for hotel = $125
Expenditure per day for food = $100
Expenditure per day for sightseeing = $95
Let the no of days Bill can stay be x.
Therefore,
Expenditure for x days for hotel = $125x
Expenditure for x days for food = $100x
Expenditure for x days for sightseeing = $95x
Therefore according to the question:
125x + 100x + 95x + 816 = 3500
=> 320x = 3500 - 816
=>x =8.3
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25.7 cm 6,3 cm 17.3 cm 26.6 cm The perimeter of the figure is on (Type a whole number or a decim ונן"
The perimeter of the figure is 83.2 cm
Here, we want to the perimeter of the figure
To get this, we simply add the lengths of the sides
Mathematically, we have this as;
[tex](7.3+17.3+25.7+6.3+26.6)\text{ cm =83.2 cm}[/tex]Solve for x 5(x - 3) = -11
In order to solve this equation for x, the first step is using the distributive property of multiplication:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]So, solving the equation for x, we have:
[tex]\begin{gathered} 1.\text{ Distributive property on the left side:}\\ \\ 5x-5\cdot3=-11\\ \\ 5x-15=-11\\ \\ 2.\text{ Add 15 to both sides:}\\ \\ 5x-15+15=-11+15\\ \\ 5x=4\\ \\ 3.\text{ Divide both sides by 5:}\\ \\ \frac{5x}{5}=\frac{4}{5}\\ \\ x=\frac{4}{5} \end{gathered}[/tex]Therefore the solution is x = 4/5 or x = 0.8.
HELP ASAP!!!!!
Point P is shown on the number line below. The distance between point Q and point P is 6 ½ units.
P
-12-10-8-6-4-2 0 2 4 6 8 10 12
a. Which number could represent point Q?
b. Explain how you determined your answer.
a: The number which could represent point Q are +2.5 or -10.5.
b. For determining the point Q add and subtract 6.5 units from point P.
What is meant by the term number line?A number line is a graphical portrayal of numbers on such a straight line in mathematics. A number line has numbers that are sequentially placed at equal distances across its length. It can be extended in any direction indefinitely and is generally denoted horizontally.A number line's numbers increase when moving from left to right as well as decrease when moving from right to left.A number line can represent any type of number, including fractions, decimals, integers, and so on.For the given question;
The distance between point Q and point P is 6 ½ units.
The location of point P is (-4) (seen from the number line).
a. The number could represent point Q are either +2.5 or -10.5.
b. Determine the number;
Add 6 ½ units = 6.5 units to (-4)
= -4 + 6.5
= + 2.5
Thus, point Q = + 2.5
Now, subtract 6 ½ units = 6.5 units to (-4).
= -4 - 6.5
= -10.5
Thus, point Q = + 2.5.-10.5.
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i have to use trig ratios to find the unknown angle measurement or side length.
In order to find x, we apply the trigonometric ratio
Given:
[tex]\begin{gathered} \text{angle, }\theta=57^0 \\ \text{adjacent = x} \\ \text{hypotenuse}=10 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \cos 57^0=\frac{\text{ adjacent}}{\text{ hypotenuse}}=\frac{x}{10} \\ \cos 57^0=\frac{x}{10} \\ x=10\times\cos 57^0 \\ x=10\times0.5446 \\ x=5.446 \end{gathered}[/tex]Therefore, the value of x, the adjacent side is 5.45 units to the nearest hundredth
