The most appropriate choice for tangent to a curve will be given by-
[tex]3x + 2y = 73[/tex] is the required equation of tangent.
What is tangent to a curve?
Tangent to a curve at a point is the straight line that just touches the curve at that point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y - y_1 = \frac{dy}{dx}|_{(x_1,y_1)} (x - x_1)[/tex]
Here,
y = B(x), B(25) = -1, B'(25) = -1.5
Equation of tangent =
[tex](y - (-1)) = -1.5(x - 25)[/tex]
[tex]y + 1=-1.5x +37.5\\y + 1 = -\frac{3}{2}x + 37.5\\2y + 2 = -3x + 75\\3x+2y = 75-2\\3x+2y=73[/tex]
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I need help with this practice problem The subject is trigonometry
SOLUTION
The range of the function is given as:
[tex](-\infty,-9\rbrack\cup\lbrack5,\infty[/tex]The asymptote of the function is at points
[tex]x=0,x=2\pi[/tex]The function is shown in the graph below
Therefore, the equation of the session is
[tex]f(x)=7\csc (\frac{x}{2})-2[/tex]The given pair of triangles are similar. Find X and Y.
Given that the pair of triangles are similar, then their corresponding sides are in proportion, this means that:
[tex]\frac{\text{longer leg of the triangle on the left}}{\text{shorter leg of the triangle on the left}}=\frac{\text{longer leg of the triangle on the right}}{\text{shorter leg of the triangle on the right}}[/tex]Substituting with the information of the diagram:
[tex]\frac{27}{x}=\frac{x}{9}[/tex]Cross multiplying:
[tex]\begin{gathered} 27\cdot9=x\cdot x \\ 243=x^2 \\ \sqrt[]{243}=x \\ 15.58\approx x \end{gathered}[/tex]Considering the triangle on the left, and applying the Pythagorean theorem with c = y (the hypotenuse), a = 27, and b = x (the legs), we get:
[tex]\begin{gathered} c^2=a^2+b^2 \\ y^2=27^2+x^2 \\ y^2=729+243 \\ y^2=972 \\ y=\sqrt[]{972} \\ y\approx31.18 \end{gathered}[/tex]
What is the answer to 6x + =5
Answer:
x = 5/6 or x = 0.83
Step-by-step explanation:
6x + =5
6x + 0 = 5
6x = 5
6x/6 = 5/6
x = 5/6 or x = 0.83
the table below shows the attendance and revenue at theme parks in the us
Let
y ------> the year
x ----> revenue
so
Plot the given ordered pairs
see the attached figure
(please wait a minute to plot the points)
In the graph the x-coordinate 0 represent year 1990
Find out the equation of the line
take two points
(1990, 5.7) and (2006, 11.5)
Find the slope m
m=(11.5-5.7)/(2006-1990)
m=5.8/16
m=0.3625
Find the equation of the line in slope intercept form
y=mx+b
we have
m=0.3625
point (1990, 5.7)
substitute and solve for b
5.7=(0.3625)(1990)+b
b=-715.675
therefore
y=0.3625x-715.675alex was late on his property tax payment to the county. he owed $6,915 and paid the tax 9 months late. the county charges a penalty of 5% simple interest. find the amount of the penalty. (round to the nearest cent as needed)
We have to use the simple interest formula.
[tex]A=P(1+rt)[/tex]Replacing the given information, we have.
[tex]\begin{gathered} A=6,915(1+0.05\cdot\frac{9}{12}) \\ A=6,915(1.0375) \\ A=7,174.31 \end{gathered}[/tex]The final amount is $7,174.31, where the penalty is $259.31.1. Are these ratios equivalent? 8:7 and 4:2
EXPLANATION
The answer is no, because 8:7 and 4:2 are different relationships.
Add or subtract. Simplify. Change the answers to mixed numbers, if possible.
Answer:
[tex]\begin{gathered} \frac{1}{8} \\ \\ \text{LCD = 8} \end{gathered}[/tex]Explanation:
Here, we start by finding the lowest common denominator
From what we have, the lowest common denominator is the lowest common multiple of both denominators which is equal to 8
We divide the first denominator by this and multiply the result by its numerator. We take the same step for the second denominator
Mathematically, we have it that:
[tex]\frac{11-10}{8}\text{ = }\frac{1}{8}[/tex]second number when the list is sorted from greatest to least
5.2% = 0.052
1/7 = 0.14
-11/5 = -2.2
From the greatest to least:
[tex]0.14>0.052>-0.8>-2.2[/tex]The second number is: 5.2%
Answer:
5.2%
hello, in the picture you can see a graph and my teacher said that the domain and range would be all real numbers possible. could you please help me because I don't understand why.
The domain is all the values of the independent variable (in this case, x) for which the function is defined.
In this case, as it is indicated with the arrows in both ends, the function continues for greater and smaller values of x.
As there is no indication that for some value or interval of x the function is not defined (a discontinuity, for example), then it is assumed that the function domain is all the real values.
Example function:
We have the function y=1/(x-2)
We can look if there is some value of x that makes the function not defined.
The only value of x where f(x) is not defined is x=2. When x approximates to 2, the value of the function gets bigger or smaller whether we are approaching from the right or from the left.
Then, the function is not defined for x=2. So, the domain of f(x) is all the real numbers different from x=2.
The domain is, by default, all the real numbers, but we have to exclude all the values of x (or intervals, in some cases like the square roots) for which f(x) is not defined.
Identify the function rule from the values in the table.
we are given a table of inputs and ouputs of a function. We notice that each output is obtained by multiplying the input by -4:
[tex]\begin{gathered} (-2)(-4)=8 \\ (0)(-4)=0 \\ (1)(-4)=-4 \\ (3)(-4)=-12 \end{gathered}[/tex]Therefore, the right answer is A.
3. The number line below represents the solution to which inequality of he 0 1 2 3 4 5 6 7 8 9 10
let x be the money daniel has. So we get that
[tex]x\ge72+15\rightarrow x\ge87[/tex]Daniel has at least $87
20 P1: a For two events, A and B.P(B) -0.5, P(AB) -0.4 andPAB) = 0.4.Calculatei PAB)ii P(A)ili P(AUB)iv P(AB)(8 marks)b Determine, with a reason, whetherevents A and B are independent ornot.(2 marks)probabilityStatistics and
We have two events A and B.
We know that:
P(B) = 0.5
P(A|B) = 0.4
P(A∩B') = 0.4
i) We have to calculate P(A∩B).
We can relate P(A∩B) with the other probabilities knowing that:
[tex](A\cap B)\cup(A\cap B^{\prime})=A[/tex]So we can write:
[tex]P(A\cap B)+P(A\cap B^{\prime})=P(A)[/tex]We know P(A∩B') but we don't know P(A), so this approach is not useful in this case.
We can try with the conditional probability relating P(A∩B) as:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, we can use this to calculate P(A∩B) as:
[tex]\begin{gathered} P(A\cap B)=P(A|B)P(B) \\ P(A\cap B)=0.4*0.5 \\ P(A\cap B)=0.2 \end{gathered}[/tex]ii) We have to calculate P(A) now.
We can use the first equation we derive to calculate it:
[tex]\begin{gathered} P(A)=P(A\cap B)+P(A\cap B^{\prime}) \\ P(A)=0.2+0.4 \\ P(A)=0.6 \end{gathered}[/tex]iii) We have to calculate P(A∪B).
We can use the expression:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=0.6+0.4-0.2 \\ P(A\cup B)=0.8 \end{gathered}[/tex]iv. We can now calculate P(A|B') as:
[tex]\begin{gathered} P(A)=P(A|B)+P(A|B^{\prime}) \\ P(A|B^{\prime})=P(A)-P(A|B) \\ P(A|B^{\prime})=0.6-0.4 \\ P(A|B^{\prime})=0.2 \end{gathered}[/tex]b) We now have to find if A and B are independent events.
To do that we have to verify this conditions:
[tex]\begin{gathered} 1)P(A|B)=P(A) \\ 2)P(B|A)=P(B) \\ 3)P(A\cap B)=P(A)*P(B) \end{gathered}[/tex]We can check for the first condition, as we already know the value:
[tex]\begin{gathered} P(A|B)=0.4 \\ P(A)=0.6 \\ =>P(A|B)P(A) \end{gathered}[/tex]Then, the events are not independent.
Answer:
i) P(A∩B) = 0.2
ii) P(A) = 0.6
iii) P(A∪B) = 0.8
iv) P(A|B') = 0.2
b) The events are not independent.
15. I need help on this question. How do you do it?
Solution:
Given the expression:
[tex]-5^2[/tex]This expression is evaluated as
[tex]\begin{gathered} -5\text{ multiplied in 2 places} \\ \Rightarrow-5\times-5 \\ =25 \end{gathered}[/tex]Hence,
[tex]-5^2[/tex]is evaluated to be 25
Select the correct choice below and, if necessary, fill in the answer box within your choice
x² - 20x + 100
Find two numbers, such that its sum gives -20 and its product gives 100
If such numbers exist, this implies that the polynomial is NOT prime
The two numbers are: -10 and -10
Replace the coefficient of x with the two numbers
x² - 10x -10x + 100
x(x-10) - 10(x - 10)
(x-10)(x-10)
(x-10)²
Therefore, the correct option is A.
x² - 20x + 100 = (x-10)²
quien me puede ayudar a resolver estos ejercicios porfa de ecuaciones
3x^2 -5x +1 =0
Aplica la formula cuadrática:
[tex]\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]Donde:
a = 3
b= -5
c= 1
Reemplazando:
[tex]\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot3\cdot1}}{2\cdot3}[/tex][tex]\frac{5\pm\sqrt[]{25-12}}{6}[/tex][tex]\frac{5\pm\sqrt[]{13}}{6}[/tex]Positivo:
(5+√13) /6 = 1.43
NEgativo:
(5-√13) /6 = 0.23
When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23. Find the value of the lesser integer.
The value of the lesser integer is 5.
According to the question,
We have the following information:
When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23.
Let's take the lesser integer to be x.
So, the next consecutive odd integer is (x+2).
Now, we have:
4(x+2)-x = 23
4x+8-x = 23
3x+8 =23
3x = 23-8
3x = 15
x = 15/3
(3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 5
Hence, the lesser integer in the given situation is 5.
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Please help asap will give Brainly!!!
The following completes the proof: D. The Alternate Interior Angles Theorem shows that the angles BAC and DCA are congruent.
The Alternate Interior Angles Theorem: What is it?
According to the alternate interior angles theorem, when a transversal cuts over two (2) parallel lines, the alternate interior angles that are created are congruent.
We can infer and logically derive from the Alternate Interior Angles Theorem that the sentence that correctly concludes the proof is that angle BAC and angle DCA are congruent.
Segment AB is parallel to segment DC, while segment BC is parallel to segment AD, according to the information provided. Create the diagonals A and C using a straight edge. By virtue of the Reflexive Property of Equality, it is congruent to itself.
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the product of (2-x)and (1-x)is equal to x^2-3x+2
So the product of (2-x) and (1-x) is equal to x^2 - 3x + 2
This graph shows the solution to which inequality?3.2)(-3,-5)O A. ys fx-2B. vfx-2O c. vfx-2OD. yzfx-2
First, find the equation of the line, given that the points (3,2) and (-3,-6) belong to that line. To do so, use the slope formula and then substitute the value of the slope and the coordinates of a point on the slope-point formula of a line:
[tex]y=m(x-x_0)+y_0[/tex]The slope of the line, is:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{(2)-(-6)}{(3)-(-3)} \\ =\frac{2+6}{3+3} \\ =\frac{8}{6} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, the equation of a line (using the point (3,2)) is:
[tex]\begin{gathered} y=\frac{4}{3}(x-3)+2 \\ =\frac{4}{3}x-\frac{4}{3}\times3+2 \\ =\frac{4}{3}x-4+2 \\ =\frac{4}{3}x-2 \end{gathered}[/tex]Since the colored region on the coordinate plane is placed above the line
y=(4/3)x-2, then the equation of the inequality is:}
[tex]undefined[/tex]the price of a gallon of unleaded gas has risen to $2.92 today. yesterday's price was $2.85. find the percentage increase. round to the nearest 10th of a percent
Given:
[tex]\begin{gathered} P_{\text{today}}=2.92,P_{today}=Price\text{ of a gallon of unleaded gas today} \\ P_{\text{yesterday}}=2.85, \\ P_{yesterday}=Price\text{ of a gallon of unleaded gas today} \end{gathered}[/tex]To Determine: The percentage increase round to the nearest 1oth of a percent
The formula for percentage increase is given below:
[tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ In\text{crease}=P_{final}-P_{in\text{itial}} \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} P_{\text{yesterday}}=P_{i\text{nitial}}=2.85 \\ P_{\text{today}}=P_{\text{final}}=2.92 \\ \text{Increase}=2.92-2.85=0.07 \end{gathered}[/tex][tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ P_{in\text{crease}}=\frac{0.07}{2.85}\times100\% \\ P_{in\text{crease}}=0.02456\times100\% \\ P_{in\text{crease}}=2.456\% \\ P_{in\text{crease}}\approx2.5\%(nearest\text{ 10th)} \end{gathered}[/tex]Hence, the percentage increase to the nearest 10th of a percent is 2.5%
I have the answers for 1 and 2 3. Use your answers from # 1 and # 2 to find the length of each arc between gondola cars . Use 3.14 for and round to the nearest hundredth . You must write out all the numbers you are multiplying together meaning show your work for full credit . ( 5 points ) Central angle = 8°Radius = 95 ft
The length of an arc = 13.26 ft
Explanation:The length of an arc is given by the formula:
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ \end{gathered}[/tex]Substitute θ = 8°, r = 95 ft, and π = 3.14 into the formula
[tex]\begin{gathered} l=\frac{8}{360}\times2\times3.14\times95 \\ \\ l=13.26\text{ ft} \end{gathered}[/tex]The length of an arc = 13.26 ft
given the function r(t)=t^2, solve for r(t)=4
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
r(t)=t^2
r(t)=4
t = ?
Step 02:
r(t)=4
t ² = 4
t = √4
t = 2
The answer is:
t = 2
Answer: t=2
Step-by-step explanation:
Because we know that for some value of t, r(t)= 4, and for ALL values of t, r(t)= t^2, then we know for some value of t, that t^2 = 4.
Based off of this information, we can take the square root of both sides, resulting in this equation.
t = [tex]\sqrt{4}[/tex]
This can be simplified.
t=2
Can you Convert 840 inches to cm. Use unit analysis to convert the rate.
we know that
1 in=2.54 cm
so
840 in
Applying proportion
1/2.54=840/x
x=(840*2.54)/1
x=2,133.6 cm
answer is
2,133.6 cmApplying unit rate or unit analysiswe have
2.54 cm/in
Multiply by 840 in
2.54*(840)=2,133.6 cm40/
The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011 $5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020)..
The given data plot will look thus:
a) Building a model using just the 1999 and 2019 years:
[tex]\begin{gathered} 1999\rightarrow0\rightarrow2196 \\ 2019\rightarrow20\rightarrow7186 \\ \text{Havng} \\ x_1=0,y_1=2196 \\ x_2=20,y_2=7186 \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}_{} \\ \text{The model will be:} \\ P_t=249.5t+2196 \end{gathered}[/tex]b) The cost of insurance in 2030
[tex]\begin{gathered} P_t=249.5t+2196 \\ t=2030-1999=31 \\ \text{The cost of insurance in 2030 therefore will be:} \\ =249.5(31)+2196 \\ =7734.5+2196 \\ =\text{ \$9930.5} \end{gathered}[/tex]c) When do we expect the cost to reach $12,000
[tex]\begin{gathered} P_t=249.5t+2196 \\ 12,000=249.5t+2196 \\ 12000-2196=249.5t \\ 9804=249.5t \\ \frac{9804}{249.5}=\frac{249.5t}{249.5} \\ 39.2946=t \\ Since\text{ t = year -1999} \\ 39.2946+1999=\text{year} \\ 2038.2946=\text{year} \\ Since\text{ we are to give our answer as an exact year} \\ \text{The year will be }2039. \end{gathered}[/tex]a carpentar has 16 1/2m of wood he cuts the wood into peices that are each 2 3/4m long PLSSSSS HURRY!!!!!!!!
The most appropriate choice for fraction will be given by
6 pieces of wood are cut by the carpenter
What is a fraction?
Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
Total length of wood = [tex]16\frac{1}{2}[/tex] m
= [tex]\frac{33}{2}[/tex] m
Length of one piece of a wood = [tex]2\frac{3}{4}[/tex] m = [tex]\frac{11}{4}[/tex]
Number of pieces of wood cut by carpenter = [tex]\frac{33}{2}[/tex] ÷ [tex]\frac{11}{4}[/tex]
= [tex]\frac{33}{2}[/tex] [tex]\times \frac{4}{11}[/tex]
= 6
6 pieces of wood are cut by the carpenter
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Hunter has $300 in a savings account. The interest rate is 8%, compounded annually.To the nearest cent, how much will he have in 3 years?
EXPLANATION
If Hunter has $300 in savings and the interest rate is 8%, compounded annualy, we can apply the following equation:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where, P=Principal=300, r=rate (in decimal form) = 8/100 = 0.08, n=number of compounded times = 1 and t = time = 3
Substituting terms:
[tex]A=300\cdot(1+\frac{0.08}{1})^{1\cdot3}[/tex]Adding numbers:
[tex]A=300\cdot(1.08)^3[/tex]Computing the powers:
[tex]A=300\cdot1.26[/tex]Multiplying numbers:
[tex]A=378[/tex]In conclusion, there will be 378.00 in three years
The function, f. is drawn on the accompanying set of axes. On the same set of axes, sketch the graph of f-?, the inverse of f
We are given the following graph:
The inverse of the graph is shown below:
Solve 39 - 5 = 13 for q.q=
We are given the following equation:
[tex]3q-5=13[/tex]We are asked to solve for "q". To do that, we will first add "5" on both sides, like this:
[tex]\begin{gathered} 3q-5+5=13+5 \\ 3q=18 \end{gathered}[/tex]Now we will divide by 3 on both sides, like this:
[tex]\begin{gathered} \frac{3q}{3}=\frac{18}{3} \\ q=6 \end{gathered}[/tex]Therefore, the value of q is 6.
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24. How many gallons of ethanol are in a 100 gal mixture that is 10%
ethanol?
By working with percentages, we will see that there are 10 gallons of ethanol in the mixture.
How many gallons of ethanol are in the mixture?We know that we have a mixture with a volume of 100 gallons, and 10% of that mixture is ethanol, so we just need to find the 10% of 100 gallons.
To work with percentages, we will use the equation:
Volume of ethanol = total volume*ratio of ethanol.
V = 100gal*(10%/100%)
V = 100gal*0.10 = 10 gal
There are 10 gallons in the mixture.
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33Select the correct answer from each drop-down menu.A75°B40°AoIn the figure, line segment AB is parallel to line segment CD.СDdegreesThe measure of angle Cisdegrees, and the measure of angles Dis>254075ResetNext
Answer:
Angle C = 40 degrees
angle D = 75 degrees
Explanation:
From the information given,
Angle A = 75 degrees
Angle B = 40 degrees
AB is parallel to CD. This means that AD and BC are transversals.
Angles A and D have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
angle D = 75 degrees
Angles B and C have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
Angle C = 40 degrees