We usually write explicit functions as one variable in terms of another variable. A simple example of an explicit function is a linear function, such as y = 4x - 7. This function is written as the dependent variable y in terms of the independent variable x.
Work out the values of a, b and k ? 30 points
Answer:
[tex]\displaystyle a=4, b= \frac{25}{4}, \text{ and } k = \frac{125}{2}[/tex]
Step-by-step explanation:
Note that the graph passes through the points: (0, 4), (1, 25), and (1.5, k).
The standard exponential function has the form:
[tex]\displaystyle y = ab^x[/tex]
The point (0, 4) tells us that y = 4 when x = 0. Therefore:
[tex](4) = a(b)^0[/tex]
Since anything raised to zero is one:
[tex]a=4[/tex]
Hence, our function is now:
[tex]y = 4(b)^x[/tex]
The point (1, 25) tells us that y = 25 when x = 1. By substituting:
[tex](25) = 4(b)^{(1)}[/tex]
Solve for b:
[tex]\displaystyle b = \frac{25}{4}[/tex]
Thus, our completed function is:
[tex]\displaystyle y = 4\left(\frac{25}{4}\right)^x[/tex]
To find k, simply substitute 1.5 for x. This yields:
[tex]\displaystyle y = k = 4\left(\frac{25}{4}\right)^{(1.5)}[/tex]
And evaluate. Hence:
[tex]\displaystyle \begin{aligned} k &= 4\left(\frac{25}{4}\right)^{3/2} \\ \\ &= 4\left(\left(\frac{25}{4}\right)^{1/2}\right)^3 \\ \\ &= 4\left(\frac{5}{2}\right)^3 \\ \\ &= 4\left(\frac{125}{8}\right) \\ \\ &= \frac{125}{2}\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle a=4, b= \frac{25}{4}, \text{ and } k = \frac{125}{2}[/tex]
Evaluate the expression: -(31 + 2) +7² - (-5²)
A) -9
B) -5
C) 41
OD -40
Answer: C. 41
Step-by-step explanation:
[tex]-\left(31+2\right)+7^2-\left(-5^2\right)[/tex]
[tex]=-33+7^2-\left(-5^2\right)[/tex]
[tex]\left(-5^2\right)=-25[/tex]
[tex]=-33+7^2-\left(-25\right)[/tex]
[tex]7^2=49[/tex]
[tex]=-33+49-\left(-25\right)[/tex]
[tex]-33+49=16[/tex]
[tex]=16-\left(-25\right)[/tex]
[tex]\mathrm{Apply\:rule\:}-\left(-a\right)\:=\:+a[/tex]
[tex]16+25=41[/tex]
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently conducted a survey to gauge support for each of the two candidates. The results of the poll are shown in the two-way frequency table below.
Answer:
3 only
Step-by-step explanation:
Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.
Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.
Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.
Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.
Therefore, the true statement is III only.
More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Data given in the table shows the data of elections between two candidates among the different cities.
What is Statistic?
Statistics is the study of mathematics that deals with relations between comprehensive data.
I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.
II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false
III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.
IV. Overall, more residents support candidate A than candidate B. it is also false.
Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
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Look at the image to see the question
Answer:
Does the answer help you
f x equals 1 / x - 3 + 7 find the inverse of f x and its domain
Answer:
A
Step-by-step explanation:
f(x) = 1/(x-3)+7
f(x)-7=1/(x-3)
x=1/(f(x)-7)+3
f^-1(x)=1/(x-7)+3, where x≠7
The correct answer is option (a) [tex]f^{-1}(x)= \frac{1}{x-7} +3[/tex] where [tex]x\neq 7[/tex].
DomainThe domain of a function is the complete set of possible values of the independent variable
How to find domain?Given [tex]f^{}(x)= \frac{1}{x-3} +7[/tex]
Let
[tex]y= \frac{1}{x-3} +7[/tex]
⇒y-7= 1/x-3
⇒x-3 =1/y- 7
⇒ [tex]x= \frac{1}{y-7} +3[/tex]
hence option a is correct
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Jack is 4 times as old as Lacy. 3 years from now the sum of their ages will be 71 . How old are they now?
Answer:
Lacy is 13 and Jack is 52
Step-by-step explanation:
In 3 years their ages will add up to 71 so you have to subtract 6 as there are two of them to get 65. Lacy's age is represented by x and since Jack is 4 times older his age is represented by 4x. So added together their age is 5x. So 5x=65. Then 65/5=13. So 13=x. So Lacy is 13 and Jack is 52 as 13x4 is 52.
Please answer this correctly without making mistakes
Answer:
1/4 miles
Step-by-step explanation:
Hey there!
Well starting at Campbell and going to Morristown it is 1/4 miles.
Going from Campbell to Clarksville it is 2/4 miles.
So to find the difference we’ll subtract.
2/4 - 1/4
= 1/4 miles
Hope this helps :)
Write expression for the sum x and 6
Answer:
X+6
Step-by-step explanation:
Sum means Addition.
Reduce to simplest form.
-3/2 - 3/8
Answer:
hope this help you a lot
have a great day
Let A and B be any two sets. Show that:
Show that (
AUB)', (BUA)' = 0
Step-by-step explanation:
(AUB)' means they are all outside the set A and B so thats 0. Hope it helps
Biểu diễn 1 ràng buộc trên mặt phẳng tọa độ Oxy là
Step-by-step explanation:
yah kaun se language mein likha hai aapane
algebra and trigonometry difference
Answer:
Algebra deals with knowing the value of unknown variables and functional relationships, while trigonometry touches on triangles, sides and angles and the relationship between them.
Algebra is more on polynomial equations, x and y while trigonometry more on sine, cosine, tangent, and degrees.
Trigonometry is much more complicated than algebra but algebra has its uses in our daily lives, be it calculating distance from point to another or determining the volume of milk in a milk container.
Step-by-step explanation:
Answer:
Although both Algebra II and Trigonometry involve solving mathematical problems, Algebra II focuses on solving equations and inequalities while Trigonometry is the study of triangles and how sides are connected to angles.
hope this answer helps u
pls mark as brainliest .-.
Please Help
Function 1 is defined by the equation: p=r+7
Function 2 is defined by the table shown in the image below
Which function has a greater slope, function 1 or function 2?
Answer:
The slope of Function 2 (m=1.1) is greater than the slope of Function 1 (m=1).
Step-by-step explanation:
First, note that p is essentially the y and that r is the x. Thus, to make this easier to see, convert p to y and r to x. Thus:
[tex]y=x+7[/tex]
From the above equation, we can determine that the slope is 1. Thus, the slope of Function 1 is 1.
To find the slope of the table, simply use the slope formula. Use any two points. I'm going to use the points (0,8) and (10,19). Let (0,8) be x₁ and y₁, and (10,19) be x₂ and y₂. Therefore:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{19-8}{10-0}=11/10=1.1[/tex]
Thus, the slope of Function 2 is 1.1.
1.1 is greater than 1.
Thus, the slope of Function 2 is greater than the slope of Function 1.
Answer:
Function 2 has the greater slope
Step-by-step explanation:
The sum of the reciprocals of two consecutive even integers is 3/4
Find the two integers.
[tex] \Large{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]
Let one of those even numbers be x, Then other even number would be x + 2.
According to question,
⇛ Their reciprocal add upto 3/4
So, we can write it as,
⇛ 1/x + 1/x + 2 = 3/4
⇛ x + 2 + x / x(x + 2) = 3/4
⇛ 2x + 2 / x² + 2x = 3/4
Cross multiplying,
⇛ 3(x² + 2x) = 4(2x + 2)
⇛ 3x² + 6x = 8x + 8
⇛ 3x² - 2x - 8 = 0
⇛ 3x² - 6x + 4x - 8 = 0
⇛ 3x(x - 2) + 4(x - 2) = 0
⇛ (3x + 4)(x - 2) = 0
Then, x = -4/3 or 2
☃️ It can't be -4/3 because it is fraction and negative number. So, x = 2
Then, x + 2 = 4
✤ So, The even numbers are 2 and 4.
━━━━━━━━━━━━━━━━━━━━
Need help please will mark brainliest
Step-by-step explanation:
Maximum = 62
Median = (34+37+39+32+48+45+53+62+58+61+60+41)/12= 47.5≈48
quartile
In increasing order
32, 34, 37, 39, 41, 45, 48, 53, 58, 60, 61, 62
Upper quartile= (58+60)/2 = 59
Lower quartile= (37+39)/2 = 38
Minimum= 32
. En el triángulo ABC, la medida del ángulo exterior en el vértice B es el triple de la medida del ángulo C y la mediatriz de BC corta a AC en el punto F. sabiendo que FC=12. Calcular AB.
Responder:
| AB | = 12m
Explicación paso a paso:
Verifique el diagrama en el archivo adjunto.
En el diagrama, se puede ver que el lado FC es igual al lado FB de acuerdo con el triángulo isósceles FBC.
Además, el lado FB es igual a AB ya que son paralelos entre sí.
De la declaración anterior, | FC | = | FB | y | FB | = | AB |
Esto significa | FC | = | FB | = | AB |
Por lo tanto desde | FC | = 12 m, | AB | = 12 m ya que ambos lados son iguales.
De ahí el lado | AB | se mide 12m
Find X using the Angle Sum Theorem
Answer:
x = 20°
Step-by-step explanation:
So when I learned it we called it the exterior angle theorem not the angle sum theorem but here goes.
Since exterior angle = 110 Degrees,
--> The Inner 2 angles's sum = 110 Degrees
so, 70 + 2x = 110
=> 2x = 40
x = 20
x = 20°
Hope this helps!
Ben and Susan are truck drivers who start at the same location. Ben drives 300 miles due west and Susan drives 160 miles due south. To the nearest mile, how far apart would they be?
Answer:
Ben and Susan will be 340 miles apart
Step by Step Solution
Step 1: We plot the problem on a graph to visualize the problem
Step 2: We notice that the problem creates a right triangle with the distance Ben and Susan travel as the legs of the right triangle
Step 3: We can use the Pythagorean Theorem: a²+b²=c² to solve the distance between Ben and Susan
Step 4: We enter the numbers into the formula
a² + b² = c²
300² + 160² = c²
90000 + 25600 = c²
115600 = c² *square root both sides
c = 340
Therefore Ben and Susan are 340 miles apart
Ben and Susan are apart by 340 miles.
After drawing diagram according to question, it is observed that a right angle triangle is formed.
The distance between Ben and Susan is represented by Hypotenuse of right angle triangle shown in attached diagram.
Applying Pythagoras theorem in right triangle shown in attached diagram.
Distance between Ben and Susan =
[tex]\sqrt{(300)^{2}+(160)^{2} } =\sqrt{90000+25600}=\sqrt{115600} =340 miles.[/tex]
Therefore, Ben and Susan are apart by 340 miles.
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k = 2; f(x) = 2x3 + 3x2 - 4x + 4; Lower bound? (1 point)
Factor 13ab3 + 39a2b5.
[tex]13ab^3+39a^2b^5\\\\\boxed{\boxed{\boxed{13ab^3(1+3ab^2)}}}\\\\[/tex]
Brazil number one.
Answer:
there's no answer for that equation
Consider exponential function h.
h(x) = 3x + 4
The function is always positive.
(0,5) is the y-intercept, since the graphed line never crosses the x axis, there is no x-intercept.
The function is positive and greater than 4 for all values of x
Not sure what the actual choices are on a couple of the questions. The choices would help answering.
Fill in the blanks
To factor the polynomial 3x2–5x - 12, find two numbers whose product is
and
whose sum is
Answer:
Step-by-step explanation:
Ooooooofkfnvkanggkmfifkfkfkdkcknavnhkgnvkic
Which of the binomials below is a factor of this expression?
16x2 + 40xy + 25y2
16x²+40xy + 25y²
(4x+5y) (4x+5y)
(4x+5y)²
I hope I helped you^_^
Find the missing side of the triangle.
Answer:
x = 2(sqrt26) or x = 10.1980390272...
Step-by-step explanation:
Right triangles can be solved using Pythagorean theorem, where the legs are squared and added together to get the hypotenuse's length squared.
If we set up the equation:
11^2 + x^2 = 15^2
which is
121 + x^2 = 225
subtract 121 from both sides
x^2 = 104
sqrt both sides
x = 2(sqrt26), or x = 10.1980390272...
Answer:
Using Pythagoras theorem
c²=a²+b²
(15)²=x² +(11)²
225=x²+ 121
-x²=121-225
-x²=-104
multiply both sides by (-1)
x²=104
x=✓104
x=10ft
If x+1/x = 12, find the value of x^2+1/x^2
[tex]\boxed{\sf (a+b)^2=a^2+b^2+2ab}[/tex]
Now
[tex]\\ \sf\longmapsto x+\dfrac{1}{x}=12[/tex]
[tex]\\ \sf\longmapsto \left(x+\dfrac{1}{x}\right)^2=12^2[/tex]
[tex]\\ \sf\longmapsto x^2+2\times x\times \dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=144[/tex]
[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}+2=144[/tex]
[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}=144-2=142[/tex]
Answer:
122
Step-by-step explanation:
x+1/x = 12
x + 1 = 12x
x = 1/11
（1/11）² + 1 / （1/11）² = 1/121 +1 /1/121 = 122
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Jane is saving to buy a cell phone. She is given a $100 gift to start and saves $35 a month from her allowance. So after one month, Jane has saved $135. Does it make sense to represent the relationship between the amount saved and the number of months with one constant rate? Why or why not? Explain your answer.
Jane is given a $100 gift to start and saves $35 a month from her allowance.
After 1 month, Jane has saved
After 2 months, Jane has saved
After three months, Jane has saved
and so on
In general, after x months Jane has saved
This means that it makes sense to represent the relationship between the amount saved and the number of months with one constant rate (in this case the constant rate is 35). It makes sense because the amount of money increases by $35 each month. Since the amount of increase is constant, we get constant rate. Also the initial amount is known ($100), so there is a possibility to write the equation of linear function representing this situation.
Step-by-step explanation:
Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 2nd longest side on quadrilateral EFGH?
Answer:
24
Step-by-step explanation:
For ABCD the three longest are:
60,40,30
60 to 40 is 20
40 to 30 is 10
so each time it's decreasing by 1/2
For EFGH the two shortest are:
6 and 12
12 to 6 is 1/2
Assuming there is a pattern
it logically would be 24
as 12(2)=24
PRACTICE ANOTHER A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? m (b) How much wire should be used for the square in order to minimize the total area? m
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
The length of the square must be 4 m in order to maximize the total area.
What are the maxima and minima of a function?When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.
We have,
Length of the wire = 18 m
Let the length of the wire bent into a square = x.
The length of the wire bent into an equilateral triangle = (18 - x)
Now,
The perimeter of a square = 4 side
4 side = x
side = x/4
The perimeter of an equilateral triangle = 3 side
11 - x = 3 side
side = (18 - x)/3
Area of square = side²
Area of equilateral triangle = (√3/4) side²
Total area:
T = (x/4)² + √3/4 {(18 -x)/3}² _____(1)
Now,
To find the maximum we will differentiate (1)
dT/dx = 0
2x/4 + (√3/4) x 2(18 - x)/3 x -1 = 0
2x / 4 - (√3/4) x 2(18 - x)/3 = 0
2x/4 - (√3/6)(18 - x) = 0
2x / 4 = (√3/6)(18 - x)
√3x = 18 - x
√3x + x = 18
x (√3 + 1) = 18
x = 18 / (1.732 + 1)
x = 18/2.732
x = 6.58
x = 7
Thus,
The length of the square must be 7 m in order to maximize the total area.
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Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.
Complete Question
Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.the correct conclusion at [tex]\alpha =0.001[/tex] is?
Answer:
There is no sufficient evidence to support the professor believe
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 18[/tex]
The sample size is [tex]n = 15[/tex]
The sample mean is [tex]\= x = 19[/tex]
The standard deviation is [tex]\sigma = 1.7[/tex]
The level of significance is [tex]\alpha = 0.001[/tex]
The null hypothesis is [tex]H_o: \mu = 18[/tex]
The alternative hypothesis is [tex]H_a : \mu > 18[/tex]
The critical value of the level of significance from the normal distribution table is
[tex]Z_{\alpha } = 3.290527[/tex]
The test hypothesis is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 18}{ \frac{1.7}{ \sqrt{15} } }[/tex]
[tex]t = 2.28[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we can see that [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis.
This mean that there is no sufficient evidence to support the professor believe
!2,19,26 what comes nxt
Answer:
12 , 19 , 26 , 33
Explaination:Here, n+7
12+7=19
19+7=26
So,
26+7=33
Hope you understand ❣
Step-by-step explanation:
12 , 19 , 26 , ?
Given
___________
a1= 12
a2= 19
a3 = 26
d= ?
a4 = ?
––——————
we can solve this by using formula from Ap .
But for this we have to find d
As we know that
common difference(d) = a2-a1 = 19 -12
= 7
so difference after every no is 7 so
a4 = a3 + d
= 26 +7
= 33
So 33 is ur answer mate
Hope it helps