It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.
Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.
Now let's analyze the functions from the problem.
[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.
Use these rules to find whether each function is increasing or decreasing.
Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.
Write an equation for a parabola with x-intercepts (-3,0) and (4,0) which passes through the point (2,-40)
The parabolic equation that passes through the points is y = 29/7x^2 + -27/7x - 342/7
What are parabolic equations?Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the equation of the parabola?The given parameters are
x-intercepts (-3,0) and (4,0)
Point = (2,-40)
From the definition above, we have the form to be
y = ax^2 + bx + c
Substitute (-3,0) and (4,0) in the above equation
So, we have
0 = a(-3)^2 + b(-3) + c
0 = a(4)^2 + b(4) + c
This gives
9a -3b + c = 0
16a + 4b + c = 0
Substitute (2,-40) in the above equation y = ax^2 + bx + c
a(2)^2 + b(2) + c = -40
So, we have
4a + 2b + c = -40
The equations become
9a -3b + c = 0
16a + 4b + c = 0
4a + 2b + c = -40
Using a graphing tool, we have
a = 29/7, b = -27/7 and c = -342/7
So, we have
y = ax^2 + bx + c
This gives
y = 29/7x^2 + -27/7x - 342/7
Hence, the equation is y = 29/7x^2 + -27/7x - 342/7
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There are 28 students in a class.
16 of the students are girls.
What proportion are boys?
Write your answer in two ways.
Answer:
3:7
Step-by-step explanation:
Given:
There are 28 students in a class16 of the students are girls.To Find:
What proportion of the students are boys.Formula used:
No. of boys = Total students - No. of girlsUsing the formula, we have
No. of boys = 28 - 16 = 12
Proportion of boys = 12/28 = 3/7
So, proportion of boys = 3:7.
Write the following using algebraic notation, using the letter x for any
unknown numbers:
think of a number, double it, then add fifteen.
[tex] = x \times 2 + 15 \\ = 2x + 15[/tex]
DOUBLING IT MEANS MULTIPLYING IT BY 2
THEN ADD 15 AS SHOWN ABOVE.
HOPE THIS HELPS
By drawing two circles, John got a figure, which consists of three regions(basically a venn diagram). At most how many regions could John get by drawing two squares?
Given mn, find the value of x.
t
(7x-1)⁰
(5X-23)°
[tex](5x - 23) + (7x - 1) = 180 \\ 5x + 7x - 23 - 1 = 180 \\ 12x - 24 = 180 \\ 12x = 180 + 24 \\ 12x = 204 \\ \frac{12x}{12} = \frac{204}{12} \\ x = 17[/tex]
x=17°
I used the reasons CORRESPONDING ANGLES AND ANGLES ON A STRAIGHT LINE.A kidney stone treatment study found that treatment A had 81 out of 87 successful trials in small stone treatments and 234 out of 270 successful trials in large stone treatments. Treatment B had 234 out of 270 successful trials in small stone treatments and 55 out of 80 trials successful in large stone treatments. Overall which treatment had a better success rate and why? 150 words no copy internet
Using proportions, it is found that due to the higher proportion of successful trials, Treatment A had the better success rate
What is a proportion?A proportion is a fraction of a total amount, and hence it is represented by the sum of the desired amounts divided by the sum of the total amounts.
For Treatment A, we have that:
There was a total of 87 + 270 = 357 trials.Of those, 81 + 234 = 315 trials were successful.Hence the proportion of successful trials for Treatment A is given by:
315/357 = 0.8824.
For Treatment B, we have that:
There was a total of 80 + 270 = 350 trials.Of those, 55 + 234 = 289 trials were successful.Hence the proportion of successful trials for Treatment B is given by:
289/350 = 0.8257.
The proportion for Treatment A is higher, as 0.8824 > 0.8257, hence it had the better success rate.
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-8>-3t-10 can someone help
Answer:
t > -2/3
Step-by-step explanation:
−8>−3t−10
Step 1: Flip the equation.
−3t−10<−8
Step 2: Add 10 to both sides.
−3t−10+10<−8+10
−3t<2
Step 3: Divide both sides by -3.
−3t/−3 < 2/−3
t > −2/3
If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has which of the following?
A. No solution
B. Infinitely many solutions
C. One solution
D. Two solutions
Answer:
C. One solution
Step-by-step explanation:
You want to know the number of solutions of a system of equation such that the graph of the linear function touches the graph of the quadratic function at its minimum.
SolutionsThe number of real solutions of the system of equations is equal to the number of points of intersection of their graphs. The problem statement tells you the graphs intersect at one point, so there is one solution.
__
Additional comment
The linear function can only touch the minimum of a quadratic if its graph is a horizontal line.
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calculate the complement of a 26° angle.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
angle = 26 degress
complement angle = ?
Step 02:
26 + x = 90
x = 90 - 26
x = 64
The answer is:
The complement angle is 64 degrees
An actor bought a pearl, diamond, and ruby necklace for his famous wife for $54,000. In 2011 this necklace was auctioned for $11,379,600. The auction price was what percent of the original purchase price?
This necklace sold at auction for $11,379,600 in 2011. The percentage of the initial purchase price was represented by the auction price is 2.1%.
Given that,
For $54,000, an actor purchased a pearl, diamond, and ruby necklace for his well-known wife. This necklace sold at auction for $11,379,600 in 2011.
We have to find what percentage of the initial purchase price was represented by the auction price.
Let us take the percentage as x%.
Necklace sold at auction=the percentage multiplied by the actual price
We get,
$11,379,600 =x%($54,000)
x%=$11,379,600/$54,000
x%=2.1%
Therefore, the percentage of the initial purchase price was represented by the auction price is 2.1%.
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Find the slope of a line containing
P1(3, 7)
and
P2(6, 9).
The slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.
Slope, also called as gradient of a line is a value or number that describes both of the directions x and y. It basically tells the steepness of the line.
To find the slope of line, formula given below is used
[tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex] = slope
Here, y2 = 9
y1 = 7
x2 = 6
x1 = 3
Thus, 9 - 7/6 - 3
= 2/3
Therefore, we can conclude that the slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.
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what is the method used to complete the table?
Answer:
see attached
Step-by-step explanation:
You want to finish filling the given 2-way table.
TotalsAny single missing value in a row or column will be the value that makes the total correct for that row or column. Filling the single missing values will fill enough of a row or column with two or more missing values so that the remaining missing values can be filled the same way.
It is basically a series of subtraction problems.
For example, the upper left cell is filled with 20 -4 = 16, so the total on that row is 16+4=20.
3. John and Savanah are saving money to go on a trip to Mexico. They need at least $2,545 in order to go. John tutors English and Savanah works as a babysitter to raise money. John charges $15 per hour and Savanah charges $20 per hour. The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled. Savanah will babysit at least 40 hours.. Write a set of constraints to model the problem, with x representing the number of hours John tutors and y representing the number of hours Savanah babysits. Answer:
The group of restrictions used to simulate the issue includes
y<5x andy [tex]\geq[/tex] 40hours How to construct a set of restrictions to represent the issue:The issue includes the following information.
They need a minimum of $2,545 divided by the hours John instructs and the hours Savanah watches children.There is a maximum of a five-fold difference between the number of hours Savanah has booked and that John has.At least 40 hours will be spent watching the children by Savanah.The following are the restrictions for modeling the issue: There is a maximum of a five-fold difference between the number of hours Savanah has booked and that John has.
Savanah will provide childcare for at least 40 hours, with no more than meaning it is not larger than that which suggests it is less than, Hence, y<5x
Meaning "at least 40 hours" is "at least 40 hours." 40 hours or more may be expressed as
y ≥ 40 hours
The two necessary restrictions are represented as y< 5x and y=> 40 hours in an inequality model.
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Katie wants to save at least $280 to go on the math team field trip. He currently has $112 saved.
If he has 8 weeks left to save, which inequality and graph represent the amount of money per week he needs to save to meet the goal?
He must save 21 dollars per week to meet the goal.
How to find the amount to be saved?Given,
Katie wants to save at least $280
He currently has $112 saved.
If he has 8 weeks left to save.
Solution:
The amount to be saved is $280 - $112 = $168
If he has 8 weeks left to save,
Per week he must save = $168/8
= $21
He must save 21 dollars per week to meet the goal.
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Find the x-intercept of the function g(x)=8x²-10x-3
To find the x-intercepts of the function g(x), we must set it equal to 0 and solve for x.
We have the following:
[tex]\begin{gathered} g(x)=8x^2-10x-3 \\ if\text{ g(x)=0} \\ \Rightarrow8x^2-10x-3=0 \end{gathered}[/tex]we can use the quadratic formula to get the roots of the polynomial:
[tex]\begin{gathered} a=8 \\ b=-10 \\ c=-3 \\ x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \Rightarrow x_{1,2}=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(8)(-3)}}{2(8)}=\frac{10\pm\sqrt[]{196}}{16} \\ \Rightarrow x_{1.2}=\frac{10\pm14}{16} \\ \Rightarrow x_1=\frac{10+14}{16}=\frac{24}{16}=\frac{3}{4} \\ \Rightarrow x_2=\frac{10-14}{16}=\frac{-4}{16}=-\frac{1}{4} \end{gathered}[/tex]therefore, the x-intercepts of the function g(x) are the points (3/4,0) and (-1/4,0)
help pls!! In the figure below, N is between M and O, and O is between N and P. If NO=2, NP = 8, and MP=15, find MO.
The distance between MO is 9.
How to find MO ?From the question MP is straight line and O & N is points between M & P.
No is 2NP is 8MP is 15so the total length of line is 15
Need to find MO , To find MO = MP - (NP - NO)
= 15 - (8 -2)
= 15 - 6 = 9
The MO is 9.
To find points in graph :
To find a line that's parallel to a line and goes through a particular point, use the point's coordinates for (x1, y1) in point slope form: y - y1 = m (x - x1).The slope intercept formula y = mx + b is used when you know the slope of the line to be examined.Use the slope and one of the points to solve for the y-intercept.One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.To learn more about finding distance refer :
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Solve all
1. (25+5) x3-13
2. 19+12x2-4
3. 42+32+4
4. 12+34x2÷2
5. (4+3) x (2+5)
6. 2+14x5-5
7. 22+4x5-13
8. 13-42+7+2
9. 15+2-14÷7
10. (18-7)x2
write 7843 to nearest thousand with explanations
Help find X-coordinate
The value of x coordinate be 0 or -2.
Given,
Vertex of the graph, f(x) = x² + 2x + 2
We have to find the x coordinate.
Here,
f(x) = x² + 2x + 2 is in the form of quadratic equation.
So, we can find x coordinate by using quadratic formula.
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = 1, b = 2 and c = 2
So,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-2(+-)\sqrt{2^{2}-4(1)(2) } }{2(1)}[/tex]
= [tex]\frac{-2(+-)\sqrt{4-8} }{2}[/tex]
= (-2±(-√4)) ÷ 2
= (-2±(-2)) ÷ 2
Solve for.
-2 + (-2) / 2 = -2 -2 / 2 = -4/2 = -2
Solve for,
-2 - (-2) / 2 = -2 + 2 / 2 = 0
That is,
The value of x coordinate be 0 or -2.
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Provide the correct reason for the statement in line 4. (please help)
Answer:
d) division property of =
Step-by-step explanation:
by step 3, the variable x is still being multiplied by 3. In order to isolate x, you must divide by 3 on both sides.
round to 1,600 to the nearest hundred
Answer:1,600
Step-by-step explanation:C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
you already have the answer :)
8. [-/1 Points]
SPRECALC7 1.7.071.
A pilot flew a jet from City A to City B, a distance of 1600 ml. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 8 h 20 min. What was the speed from
City A to City B?
mi/h
DETAILS
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
The speed from City A to City B is 352 miles/hour.
What is the relationship between speed, distance, and time?By dividing the distance traveled by the time required to travel it, speed is calculated.Speed is inversely correlated with time and directly correlated with distance. Thus, distance equals speed times time.Distance divided by speed equals time; as speed rises, time goes down, and vice versa.Given:
Distance for trip = 1600 miles
Distance for return trip = 1600 miles
The round-trip took 8 h 20 min.
Total time taken for both trips = 8 hours 20 minutes = 8 + (1/3) hours = 25/3 hours
It is mentioned that on the return trip, the average speed was 20% faster than the outbound speed.
Let's assume x is the speed for an outbound trip.
So, x + 20% of x is the average speed of the return trip
x + 20% of x = x + 0.2x = 1.2x
Speed for the return trip = 1.2x
Total time = (distance/speed of outbound trip) + (distance/speed of return trip)
⇒ [tex]\frac{25}{3} =\frac{1600}{x} +\frac{1600}{1.2x}[/tex]
⇒ [tex]\frac{25x}{3} =\frac{1600*1.2 +1600}{1.2}[/tex]
⇒ [tex]10x = 3520[/tex]
⇒ [tex]x = 352[/tex]
Therefore, the speed from City A to City B is 352 miles/hour.
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Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you created? (10 points)
A situation in which positive and negative numbers are used to describe values that have opposite meaning is that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.
The thing that 0 represents is the addition in the sea level.
How to illustrate the information?Based on the information illustrated, the situation will be that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.
Therefore, the addition will be:
= 2000 + (-2000)
= 2000 - 2000
= 0
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find x if AC=15 , AB=x+14 , and BC= x+13
Given the information, we have the following:
Now, since AC=15, we have the following expression:
[tex]\begin{gathered} AB+BC=AC \\ \Rightarrow(x+14)+(x+13)=15 \end{gathered}[/tex]Solving for x we get:
[tex]\begin{gathered} (x+14)+(x+13)=15 \\ \Rightarrow2x=15-14-13=-12 \\ \Rightarrow2x=-12 \\ \Rightarrow x=\frac{-12}{2}=-6 \\ x=-6 \end{gathered}[/tex]Therefore, x=-6
Find the center, transverse axis, vertices, foci, and asymptotes. Graph the equation.y² -x² =25
What are the asymptotes?
The asymptote with positive slope is, and the asymptote with negative slope is.
The values are as follows:
center: y²/25-x²/25 = 1
transverse axis : b = 5
Vertices: (0,5) and (0,-5)
Foci: (0,5√2) and (0,-5√2)
Asymptotes: y = x and y = -x
An asymptote is a line being approached by a curve but never touching the curve. i.e., an asymptote is a line to which the graph of a function converges. We usually do not need to draw asymptotes while graphing functions.
Types of Asymptotes:
1) Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.
2) Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.
3) Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b.
y² -x² =25 up down hyperbola with (h,k) = (0,0) a = 5 and b = 5
(y-k)²/a²-(x-h)²/b² = 1 is the standard equation of up-down hyperbola.
With semi-axis is a and semi-conjugate axis is b.
and centre (h,k).
Center = (y-0)²/5²-(y-0)²/5² = 1
= y²/25-x²/25 = 1
The axes are a = 5 and b = 5
transverse axis is b = 5
The foci are given by (h, k+c) and (h, k-c), where c = √a²+b²
c = √5²+5² = 5√2
therefore, the foci are (0,5√2) and (0,-5√2).
The vertices are (h, k+a) and (h, k-a)
(h,k) = (0,0) and a = 5 and b = 5
vertices are (0,5) and (0,-5)
Asymptotes are y = x and y = -x.
Therefore, the summary is as follows:
center: y²/25-x²/25 = 1
transverse axis : b = 5
Vertices: (0,5) and (0,-5)
Foci: (0,5√2) and (0,-5√2)
Asymptotes: y = x and y = -x
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1 3/4 x 4 2/6 nnnnnnnnnnn
The result of the multiplication operation yields 7 7/12
Multiplication of numbersFrom the question, we are to multiply the given fractions. The given fractions are
1 3/4 and 4 2/6
First, we will convert the fractions to improper fractions
Converting 1 3/4 to an improper fraction
1 3/4 = 7/4
Converting 4 2/6 to an improper fraction
4 2/6 = 26/6
Thus,
The multiplication operation becomes
7/4 × 26/6
= 7/4 × 13/3
= 91/12
= 7 7/12
Hence, the product of the given numbers is 7 1/12
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show work help plsss
The required quotient is 6.5625 when -5 2/8 is divided by (-4)/5.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
The quotient is given in the question:
-5 2/8 ÷ (-4)/5
-(42/8) / (-4)/5
Reciprocal the term in the denominator
-(42/8) × -(5)/4
210/32
6.5625
Therefore, the required quotient is -5 2/8 ÷ (-4)/5 = 6.5625.
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Solve I =prt for p when I =5,480,r =.04, and t=7. Round your answers to two decimal pla
We are asked to find the simple interest associated with a principal of 5480 , an annual rate of 0.04 (4%) and at the end of 7 years:
We use the simple interest formula:
I = P r t
in our case: I = (5480) (0.04) (7) = 1534.4
So the interest is: 1534.40
We answer using two decimal places because this is refering to cents of a dollar.
In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or
spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below.
Using the probability concept, we have that:
a) The probability is of 0.244.
b) The probability is of 0.756.
c) A student given a $1 bill is more likely to have kept the money.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
For item a, we have that out of 11 + 34 = 45 students who were given a $1 bill, 11 spent the money, hence the probability is given as follows:
p = 11/45 = 0.244.
For item b, we have that out of 11 + 34 = 45 students who were given a $1 bill, 34 kept the money, hence the probability is given as follows:
p = 34/45 = 0.756.
For item c, we have that a student given a $1 bill is more likely to have kept the money, as 0.756(kept) > 0.244(spent), which are the two probabilities we found in the previous items.
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For the function f(x)=4x+4,
find (a) f(x+h),
(b) f(x+h)−f(x), and
(c) f(x+h)−f(x) h.
(a) f(x+h)=?
Step-by-step explanation:
a)
[tex]f(x+h) = 4(x+h)+4[/tex]
[tex]f(x+h)=4x+4h+4[/tex]
b)
[tex]f(x+h)-f(x)=4x+4h+4-(4x+4)[/tex]
[tex]f(x+h)-f(x)=4x+4h+4-4x-4[/tex]
[tex]f(x+h)-f(x)=4h[/tex]
c)
[tex]f(x+h)-f(x)h=4x+4h+4-h(4x+4)[/tex]
[tex]f(x+h)-f(x)h=4x+4h+4-4hx+4h[/tex]
[tex]f(x+h)-f(x)h=-4hx+8h+4x+4[/tex]