You have two exponential functions. One has the formula h(x) = 3x – 2. The other function, g(x), has the graph shown below.
Which inequality below is true for all points on the indicated interval?
A g( x) ≥ h( x) on the interval –3 ≤ x ≤ 3
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2
C g( x) ≤ h( x) on the interval –3 ≤ x ≤ 3
D g( x) ≤ h( x) on the interval –2 ≤ x ≤ 2
Answers
The correct statement regarding the exponential functions g(x) and h(x) is given as follows:
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.
What is an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the coefficients of the function are described as follows:
a is the y-intercept, the value of y at which the function crosses the y-axis.b is the rate of change of the exponential function.Function h(x) is defined as follows:
h(x) = 3^x - 2.
For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:
a = 4.
When x = 1, y = 5, hence the rate of change of the function is obtained as follows:
b = 5/4.
b = 1.25.
Then function g(x) is given as follows:
g(x) = 4(1.25)^x.
Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.
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Related Questions
power 121.three consecutive prime numbers, each less than $100$, have a sum that is a multiple of $5$. what is the greatest possible sum?
Answers
The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.
We have,
To find the three consecutive prime numbers with a sum that is a multiple of 5 and each less than 100, start by listing the prime numbers less than 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Check each combination:
(2, 3, 5): Sum = 2 + 3 + 5 = 10 (which is a multiple of 5)
(3, 5, 7): Sum = 3 + 5 + 7 = 15 (which is a multiple of 5)
(5, 7, 11): Sum = 5 + 7 + 11 = 23 (not a multiple of 5)
(7, 11, 13): Sum = 7 + 11 + 13 = 31 (not a multiple of 5)
(11, 13, 17): Sum = 11 + 13 + 17 = 41 (not a multiple of 5)
(13, 17, 19): Sum = 13 + 17 + 19 = 49 (which is not a multiple of 5)
(17, 19, 23): Sum = 17 + 19 + 23 = 59 (not a multiple of 5)
(19, 23, 29): Sum = 19 + 23 + 29 = 71 (not a multiple of 5)
(23, 29, 31): Sum = 23 + 29 + 31 = 83 (not a multiple of 5)
(29, 31, 37): Sum = 29 + 31 + 37 = 97 (not a multiple of 5)
(31, 37, 41): Sum = 31 + 37 + 41 = 109 (which is not a multiple of 5)
(37, 41, 43): Sum = 37 + 41 + 43 = 121 (which is not a multiple of 5)
(41, 43, 47): Sum = 41 + 43 + 47 = 131 (not a multiple of 5)
(43, 47, 53): Sum = 43 + 47 + 53 = 143 (which is not a multiple of 5)
(47, 53, 59): Sum = 47 + 53 + 59 = 159 (which is not a multiple of 5)
(53, 59, 61): Sum = 53 + 59 + 61 = 173 (not a multiple of 5)
(59, 61, 67): Sum = 59 + 61 + 67 = 187 (not a multiple of 5)
(61, 67, 71): Sum = 61 + 67 + 71 = 199 (not a multiple of 5)
(67, 71, 73): Sum = 67 + 71 + 73 = 211 (not a multiple of 5)
(71, 73, 79): Sum = 71 + 73 + 79 = 223 (not a multiple of 5)
(73, 79, 83): Sum = 73 + 79 + 83 = 235 (which is a multiple of 5)
(79, 83, 89): Sum = 79 + 83 + 89 = 251 (not a multiple of 5)
(83, 89, 97): Sum = 83 + 89 + 97 = 269 (not a multiple of 5)
Thus,
The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.
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Given that log,m=n, express 25n+2 in terms of m.
Answers
Answer:
25n+2 can be expressed as log,m^25+2.
Step-by-step explanation:
Since log,m=n, we can write 25n+2 as 25*log,m+2.
Using the property of logarithms that log,a+log,b=log,ab, we can rewrite 25*log,m as log,m^25.
1/2 - 1/7 =
3/5 - 1/2
Answers
Answer:
1/2 - 1/7 = 5/14
3/5 - 1/2 = 1/10
Step-by-step explanation:
A hospital is going to be built in the land of the shape of a rhomus having its
diagonals 250 m and 480 m respectively in a mountainous district of Nepal. Find
the area covered by the hospital in Ropani. (1 Ropani = 508.72 m²).
Answers
Answer:
117.94 Ropani
Step-by-step explanation:
Area Of Rhombus=½×d1×d2
=½×480×250
=60,000m²
1Ropani=508.72 {As Given}
60,000m²=(60,000÷508.72)Ropani
=117.94 Ropani
Answer:
60000 m^2
117.943 ropani
Step-by-step explanation:
the area of rhombus = 250 × 480 ÷2=60000 m^2
60000 m^2 = 117.943 ropani
. if you start with 1/4, you can create an entire class of fractions equivalent to 1/4 like the one above, by multiplying 1/4 by different forms of what number?
Answers
If you start with 1/4, you can create an entire class of fractions equivalent to 1/4 by multiplying 1/4 by different forms of the number 1.
What are fractions?The connection between two numbers, known as the numerator and the denominator, is expressed mathematically as fractions. The number of pieces is represented by the numerator, while the total number of components is represented by the denominator. For instance, if a pizza is cut into 8 slices and someone eats 3 of them, the fraction corresponding to the quantity consumed would be 3/8.
Diverse mathematical ideas, including division, ratios, and proportions, can be represented using fractions. They can also be used to represent decimal and percentage values, with the decimal point placed to the right of the numerator and the number of decimal places represented by the denominator.
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Solve each system by elimination: x+5y=4 3x-7y=-10
Answers
Answer: x= -1 y= 1
Step-by-step explanation: Times -3 to get the same x
-3x - 15y = -12
3x - 7y = -10
-22y = -22
y= 1
Then put 1 back in for letter y and you get x= - 1
identify the maximum or minimum volume to the domain and range of the graph of the function y=2(x-3)^2-4
Answers
The minimum value of the function y = 2(x - 3)² - 4 is -4. Domain of the function is set of all real numbers and the range is all real numbers ≥ -4.
What is Domain and Range of a function?Domain of a function y = f(x) is the set of all the values of x where the function is defined.
The range of the function is the set of all values of the function on the defined domain.
The given function is,
y = 2(x - 3)² - 4
y = 2(x² - 6x +9) - 4
y = 2x² - 12x + 14
This is a quadratic function and the graph of the function will be a parabola.
The parabola is directed upwards if the coefficient of x² in a quadratic equation is positive and so will be having a minimum value.
The parabola is directed downwards if the coefficient of x² is negative and so will be having the maximum value for the function.
Here, coefficient of x² = 2, is positive.
So there will be a minimum value.
The value of [tex]\frac{-b}{2a}[/tex] in the quadratic equation ax² + bx + c, is the x value of the vertex of the parabola.
x = - (-12) / (2 × 2) = 3
∴ Minimum value, y = 2 (3 - 3)² - 4 = -4
Domain of the function will be the set of all real numbers because the function is defined for all real numbers.
The range will be all real numbers ≥ -4, because any values of x in the function does not make the value of the function less than -4.
Hence the minimum value of the function is -4 and the domain and the range of the function is set of all real numbers and all real numbers ≥ -4 respectively.
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9. You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula A = P(1 + r/n) ^nt to give:
a. The future value in 4 years.
b. The interest gained in 4 years.
Answers
The compound interest formula [tex]A = P(1 + r/n) ^nt[/tex] Monthly compounding is a common strategy used by interest-bearing CDs to boost returns. The annual interest rate is divided by twelve in this scenario.
How to calculate interest ?After 4 years, you should have $763 in your account.After four years of saving $4 every month, your funds may reach $762.90. This includes a $500.00 initial balance and a 2.85% yearly rate of return.
Invest $500 in a 4-year certificate of deposit (CD) earning 2.85% interest compounded monthly.utilizing the compound interest formula [tex]A = P ( 1 + r / n ) ^{nt}[/tex]
The formula for calculating simple interest is S.I. = P R T, where P stands for principal, R for the annual percentage rate of interest, and T for time, which is typically expressed as the number of years. The interest rate is expressed as a percentage, or r%, and should be represented as r/100.
Many interest-bearing CDs use monthly compounding to increase returns. This model divides the annual interest rate by twelve.
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Add. State the sum in simplest terms.
16-p
(p+4)(p-6)
+ 1⁄4 › P‡ − 4,6
p+4
Answers
The sum in simplest terms is 1/(p-6)
What is LCM?
Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least common multiple (LCM) of two numbers. It can also be computed for two or more different numbers. There are numerous ways to calculate the LCM of a given collection of numbers. Utilizing the prime factorization of each number and then calculating the product of the highest powers of the common prime factors yields the LCM of two integers in a short amount of time.
(16-p)/[ (p+4)(p-6) ] + 2/ (p+4)
Take LCM = (p+4)(p-6)
= [ 16-p + 2(p-6) ] / [ (p+4)(p-6) ]
= [ 16-p + 2p-12) ] / [ (p+4)(p-6) ]
= ( p +4 ) / [ (p+4)(p-6) ]
= 1/(p-6)
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Find the measure of angle f given the information below.
A= 122 degrees
E=48 degrees the image is below!!
Answers
Answer:
74
Step-by-step explanation:
if a is 122 b is 58
b is congruent to g to g=58
58+48=106
180-106=f
180-106=74
A shopper at a clearance sale is pleased to discover some lamps on sale for $9 each. The original price tags read $30. What percentage is the discount?
Answers
Answer: 70% of a discount
Step-by-step explanation:
what is x and what is the reason why (circle theorems)
Answers
Check the picture below.
Ben bought one share of stock for $40. He watched the
price of his stock every day for a week. On Monday, the
stock moved 2.5 points up. On Tuesday, it moved 1.75
points down. On Wednesday, it moved p points. On
Thursday and Friday, the stock moved 0.75 points up
each day. If the price of the stock was $45 at the end of
the week, what is the value of p?
Answers
Answer:2p
Step-by-step explanation:
1/2 of a 360
circle in degrees
Answers
Answer:
Step-by-step explanation:
180 because if you add 180 + 180 = 360
(a) at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?
Answers
The number of sets to be printed to ascertain at least 4 identical subset is there on the list when a computer is printing out subsets of a 5 element set is 97.
The total number of subset for a n element set is 2^{n}. Therefore, for a 5 element set is 2^{5} = 32.
Thus to ensure there are at least 4 identical subset, the computer should print 3 times the total number of subsets possible plus 1 additional subset, i.e. 3×32 + 1 = 97.
-- The question is incomplete, the correct question is as follows --
"A computer is printing out subsets of a 5 element set (possibly including the empty set). a. at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?"
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Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y =
Answers
The solution for the system of equations is the point (3, 5), and the difference x - y gives:
x - y = -2
How to solve the system of equations?Here we have the following system of equations:
5x + 3y = 30
-5x - 2y = -25
Notice that in the two equations we have the "5x", but in one case is positive and in the other negative, then we can just add them so we get:
(5x + 3y) + (-5x - 2y) = 30 - 25
(5x - 5x) + (3y - 2y) = 5
0 + y = 5
y = 5
So we found the value of y, by evaluating the second linear equation in y = 5 we will get:
-5*x - 2*5 = - 25
-5x = -25 + 2*5
-5x = -25 + 10
-5x = -15
x = -15/-5 = 3
So y = 5 and x = 3, the difference x - y gives:
3 - 5 = -2
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Olivia want to have a 90 average in algebra, where tet count for 55%, quizze count for 30ge % and homework count for 15%. If he ha a 92 tet average and 100% HW average, what mut her quiz average be? Let x = the average of the
Answers
In order to score 90 average in algebra her quiz average should be 82%.
It involves calculating the result of multiplying a number of quantities by their sum, then dividing the result by the total number of quantities.
Given,
She has a test grade of 55%, a quiz grade of 30%, and a homework grade of 15%.
If she achieved a score of 92% on the test
Make x the number of tests,
x = (90 - (0.55(92) + 0.15(100)))/0.30
x = 82
To receive a 90 in math, Olivia needs to have a quiz average of 82.
One of the oldest subfields of mathematics, algebra covers number theory, geometry, and analysis. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.
Algebra covers a wide range of topics, from the study of abstractions to the solution of simple equations.
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What value of x makes the perimeters of the figures below equal? (see imagine attached) :)
Answers
The value of x that makes the perimeters of the figures equal is; x = 3.
What is the Perimeter of a Figure?To find the perimeter of a figure, add all its side together. That is, the sum of all its sides will give you the perimeter.
Perimeter of the triangle = (x + 6) + 5x + (3x + 3)
Open the bracket and simplify
x + 6 + 5x + 3x + 3
Combine like terms
= 9x + 9
Perimeter of the square = 4(x + 6)
= 4(x) + 4(6)
= 4x + 24
Make both equation equal to each other and find x:
9x + 9 = 4x + 24
9x - 4x = -9 + 24
5x = 15
x = 3
The value of x is 3.
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7. What is the number?
The number is between 10 and 20.
The number is composite.
The number is odd.
Answers
Answer:
The number is 15
Answer:
15
Step-by-step explanation:
The number is between 10 and 20.
10 11 12 13 14 15 16 17 18 19 20
The number is composite or have more than 2 factors.
10 12 14 15 16 18 20
The number is odd.
15
Roger is moving 40 1/2pounds of bricks for a landscaping project. He moves 7 1/3 pounds of bricks in each load, then takes a short break. Which equation will help you solve to find out how many whole loads of bricks, b, Roger will move?
Answers
The equation to find how many loads of bricks that Roger move will be 44x=243.
What does linear equation mean?A linear polynomial over a field with zero coefficients can be used to create a linear equation. The answers to such an equation are the numbers that, when the unknowns are replaced, make the equality true.
This particular situation, in which the variable is accurately referred to as the unknown, is commonly referred to as a "linear equation."
In the case of two variables, each solution can be thought of as a point's Cartesian coordinates on the Euclidean plane. The answers to a linear equation result in a line.
Given,
Total amount of bricks load carried by Roger=40 1/2pounds
=81/2 pounds
Per each load --- 7 1/3pounds
1 load --------- 22/3 pounds
x -----81/2 pounds
(81/2)(3/22)=x
243=44x
44x=243
Therefore, the equation to find how many loads of bricks that Roger move will be 44x=243.
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The angles of a triangle are 44 degrees, 110 degrees, and 26 degrees. Classify the triangle
Answers
The measure of angles form an scalene triangle.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
An angle requires two straight line, such that they're connected on one of their endpoints. The point of their joint is called vertex of that angle.
We are given that the angles of a triangle are 44 degrees, 110 degrees, and 26 degrees.
Since we know that angle sum property of a triangle;
44 + 110 + 26
180
Therefore, the measure of angles form an scalene triangle.
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Hillary is using the figure shown below to prove Pythagorean Theorem using triangle similarity: In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC. The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC. Which of these could be a step to prove that BC2 = AB2 + AC2? (6 points) By the addition property of equality, AC2 plus AD2 = AB multiplied by DC plus AD2. By the addition property of equality, AC2 plus AD2 = BC multiplied by DC plus AD2. By the addition property of equality, AC2 plus AB2 = AB multiplied by DC plus AB2. By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.
Answers
Answer: By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.
Write a rule for the n th term of the sequence. Then find a_{20}
$51,48,45,42,...$
Answers
The rule for the nth term of arithmetic sequence is a + (n - 1)d.
What is the nth term of arithmetic sequence?The difference between consecutive terms in an arithmetic sequence is always the same.An arithmetic sequence's nth term is given by a = a + (n - 1)d. The number d is known as the common difference because any two consecutive terms of an arithmetic sequence differ by d, and it can be found by subtracting any two terms a and an+1.Here also,
We use the definition for the nth term of an arithmetic sequence:
an = a1 + (n - 1) d
Here first term (a1) = 51
common difference (d) = a2 - a1
= 48 - 51
= -3
We have to find 20th term,
a[20] = a1 + (20 - 1) d
= 51 + 19 x -3
= 51 - 57
= - 6
Therefore 20th term of the sequence 51,48,45,42,... is -6.
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The rate of change is how a quantity is changing with respect to a change in another quantity.
True false question.
True
False
Answers
Answer: True
Step-by-step explanation:
The rate of change or the slope is the changes to another quantity with a constant.
Are any of these numbers linear expressions? 5x+3, 8xy, 14, or 3x^2
Answers
Answer: 5x+3 is a linear expression
Step-by-step explanation:
The linear expression is y=mx+b
5x +3 has a slope and y-intercept, so it is a linear expression!
8xy is not because it is just a variable
3x^2 is not because it has ^2
there are 5 children on your guest list and 40 people in total. what percentage of the people are children?
Answers
Answer: 12.5%
Step-by-step explanation:
5/40
0.125 x 100
12.5%
Answer:
2 children I believe so
Step-by-step explanation:
because you take 40%×5 and u will get 2
A washer and dryer cost a total of $1132. The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Cost of washer:
Cost of dryer:
Answers
Answer:
Washer = $849
Dryer = $283
Step-by-step explanation:
Dryer = x
Washer = 3x
3x + x = 1132
Simplify:
4x = 1132
Divide both sides by 4:
x = 283
The dryer costs $283, and since the washer is three times the cost of the dryer, the washer is:
283x3 = 849
Ome of the children at a chool arrive by car
- 30% of the tudent at the chool are boy
- 60% of the boy at the chool arrive by car
- 80% of the girl at the chool arrive by car
what i the probability a child choen at random from the chool arrive by car
Answers
The probability that a child chosen at random from the school arrives by car is the total of the column Car 74%.
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained.
The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.
You can build a two-way relative frequency table to represent the data:
These are the columns and rows:
Car No car Total
Boys
Girl
Total
Fill the table
30% of the children at the school are boys
Car No car Total
Boys 30%
Girl
Total
60% of the boys at the school arrive by car
That is 60% of 30% = 0.6 × 30% = 18%
Car No car Total
Boys 18% 30%
Girls
Total
By difference you can fill the cell of Boy and No car: 30% - 18% = 12%
Car No car Total
Boy 18% 12% 30%
Girl
Total
Also, you know that the grand total is 100%
Car No car Total
Boy 18% 12% 30%
Girl
Total 100%
By difference you fill the total of Girls: 100% - 30% = 70%
Car No car Total
Boy 18% 12% 30%
Girl 70%
Total 100%
80% of the girls at the school arrive by car
That is 80% of 70% = 0.8 × 70% = 56%
Car No car Total
Boy 18% 12% 30%
Girl 56% 70%
Total 100%
Now you can finish filling in the whole table calculating the differences:
Car No car Total
Boy 18% 12% 30%
Girl 56% 14% 70%
Total 74% 26% 100%
Having the table completed you can find any relevant probability.
The probability that a child chosen at random from the school arrives by car is the total of the column Car 74%.
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What is the y-intercept of this line?
Answers
Answer: b=13
Step-by-step explanation:
This equation is in point-intercept form: y = mx + b
slope = m = 4/3
y-intercept = b = 13
Determine the equation of the parabola with vertex (7,4) and a directrix y=10.
Answers
The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application",
What is the parabola?pa·rab·o·la pə-ˈrab-ə-lə : a curve formed by the intersection of a cone with a plane parallel to a straight line in its surface : a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. : something that is bowl-shaped.This form is called the standard form of a quadratic function. The graph of the quadratic function is a U-shaped curve is called a parabola. The graph of the equation y=x2, shown below, is a parabola.The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax. Some of the important terms below are helpful to understand the features and parts of a parabola.
The equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .
It is given to us that -
The vertex of the parabola = (-8,5)
The directrix of the parabola is y = -3
We have to find the equation of the parabola with the given vertex and directrix.
We know that any point on a given parabola represented as () is equidistant from the directrix and the focus.
So, the equation for the point can be represented as
[tex][y-(-3)]=\sqrt{([x-(-8} ]^{2} +(y-5)^{2}[/tex]
[tex](y+3)^2} =(x+8)^{2} +(y-5)^{2} \\=y^{2}+9+2*y*3=(x+8)^{2} +y^{2}+25-2*y*(-5)=6y-10y=(x+8)^{2} +16=-4y=(xx+8)^{2} +16=y=\frac{-1}{4} (x+8)^{2}+4[/tex]
Thus, the equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .[tex]=y=\frac{-1}{4} (x+8)^{2} +4[/tex]
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