The value of the function h(x) is x² - 4x +6 and 4-6 x².
What is a formula for a function?Any function's x-intercept, y-intercept, and slope can be calculated using function formulas. You could also determine a quadratic function's vertex. Additionally, the function can be graphed for various x values.
Simply adding the values of the functions f(x) and g will yield the value of the function f(x) and g(x).
Therefore, we get
f(x) = x² and we have g(x) = 4x - 6
h(x) = f(x) - g(x)
h(x) = x² - 4x +6
h(x) = f(g(x))
= x²( 4x - 6)
= 4-6 x²
h(x) is the inverse of g(x)
= inverse of 4x - 6
= 1/ 4x - 6
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please help me thank you.
Answer:
62 degrees.
Step-by-step explanation:
I think this because it appears that ABC makes a 90 degree angle and I would think that you would just subtract 28 from 90 and get 62.
Hope it helps! =D
the cost,y, of red grapefruit can be represented by the equation y=2x, where x is the number of pounds of red grapefruit. the graph shows the cost of pink grapefruit. which type of grapefriut costs more per pound?
We can conclude that, if --
m{pink} > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m{pink} < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that the cost (y) of red grapefruit can be represented by the equation y = 2x, where {x} is the number of pounds of red grapefruit. Also the graph shows the cost of pink grapefruit.
The cost (y) of red grapefruit can be represented by the equation y = 2x. So, we can write that the cost per unit pound of red grape is $2. The graph of the pink grapefruit is not given, but its slope {m} will tell us its costs per pound.
Now, if -
m > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.Therefore, we can conclude that, if -
m{pink} > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m{pink} < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.To solve more questions on straight lines, visit the link below -
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Richard has 11 markers in a backpack. One of them is red and one is purple. What is the probability Richare
will reach into the backpack without looking and grab the red marker and then reach in a second time and
grab the purple marker if:
(a) the first marker is not replaced?
(b) the first marker is replaced?
Express your answers as fractions in simplest form.
The probability Richard marker is 11.The probability of anything occurring is known as probability.
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.
According to question:-
11/1 = 11
11/1 = 11
The probability Richard marker is 11.The probability of anything occurring is known as probability.
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solue, giving all solutions between 0 and 360 degrees 8 (COS X)² - 10 COS X+3=0
Step-by-step explanation:
please refer to the sketch
Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
X
6
-
X
The equation has Select an option
0
attempt 1 out of 2
The equation has one solution.
A value of x that makes the equation true is 6 which when substituted into the equation and simplified makes the equation turn into x = 0.
A value of x that makes the equation false is 8 which when substituted into the equation and simplified makes the equation turn into x = 2.
How to evaluate the equation?From the information provided, we have the following equation:
x - 6 = 6 - x
Rearranging the equation by collecting like terms, we have the following solution:
x + x = 6 + 6
2x = 12
x = 12/2
x = 6
Substituting the value "6" into the equation, we have the following solution;
x - 6 = 6 - 6
x - 6 = 0
Assuming x = 8, we have the following solution;
x - 6 = 8 - 6
x - 6 = 2
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Complete Question:
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
x - 6 = 6 - x
The equation has _____.
A value of x that makes the equation true is ___ which when substituted into the equation and simplified makes the equation turn into ____.
A value of x that makes the equation false is ___ which when substituted into the equation and simplified makes the equation turn into ___.
4 3/5+ 2 2/3= l need someone to help me out
5
Jasmine is a receptionist at a doctors office. She books 36 appointments each day.
Four out of every 24 appointments are cancelled. How many appointments are cancelled
each day?
6
Kendrick's Kennel has 2/spots for cats for every spots for dogs. If he has a total of
(144 spots for both cats and dogs, then how many more spots does he have for dogs
Answer:
5. 6 appointments are cancelled
6. 80 more spots
Step-by-step explanation:
5. Jasmine has 36/24 = 1.5 times as many appointments as cancellations each day.
Since 1.5 times 4 is 6, Jasmine has 6 cancellations each day.
6. Kendrick's kennel has 2 spots for cats for every 7 spots for dogs. If he has a total of 144 spots for both cats and dogs;
Spots for cats = 2x ;
So, spots for dogs will be = 7x ;
Total spots for cats and dogs will be = 2x + 7x = 144 ;
x = 144/9 = 16 ;
So, spots for cats = 2 * 16 = 32 ;
Spots for dogs = 7 * 16 = 112 ;
spots for dogs more than cats are = 112 - 32 = 80 .
Kendrick kennel has 80 more spots for dogs than cats.
In triangle ABC, the measurement of angle A is is greater then the measurement of angle C, then BC> AC is this conditional true? If so, why?
Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.
What is the law of sines?We suppose a general triangle, for which:
Side with a length of a is opposite to angle of measure A.Side with a length of b is opposite to angle of measure B.Side with a length of c is opposite to angle of measure C.The lengths and the sine of the angles are proportionally related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The segments in this problem are given as follows:
BC opposite to angle A.AB opposite to angle C.Hence it can be affirmed that:
BC > AB.
As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.
As for segment AC, we need the measure of angle B, hence nothing can be affirmed.
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Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)
The following statements are true based on the diagram below
I is a vertex of right angleK is a vertex of right angleWhat is vertex?When two or more curves, lines, or edges come together, it is called a vertex (plural: vertices or vertexes) in geometry. As a result of this definition, polygonal and polyhedral corners as well as the intersection of two lines to form an angle are referred to as vertices.
The vertex of an angle is the point at which two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location.
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3x+1
1. A function f: x →
X-1
(i)
Find the images of -1 and 3.
(ii)
Find the value of x for which f(x) = 7
2. The set P = {-2,-1,0,1,2} maps onto Q by the function f(x)=x²-2, where x E P.
(i)
Find the elements of Q.
(ii)
3. Given that f(x) = 2x - 1 and g(x) = x² +1:
Find f(1 + x):
Find the range of values of x for which f(x) < -3;
Simplify f(x) - g(x).
(i)
(ii)
(iii)
,x # 1, is defined on the set (-1, 0, 2, 3, 4, 5)
Draw a diagram showing the mapping between P and Q.
(i)
4. The function f and g are defined as follows: f:x →→ 2
x-1 and g:x→ 3x + 1
Evaluate f(-) +1
(ii)
Solve f(x) = g(-2)
5. Given that f(x) = px + q, find the values od p and q, if f(2)= 4 and f(4) == 10
The function f is defined as f:x→ 3x² - 5x.
6.
(i)
Evaluate f(--3)
(ii)
7. The functions f and g are defined as: f:xx-2 and g: x2x²-1. Solve:
(i) f(x) = g(-²/-) (ii) f(x) + g(x)= 0
4
Find the values of x for which f(x) = -² 3
On solving the provide the question, we can say that - the value of the following function is f(x) = -5x - 1.
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
[tex]x = -2, y = 9; x = -1 , y = 4; x =0, y = -1.[/tex]
x = 0 , y = -1 so c = -1.
slope of line [tex]= (4-9) / (-1-(-2)) = -5/ 1 = -5.[/tex]
function f(x) = -5x - 1.
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Answer:
Step-by-step explanation:
1. (i) f(-1) = 3(-1) + 1 = -2 and f(3) = 3(3) + 1 = 10
(ii) To find the value of x for which f(x) = 7, we can set f(x) equal to 7 and solve for x:
3x + 1 = 7
3x = 6
x = 2
2. (i) Q = {x² - 2 | x E P} = {(-2)² - 2, (-1)² - 2, (0)² - 2, (1)² - 2, (2)² - 2} = {4, 0, -2, -1, 2}
(ii) As f(x)=x²-2, and P = {-2,-1,0,1,2} mapping into Q is {-2,-1,0,1,2} to {4,0,-2,-1,2}
3. (i) f(1 + x) = 2(1 + x) - 1 = 2x + 1
(ii) To find the range of values of x for which f(x) < -3, we can set f(x) equal to -3 and solve for x:
2x - 1 < -3
2x < -2
x < -1
so x can be any value less than -1
(iii) f(x) - g(x) = (2x - 1) - (x² + 1) = 2x - x² - 2
4. (i) f(-1) + 1 = 2(-1) - 1 + 1 = -1
(ii) To solve f(x) = g(-2), we can substitute the expressions for f(x) and g(x) into the equation:
2x - 1 = 3(-2) + 1
2x - 1 = -5
2x = -6
x = -3
5. f(x) = px + q, given that f(2)= 4 and f(4) == 10
so
4 = 2p + q
10 = 4p + q
solving for p and q we get p = 3 and q = -2
6. (i) f(--3) = 3(-3)² - 5(-3) = -27
7. (i) To solve f(x) = g(-2/-4), we can substitute the expressions for f(x) and g(x) into the equation:
x-2 = (1/4)x² - 1
x-2 = x²/4 - 1
4x-8 = x²-4
x²-4x+4 = 0
x = 2, -2
(ii) To solve f(x) + g(x) = 0
x-2 + x²-1 = 0
x²-2x+1 = 0
(x-1)² = 0
x = 1
for f(x) = -² 3 the expression does not make sense, but assuming the -² is just typo then we can solve for x by substituting f(x) = -3
into the expression of f(x) = 3x² - 5x
3x² - 5x = -3
3x² - 5
Find the midpoint and distance between (-3,10) and (15,-2)
Which equation can be used to find B in the triangle below?
Right triangle A B C is shown. Side A B has a length of 6, side B C has a length of 10, and side A C has a length of 8.
The measure of angle B is 53°.
The equation used to find B is
B = [tex]sin^{-1}[/tex](4/5).
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Right triangle ABC.
AB = 6
BC = 10
AC = 8
In order for the triangle to be a right triangle it must satisfy the Pythagorean theorem.
So,
BC² = AB² + AC²
100 = 6² + 8²
100 = 36 + 64
100 = 100
This means,
B
| \
| \
| \
A_________C
Now,
Sin B = 8/10 = 4/5
B = [tex]sin^{-1}[/tex] (4/5)
B = 53°
Sin C = 6/10 = 3/5
C = [tex]sin^{-1}[/tex] (3/5)
C = 37°
We see that,
∠A + ∠B + ∠C = 180
90 + 53 + 37 = 180
90 + 90 = 180
180 = 180
Thus,
The equation used to find B is
Sin B = AC / BC = 8/10
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Answer:
Tangent B=8/5
Step-by-step explanation:
Just look at the answer
Simplify and state restrictions
5x³3y² ÷ 27x × 9xy ÷ 25x²y²
The simplified form of the expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y² is
[1/15(xy)³] and (x, y) ≠ 0.
What is a numerical expression?A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
Given, An expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y².
= 5x³3y² ÷ 243x⁴y³ ÷ 25x²y².
= 5x³3y² ÷ 25x²y² ÷ 243x⁴y³.
= (3/5)x ÷ 243x⁴y³.
= (3/5)x/(243x⁴y³).
= (3/5)/(243x³y³).
= 1/(81×5x³y³).
= [1/15(xy)³].
The restriction should be x and y can not be equal to zero as it would make the expression undefined.
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Carmen and her dog, Duke, walk 5 blocks in 8 minutes. Terell and his dog, Lady, walk 8 blocks in 12 minutes. Who walks at a slower rate? How long whould it take that person to walk 12 block?
Carmen and her dog, Duke walked at a slower rate at 0.625 blocks/min
Carmen and her dog, Duke would take 19.2 minutes to work 12 blocks.
What is rate?In math, a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in problems.
Carmen/Duke walks 5/8 = 0.625
Terell/Lady walks 8/12 = 0.677
Therefore, from the average time, Carmen and Duke walk slower.
Carmen and Duke will walk 12 blocks in;
= 12/0.625
= 19.2 minutes
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1000(9x-10)=50(976+100x)
(5 x 7) + (n x 4) = 5 x (7+ 4) write each missing number
The missing number in the expression (5 x 7) + (n x 4) = 5 x (7+ 4) is 5.
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given, An expression (5 × 7) + (n × 4) = 5 × (7 + 4).
Now, If we expand the RHS we have,
5×(7 + 4).
= (5 × 7) + (5 × 4).
Now, Writing the obtained RHS with LHS we have,
(5 × 7) + (n × 4) = (5 × 7) + (5 × 4).
So, The missing number is 5.
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Please help me I can’t figure it out
The number of times each number divides is 8 divides LCM into 11 times
11 divides into LCM 8 times and 22 divides into LCM 4 times .
What is LCM ?
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.
Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.
The LCM of 8 , 11 and 22 is 88
∴ 8 divides into LCM 11 times
11 divides into LCM 8 times
22 divides into LCM 4 times
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3b. There is a line of bushes that grows along one side of Babajide's
backyard. He decides he doesn't need to buy fence for that side since there
are already bushes there. Based on that information, could you decide how
much total fencing Babajide needs? Explain why or why not.
On solving the provided question, we can say that we can assume that it is a rectangular backyard. Since no dimensions are provided therefore, neither volume nor area can be calculated.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
here,
we can assume that it is a rectangular backyard.
since no dimensions are provided therefore, neither volume nor area can be calculated.
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The distribution of the amount of money undergraduate students spends on books for a term is slightly right-skewed, with a mean of $400 and a standard deviation of S80. If a simple random sample of 100 undergraduate students is selected, what is the probability that these students spend, on average, more than $425 on books?
The probability that on average these students spend more than $425 on books is given as follows:
0.0009 = 0.09%.
How to obtain the probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]
The desired probability is one subtracted by the p-value of Z when X = 425, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{425 - 400}{8}[/tex]
Z = 3.125.
Z = 3.125 has a p-value of 0.9991.
1 - 0.9991 = 0.0009 = 0.09%.
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What is the equation of the line that passes through the point (7, -4) and has an
undefined slope?
What is the meaning of conditionally promoted in school
A(n)___ is a convex in which both pairs of opposite side are parallel
4th option: parallelogram
A family has a budget of $400 to spend on groceries each month.
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a jack or a ten
If you are dealt one card from a 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.
How to find the probability?Since there are 4 aces in a deck of card 52 first step is to find the number of cards not aces in a deck of 52
Number of cards not aces in a deck = 52 -4
Number of cards not aces in a deck = 48
Now let find the probability that you won't draw an ace.
Probability = 48/52
Probability = 24/26
Probability = 12/13
Therefore we can conclude that the probability is 12/13.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
B, C, E
Step-by-step explanation:
Let y = length.
Then, y - 5 = width.
area = length × width
area = y(y - 5)
area = 750
y(y - 5) = 750
y² - 5y = 750
A: y(y + 5) = 750
Since y = length, width must be y - 5, not y + 5, so A does not work.
B: y² - 5y = 750
This is what we got above, so this equation works.
C: 750 - y(y - 5) = 0
750 = y(y - 5)
750 = y² - 5y
This is the same as B and works.
D: y(y - 5) + 750 = 0
y(y - 5) = -750
The area cannot be -750, so this equation does not work.
E: (y + 25)(y - 30) = 0
y = -25 or y = 30
This also works.
Answer: B, C, E
The composite number 50 is between what two prime numbers?
Answer:
47 and 53
Step-by-step explanation:
list of prime numbers to 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
50 is between 47 and 53
What are the origins of matrices?
Answer: The origins of matrices can be traced back to the 18th century, with the work of mathematicians such as Gabriel Cramer, Leonhard Euler, and Joseph-Louis Lagrange. These mathematicians developed the idea of using arrays of numbers to represent systems of linear equations, which led to the development of the concept of matrices.
The term "matrix" itself was first used by James Joseph Sylvester in 1850, although it had been in use informally for some time before then. In 1858, the English mathematician Arthur Cayley first published a systematic theory of matrices, which further developed the field.
Matrix theory was primarily used in the early days to solve systems of linear equations, but it soon found applications in areas such as linear algebra, multivariate statistics, and even quantum mechanics.
In summary, the origins of matrices can be traced back to the 18th century as an idea to represent systems of linear equations, which developed over time with contributions of many mathematicians over the centuries, and now it plays an important role in many field of mathematics and science.
Step-by-step explanation:
Six families went to the food festival. Each family has 2 adults and 4 children. The entry fee for each child ticket costs $4, and an adult ticket costs $8. What would be the total cost of the festival tickets?
By solving an expression we will see that the total cost for the tickets is $192.
What would be the total cost of the festival tickets?We know that six families went to the food festival, each family has 2 adults and 4 children, then there are:
6*2 = 12 adults in total.
6*4 = 24 children in total.
We know that each child ticket costs $4, and an adult ticket costs $8, then the total cost of all the tickets is what we get when we solve the expression below:
12*$8 + 24*$4
That is, the number of adults times the cost of an adult ticket plus the number of children times the cost of a children ticket.
The total cost is then:
12*$8 + 24*$4 = $192
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The table below shows the number of bacteria in a laboratory sample after x minutes. Fill in the missing blanks (HELP!!!)
Answer:
2.25
4.5
9
18
36
72
144
288
Step-by-step explanation: you take the number and multiply it by itself. but went it comes to the negative numbers you have to divide the number by 2 then take the answer you get from that and add it by itself so 4.5+4.5=9. its pretty simply when you under stand how to do it.
4 out 18 students will ride in a car instead of a van