The value of the composite function (h⁰ g)(x) calculated by function operation is -x-10 .
A function is defined as the relation between element of two sets, domain and range. A function is usually denoted using f, g or h .
A algebraic function is defined as y=g(x) such that each element y is related to a single value of x.
(h ∘ g)(x) is also written as h[g(x)] is called a composite function where which means the value of x=g(x) will be substituted in the function h(x).
Composite function is a process that joins two functions to create a third, unique function.
The output of one function becomes the input of another function in h of g of x.
Given functions are:
g(x)=1/2 x+7 and h(x)=-2 x+4
Therefore (h ∘ g)(x)=h[g(x)]
=h(1/2 x+7)
=-2(1/2 x+7)+4
=-x-14+4
=-x-10
Hence the value of the function operation (h⁰ g)(x) is -x-10 .
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In AJKL and APQR, if JK PQ, LJ ZP, and ZK ZQ, then AJKL must be
congruent to APQR.
True or False
ΔJKL is congruent to ΔPQR. This statement is true.
Two figures are congruent if they have the same area and one figure is an exact image of the other.
Two triangles can be proven congruent by 4 axioms or rules.
SSS axiom. When all three corresponding sides of one triangle is equal to the sides of the other triangle then the triangles are congruent.SAS axiom . When two sides and the included angle of two triangles are equal, then both triangles are congruent.AAS axiom . When two angles and one side of a triangle is equal then the triangles are congruent.HL axiom . When the Hypotenuse and one leg of a right angled triangle is equal to the hypotenuse and leg of another triangle then the triangles are congruent.Given: in triangles ΔJKL and ΔPQR:
JK=PQ∠J=∠P∠K=∠QHence by AAS axiom of congruency triangles are congruent.
ΔJKL ≅ ΔPQR
The statement is true.
Disclaimer: The complete question is : In ΔJKL and ΔPQR, if JK= PQ, ∠J=∠P, and ∠K =∠Q, then ΔJKL must be congruent to ΔPQR.
True or False
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I need help with algebra
Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
To solve an algebraic word problem:
Define a variable.
Write an equation using the variable.
Solve the equation.
If the variable is not the answer to the word problem, use the variable to calculate the answer.
To know about algebra you have to know about your Arithmetic.
Remember PEMDAS.
Get Positively Comfortable with Negative Numbers.
Show Your Work.
Don't Let the Letters Scare You.
Formulas Are Your Friends.
Be Sure to Answer the Right Question.
Work Practice Problems.
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f(x)= 2x-7/3x-4
Vertical and horizontal asymptotes.
We need to know about asymptotes to answer this question. The vertical asymptote is x=4/3 and the horizontal asymptote is y=2/3
When the graph of a function lies very close to the axis and extends to infinity it is called an asymptote. Vertical asymptote is a vertical line that directs but does not form a part of the graph of a function. Horizontal asymptote is a horizontal line that shows how the function behaves at extreme edges. Horizontal asymptote exists for functions whose numerator and denominator have same degree or degree of numerator is less than numerator of denominator.
f(x)=2x-7/3x-4
The horizontal asymptote of the function can be given by dividing the leading coefficients.
HA=2/3
The vertical asymptote can be found by equating the denominator to zero.
3x-4=0
x=4/3
Therefore the horizontal asymptote is y=2/3 and the vertical asymptote is x=4/3.
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What is the difference in the approximate number of wins between the first place team and the last place team?
A. 50
B. 45
C. 40
D. 35
Answer:
65-72
Step-by-step explanation:
At the beginning of the day the stock market is 70 1/2 points and stays at this level for most of the day. At the end of the day, the stock market goes down 120 1/4 points from at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
Answer: 50 1/4
Step-by-step explanation:
what value (s) of x will make x[tex]x^{2}[/tex] =9 true?
The values of x that will make x² = 9 are positive 3 and negative 3.
What is a quadratic equation?A quadratic equation is an algebraic equation that has highest degree of 2, therefore, it also has two roots or we can say it has two solutions.
We know sign distributions that negative distributed to a negative is positive and positive distributed to a positive also results in positive.
∴ 9 can be obtained by either multiplying (-3)(-3) or (3)(3).
So, the value of x that will make x² = 9 is
x = ± √9
x = ± 3.
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Tom Harris is twenty-four years old. He wishes to purchase $7,000 of a ten-year term insurance. What will be his annual premium?
The annual premium of Tom Harris is $29.05
What is annual premium?Annual premium is the amount of money that policyholder has to pay in a policy year.
Annual formula = (face value of policy per $1000)* (rate of insurance)
Given that Tom Harris is twenty four years old man want to purchase a $7000 for a ten year term insurance.
From the given table we can say that the rate of insurance for a 24 year old man per $1000 for a 10 year terms is 4.15
Face value of insurance = $7000
Face value of insurance per $1000 = 7000/1000 =$7
Then the annual premium = $7 * 4.15 =$ 29.05
Therefore, the annul premium paid by Tom Harris is $29.05
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Luisa sells stuffed animals. She sells a stuffed elephant for $34.90, and the sales tax is 9% of the sale price. About how much is the sales tax on the elephant?
$4.90
$0.32
$4.95
$3.15
Answer: $3.15
Step-by-step explanation: 9% of 34.90 is 3.15
Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6:10. A multiplication table. Which statement explains whether Juliana is correct? She is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. She is correct because 6:10 can be written as 1:2 and there are an infinite number of ratios for 1:2. She is not correct because the multiplication table does not include multiples of 10. She is not correct because 6:10 is equivalent to 3:5 and there are only 9 ratios in the multiplication table that are equivalent to 3:5.
The statement that explains whether Juliana is correct is A. She is correct because she can multiply 6 and 10 by any number to form an equivalent ratio.
How to illustrate the information?From the information, it should be noted that
Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6:10.
It should be noted that she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio.
An example is (6 × 2)/(10 × 2) = 12/20
It should be noted that 6/10 is equivalent to 12/20.
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a jet plane traveling at 480 mph overtakes a propeller plane traveling at 200 mph that had a 3 hour head start. how far from the starting point are the planes?
The distance of both the planes from the starting point will be 1029 miles.
This is a question of time, speed and distance.
Given that:-
Speed of jet plane = 480 mph
Speed of propeller plane = 200 mph
Also, the propeller plane has a 3 hour head start.
We have to find the distance of both the planes from the starting point.
When the jet plane overtakes the propeller plane both of them would have covered the same distance.
Let the time taken by the jet plane to overtake the propeller plane be t hours.
Hence, the propeller plane would have travelled for (t+3) hours.
Hence, we can write,
480*t = 200*(t+3)
480t = 200t + 600
280t = 600
t = 600/280 = 15/7 hours.
Hence, distance from both the planes from the starting point = (15/7)*480 = 1028.57 miles = 1029 miles.
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Confused on how to solve this
The statement [tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex] will be true. Then the correct option is D.
What is the limit?The value that approaches the output for the given input value. Limits are a very important tool in calculus.
The graph of the function is shown below.
The function is a piecewise function. The function is continuous between o to a, a to b, and b to till ∞.
The value of the function at b will be 1 which can be shown as,
[tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex]
The statement [tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex] will be true. Then the correct option is D.
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The average temperature in the mountains is 65° in April. The average temperature in that same spot is −5° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
Answer:
65 + |-5| = 70, 65 is the farthest away from 0
Step-by-step explanation:
The length and width of a rectangle are consecutive odd integers. The perimeter of
the rectangle is 80 centimeters. Find the length and width of the rectangle.
The length of the rectangle = 21 cm
and the width of the rectangle = 19 cm
In this question, the length and width of a rectangle are consecutive odd integers.
Let n, n + 2 be the width and the length of a rectangle.
The perimeter of the rectangle is 80 centimeters.
Using the formula of the perimeter of the rectangle ,
P = 2 × [n + (n + 2)]
80 = 2(2n + 2)
40 = 2(n + 1)
20 = n + 1
n = 19
This means, the width of the rectangle is 19 centimeters.
And the length = n + 2
= 19 + 2
= 21 cm
Therefore, the length of the rectangle = 21 cm
and the width of the rectangle = 19 cm
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1 1/2 ⋅ 2 1/3 (those are fractions help me please)
Answer:
3.5 in decimal form or 3 1/5
Step-by-step explanation:
Answer:
= - 1 1/6
Step-by-step explanation:
1 1/2 - 2 1/3
= 1 2/6 - 2 3/6
= 8/6 - 15/6
= - 7/6
= - 1 1/6
421 Students go on a field trip. There are 19 vehicles, some vans and some buses. 7 students can fit in a van, and 25 students can fit in a bus.
There were ___ buses.
There were ___ vans.
The number of vans and buses conveying the students to the field trip is 3 and 19 respectively
How to solve number of buses and Vans simultaneouslylet
number of van = xNumber of bus = yx + y = 19
7x + 25y = 421
From (1)
x = 19 - y
Substitute x = 19 - y into (2)
7x + 25y = 421
7(19 - y) + 25y = 421
133 - 7y + 25y = 421
- 7y + 25y = 421 - 133
18y = 288
y = 288/18
y = 16
Substitute y = 16 into (1)
x + y = 19
x + 16 = 19
x = 19 - 16
x = 3
Therefore, there are 3 vans and 16 buses conveying the be students to the field trip.
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Find any points of discontinuity for each rational function. y=x+5 / x²+9 x+20
points of discontinuity for each rational function. y=x+5 / x²+9 x+20 is x = -4
Given,
y=x+5 / x²+9 x+20
It can be expressed in the form of -
⇒ y = (x+5) / (x+5) (x+4)
⇒ y = 1 / (x+4)
The function will be undefined if the denominator will be 0
⇒ x+4 = 0
⇒ x = -4
So, we can conclude that the given function will be having points of discontinuity as x = -4
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If I don't get an A in math my mom will hit me again
What is the product?
Enter your answer as a fraction, in simplified form, in the box.
-1/4 x -6/11
Answer:
[tex]\frac{3}{22}[/tex]
Step-by-step explanation:
To multiply fractions, just multiply the numerators (tops) times each other and the denominators (bottoms) times each other:
[tex]\frac{-1}{4}[/tex] x [tex]\frac{-6}{11}[/tex] = [tex]\frac{6}{44}[/tex]
Now all we have to do is to simplify. In this case, just find the largest number that goes evenly into the numerator and the denominator: it is 2. Divide numerator and denominator by 2 to get the final answer: [tex]\frac{3}{22}[/tex]
If 3(x-2)= 2x+6 then x equals?
Answer:
x = 12
Step-by-step explanation:
First, distribute the 3 into the parentheses:
3(x-2) = 2x+6 ----> 3x-6 = 2x+6
Next, combine like terms by adding 6 to both sides of the equation:
3x-6 = 2x+6 ----> 3x = 2x+12
Then, subtract 2x from both sides:
3x = 2x+12 ----> 1x = 12
Finally, divide both sides by 1 to get x by itself:
x = 12
Find the difference.
(9ab+7a-7) (4ab-5)
The difference is 5ab + 7a + 13
What is Arithmetic Operation?An arithmetic operation is specified by combining operands with one arithmetic operator. Arithmetic operations can also be specified by the ADD, SUBTRACT, DIVIDE, and MULTIPLY
given:
(9ab+7a-7) (4ab-5)
So, the difference is
(9ab+7a-7) - (4ab-5)
=9ab + 7a - 7 -4ab + 20
=9ab - 4ab +7a -7 +20
=5ab + 7a + 13
Hence, the difference is 5ab + 7a + 13.
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Factor each expression.
x²-5 x+6
After solving, the factors of equation x²-5x+6 are:
(x-3) and (x-2)What is an equation, exactly?A mathematical statement made up of two representations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We obtain the value for the variable x as x = 7 after solving this equation.So,
Given the equation: x²-5x+6
Then,
x²-5x+6x²-x( + )+6x²-x(3+2)+6x²-3x-2x+6x(x-3)-2(x-3)Factors are: (x-3) and (x-2)
Therefore, after solving, the factors of equation x²-5x+6 are:
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Albert invested money into the stock market, and the table represents his earnings. What type of function could be used to model his bank account as a function of time? Justify your answer.
Week Balance ($)
1 1,400.00
2 1,470.00
3 1,543.50
4 1,620.68
This is a linear function because there is a common difference in the balance between the weeks.
This is a linear function because there is a common ratio in the balance between the weeks.
This is an exponential function because there is a common difference in the balance between the weeks.
This is an exponential function because there is a common ratio in the balance between the weeks.
The correct option regarding the bank amount as a function of time is:
This is an exponential function because there is a common ratio in the balance between the weeks.
When a linear function should be used and when an exponential function should be used?A linear function should be used when there is a common difference between the amounts.An exponential function should be used when there is a common ratio between the amounts.For this problem, the differences are given as follows:
1620.68 - 1543.5 = $77.18.1543.5 - 1470 = $73.5.1470 - 1400 = $70.The ratios are given as follows:
1620.68/1543.5 = 1.05.1543.5/1470 = 1.05.1470/1400 = 1.05.Due to the same ratios, an exponential function should be used, and the correct option is given by:
This is an exponential function because there is a common ratio in the balance between the weeks.
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Answer:c
Step-by-step explanation:
3. Between which two numbers is √74?
(A) 5 and 6
B) 6 and 7
7 and 8
C
D
8 and 9
A bean plant grew 15 feet in eight days after 16 days the plant was 30 feet tall is the ratio of feet to days equivalent
Based on the height that the bean plant grew after a certain number of days, the ratio of feet to days is equivalent.
How to find equivalent ratios?The bean plant was able to grow 15 feet in 8 days and then doubled to 30 feet when the number of days doubled to 16 days.
The ratio of feet to days can be found as:
(Number of feet after 16 days / Number of feet after 8 days) : 16 days / 8 days
Solving for the ratio of feet to days gives:
30 / 15 : 16 / 8
2 : 2
The ratio of feet to days is the same which means that it is equivalent.
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What is the solution to x 4 + 4x 3 ≤ 12x 2?
Answer:
16<24
Step-by-step explanation:
4+(4×3)<(12×2)
4+12<24
=16<24
Find the value of x and A C if B is between points A and C. (Lesson 1-2)
A B=12, B C=8 x-2, A C=10 x
If B is collinear and between points A and C, then the value of x is 5 and the value of AC is 50.
Collinear points refers to the points that lies on the same straight line.
If B is collinear with points A and C, and lies between them, then the sum of the distance from A to B and the distance from B to C is equal to the distance from A to C.
AB + BC = AC
Given:
AB = 12
BC = 8x - 2
AC = 10x
Substitute the expressions given to the equation and solve for x.
AB + BC = AC
12 + 8x - 2 = 10x
8x - 10x = 2 - 12
-2x = -10
x = 5
Substitute the value of x in the expression for AC.
AC = 10x
AC = 10(5)
AC = 50
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Write each equation in logarithmic form.
10⁴=10,000
The equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.
Given that
10^4 = 10000 - - - - - -( 1 )
We have [tex]a^{y}[/tex] = x - - - - - ( 2 )
Comparing ( 1 ) and ( 2 ) we get
a = 10, y = 4, x = 10000
The logarithmic form is written as logₐ (x) = y .It is rearrangement of the exponential form [tex]a^{y}[/tex] = x.
By logarithmic definition
y = logₐ (x)
so we got 4 = log₁₀ (10000)
Therefore, the equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.
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The point k lies on the segment JL. Find the coordinates of k so that jk is 1/4 of JL L(19,10) J(-1,-2)
(4,5) i'm pretty sure I can't explain why but just go with it
The points T, U, V and W all lie on the same line segment, in that order, such that the ratio of TU:UV:VWTU:UV:VW is equal to 1:5:2.1:5:2. If TW=32,TW=32, find UW.UW.
Answer:
The length of UV is 10 units.
Step-by-step explanation:
It is given that the points T, U, V and W all lie on the same line segment, in that order, such that the ratio of TU:UV:VW is equal to 1:5:2.
Now, we need to calculate UW if TW = 32.
So, TU : UV : VW = 2 : 5 : 5
=> TW = 24
From the above conditions it can be observed that;
=> Ratio of TU = 2
=> Ratio of UV = 5
=> Ratio of VW = 5
Firstly, we have to sum up the total ratio that is;
=> Total = Ratio of TU + Ratio of UV + Ratio of VW
=> Total = 2 + 5 + 5
=> Total = 12
Now, we need to calculate the length of UV from which we get;
=> UV = 5/12 * 24
=> UV = 10
Therefore; length of UV is 10 units.
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Martha spent of her pocket money on
magazines.
She then spent
of what she had left on a
present.
After that, she had £3 left.
How much pocket money did she have to start
with?
Give your answer in pounds (£).
Answer:
Step-by-step explanation:
Martha spent 1/6 of her pocket money on magazines.
What are some reasons you should be intentional about saving money? in other words,
Answer:
Step-by-step explanation:
The reason why you should save money because if you spend all of your money you won't able to take care of yourself, your house, or have nothing to do