Answers
(h + k)(2) = 5
(h - k)(3) = 9
evaluate 3h(2) + 2k(3) = 17
The composition of functions is solved
a) ( h + k ) ( 2 ) = 5
b) ( h - k ) ( 3 ) = 9
c) 3h ( 2 ) + 2k ( 3 ) = 17
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
Now , the value of f ( x ) is
h ( x ) = x² + 1
Let the second function be represented as g ( x )
Now , the value of g ( x ) is
k ( x ) = x - 2
Now , the composition of function is
To calculate (h+k)(2), we substitute x = 2 in both h(x) and k(x), add them together and simplify:
h(2) = 2² + 1 = 5
k(2) = 2 - 2 = 0
(h+k)(2) = h(2) + k(2) = 5 + 0 = 5
To calculate (h-k)(3), we substitute x = 3 in both h(x) and k(x), subtract k(x) from h(x), and simplify:
h(3) = 3² + 1 = 10
k(3) = 3 - 2 = 1
(h-k)(3) = h(3) - k(3) = 10 - 1 = 9
To evaluate 3h(2)+2k(3), we substitute x = 2 and x = 3 in h(x) and k(x), respectively, and simplify:
3h(2) + 2k(3) = 3(5) + 2(3-2) = 15 + 2 = 17
Therefore , ( h + k ) ( 2 ) = 5 , ( h - k ) ( 3 ) = 9, and 3h( 2 ) + 2k( 3 ) = 17
Hence , the composition of functions is solved
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Step-by-step explanation:
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The value of the digit 9 is ten times as much as the 9 in 893,417.
Answers
Answer: 943,212
Step-by-step explanation:
Suppose that you want to know the value of a given digit in a given number, where the digit is x.
Now, you should count the position of this digit, starting at the decimal point and counting to the left.
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Answers
Answer:
1
Step-by-step explanation:
Anything to the power is 0 is equal to 1.
Answer:
the answer is 1
Step-by-step explanation:
What’s the perimeter of the tabletop in feet?
Answers
Answer:
Perimeter = 14.0942 ft (aprox)
Step-by-step explanation:
1 ft = 12 inches
1 inch = 1/12 = 0.08333 ft
4 inch = 4*0.08333 = 0.3333 ft
then:
there are:
4 quarters of circle = 4/4 = 1 complete circleperimeter = 2π r
π = 3.1416
r = radius
perimeter = 2*3.1416*0.3333ft
perimeter = 2.0942 ft (aprox)
4 sides (3ft each)perimeter = 4*3ft
perimeter = 12ft
Total perimeter:
2.0942ft +´12ft = 14.0942 ft
What is the volume of the cube shown?
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Please help !
Answers
Answer:
11 25/64 in ^3
Step-by-step explanation:
Volume of a cube is given by
V = s^3
s = 2 1/4 = 9/4
V = (9/4) ^3
= 729/64
=11 25/64 in ^3
Which of state of matter has no definite shape but does have a definite volume? (A) Liquid B) Element OC) Solid OD) Gas
Answers
Answer:
Liquid
Step-by-step explanation:
solids :have definite shape and definite volume.
Liquids :have definite volume and shape of the container.(or no definite shape)
Gas: has no definite volume and no definite shape.
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A map has a scale of
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If necessary, round your answer to the nearest tenth.
Answers
Answer:
161.5 miles
Step-by-step explanation:
19 inches is 9.5 times 2 inches. So, the actual distance is 9.5 times 17 miles:
9.5 × 17 miles = 161.5 miles
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Answers
Answer: Choice C
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===============================================
Explanation:
The exponent for the y term inside the parenthesis is 1/6 and then that expression is raised to the 3rd power. The exponents multiply to (1/6)*3 = 3/6 = 1/2
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Write 80% as a fraction in Simplest form
Answers
Answer:
Step-by-step explanation:
80/100 = 8/10= 4/5
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Answers
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Answers
Answer:
Fraction of the number that received an A= = 27/50
Step-by-step explanation:
In a class of 50 statistics students, 27
students received an A.
Total number of students=50
Number that received an A= 27
Fraction of the number that received an A= Number that received an A/Total number of students
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Answer:
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Answers
Answer:
153/40
Step-by-step explanation:
The first step to finding the fraction is to get rid of the decimal points as fractions do not have decimals. To do this we can multiply it by 1000 which gives us 3825. To have this equal to the original number we add ÷1000 on the denominator which gives us 3825/1000 which is a fraction still equal to the original number (3825÷1000=3.825). Which can further be simplified to 153/40 (both numbers divisible by 25). This is the simplest fraction which can express the number 3.825 (153/40=3.825).
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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↓
a= -1
Since the a-value is negative, the parabola will be reflected over the x-axis which will change the curve from (U-shaped) to (∩-shaped).
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Answers
Answer:
X=7
Step-by-step explanation:
(2) means time 2 so use 5 times 2 and get 10 and take away 3 you get 7 and 7 is X
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Answer:
f(2) = 5(2) -3
10 - 3
f(2) = 7
1. The average distance from the Earth to the moon is about 384,000 kilometers. What is this number written in scientific notation?
Answers
Answer:
3.84 x 10^5
Step-by-step explanation:
Answer:
3.84x10^5
Step-by-step explanation:
count how many times the decimal was moved to the right and that is the exponent
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Answer:
6
Step-by-step explanation:
Petra is making necklaces to sell at craft. the hardware for each necklace is 3.75 and each bead costs 0.50. The number of beads Petra needs depends on the design she chooses. which expression gives the total cost to make 30 necklaces.
Answers
Answer:
T=112.5+0.50*b (since there was not a given number of beads)
Look at the correlation between Risk-Taking (R) and Relationship Happiness (HAPPY). Use the standard alpha level of 5%. How would you describe the relationship?
1. The relationship is non-significant.
2. There is a significant negative relationship.
3. There is a significant positive relationship.
4. The correlation is zero.
Answers
Image of the correlation between Risk-Taking (R) and Relationship Happiness (HAPPY) is missing, so i have attached it.
Answer:
Option 1 - The relationship is non - significant
Step-by-step explanation:
From the image attached, we can see that under the correlations table;
For correlation between relationship happiness and risk taking;
σ(sigma) = 0.053
Similarly, for correlation between risk taking and relationship happiness;
σ(sigma) = 0.053
.
Now,σ(sigma) = 0.053 is more than the standard alpha level of 5%(0.05). Thus, we fail to reject the null hypothesis since it is non - significant.
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Answers
The ratio is (8/3 cups of flour : 1 batch or recipe)
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Evaluate the limit with either L'Hôpital's rule or previously learned methods.lim Sin(x)- Tan(x)/ x^3x → 0
Answers
Answer:
[tex]\dfrac{-1}{6}[/tex]
Step-by-step explanation:
Given the limit of a function expressed as [tex]\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3}[/tex], to evaluate the following steps must be carried out.
Step 1: substitute x = 0 into the function
[tex]= \dfrac{sin(0)-tan(0)}{0^3}\\= \frac{0}{0} (indeterminate)[/tex]
Step 2: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the function
[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ sin(x)-tan(x)]}{\frac{d}{dx} (x^3)}\\= \lim_{ x\to \ 0} \dfrac{cos(x)-sec^2(x)}{3x^2}\\[/tex]
Step 3: substitute x = 0 into the resulting function
[tex]= \dfrac{cos(0)-sec^2(0)}{3(0)^2}\\= \frac{1-1}{0}\\= \frac{0}{0} (ind)[/tex]
Step 4: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 2
[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ cos(x)-sec^2(x)]}{\frac{d}{dx} (3x^2)}\\= \lim_{ x\to \ 0} \dfrac{-sin(x)-2sec^2(x)tan(x)}{6x}\\[/tex]
[tex]= \dfrac{-sin(0)-2sec^2(0)tan(0)}{6(0)}\\= \frac{0}{0} (ind)[/tex]
Step 6: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 4
[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ -sin(x)-2sec^2(x)tan(x)]}{\frac{d}{dx} (6x)}\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^2(x)sec^2(x)+2sec^2(x)tan(x)tan(x)]}{6}\\\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^4(x)+2sec^2(x)tan^2(x)]}{6}\\[/tex]
Step 7: substitute x = 0 into the resulting function in step 6
[tex]= \dfrac{[ -cos(0)-2(sec^4(0)+2sec^2(0)tan^2(0)]}{6}\\\\= \dfrac{-1-2(0)}{6} \\= \dfrac{-1}{6}[/tex]
Hence the limit of the function [tex]\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3} \ is \ \dfrac{-1}{6}[/tex].
Brenda received $25 for babysitting for 3 hours. If she is paid proportionally, how much should she get for 7.5 hours?
Answers
Answer:
$187.5
Step-by-step explanation:
25 times 7.5 is 187.7
To make fruit salad,Maria bought 2 1/4 pounds of apples,and 1 1/3 pounds.How much fruit salad did this make
Answers
Answer:
If this was all the fruit, 3 and 7/12
Step-by-step explanation:
1/4 and 1/3 LCM is 12
1/4=3/12
1/3=4/12
2+1=3
3/12+4/12=7/12
3+7/12= 3 7/12
I need help with these questions
Answers
Answer:
28. m<A=20°, m<B=70°
32. m<A=103°, m<B=77°
Step-by-step explanation:
complementary angle=a+b=90°
supplementary angle=a+b=180°
28. A+B=90°
5x+17x+2=90°
22x+2=90°
22x=90-2
22x=88
22x/22=88/22
x=88/22=4
m<A=5x=5*4=20°
m<B=17x+2=17*4+2=68+2=70°
Check
A+B=90°
20+70=90°
90°=90°
32. A+B=180°
x+11+x-15=180°
2x-4=180°
2x=180+4
2x=184
2x/2=184/2
x=184/2
x=92
m<A=x+11=92+11=103°
m<B=x-15=92-15=77°
Check
A+B=180°
103+77=180°
180°=180°
(-2ab^-5)(4a^-2b)^-2
Answers
Answer:
-a^5/(8b^7)
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^-b = 1/a^b
__
[tex](-2ab^{-5})(4a^{-2}b)^{-2}=(-2ab^{-5})(4^{-2}a^{-2(-2)}b^{-2})\\\\=\dfrac{-2}{16}a^{1+4}b^{-5-2}=\boxed{-\dfrac{a^5}{8b^7}}[/tex]