Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x)).
Answers
The x–intercept of g(h(x)) is the option;
[tex] \displaystyle {-\frac{2}{3}}[/tex]
What is a The x–intercept of a function?The x–intercept of a function is given by the point where the function intersects the x–axis.
From the given table, the slope of the graph of g(x), [tex] m_1 [/tex] is given by the equation;
[tex] \displaystyle{ m_1 = \frac{ - 4 - ( - 8)}{ - 4 - ( - 6))} = \frac{4}{2} = 2}[/tex]
The equation of g(x) in point slope form is therefore;
g(x) - (-4) = 2×(x - (-4)) = 2•x + 8
g(x) = 2•x + 8 - 4 = 2•x + 4
g(x) = 2•x + 4
The slope of the function h(x), [tex] m_2 [/tex] is found using the equation;
[tex] \displaystyle{ m_2 = \frac{ 8 - 14}{ - 4 - ( - 6))} = \frac{ - 6}{2} = - 3}[/tex]
h(x) presented in point and slope form is therefore;
h(x) - 8 = (-3)×(x - (-4)) = -3•x - 12
h(x) = -3•x - 12 + 8 = -3•x - 4
h(x) = -3•x - 4
g(h(x)) = 2•h(x) + 4
Plugging in the value of h(x) gives,;
g(h(x)) = 2×(-3•x - 4) + 4 = -6•x - 8 + 4
g(h(x)) = -6•x - 4
The x–intercept of g(h(x)) is given by the point where g(h(x)) = 0, which gives;
At the x–intercept, g(h(x)) = 0 = -6•x - 4
[tex] \displaystyle{ x = \frac{4}{-6} = -\frac{ 2}{3} }[/tex]
The x–intercept is [tex] \displaystyle{ -\frac{ 2}{3} }[/tex]
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Related Questions
A = {2, 3, 4, 5, 6, 7}
B = {2, 4, 7, 8)
C = {2,4}.
Which of the following mathematical statements is true?
Answers
The mathematical statement is as follows:
(a) B ⊄ A
(b) C ⊂ A
(c) B ⊄ C
(d) ∅ ⊂ B
(e) C ⊂ C
(f) C ⊂ B
What is meant by sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
The way that sets are represented by a person is always the same: as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.
Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) and C = {2, 4}.
The mathematical statement is as follows:
(a) B ⊄ A
(b) C ⊂ A
(c) B ⊄ C
(d) ∅ ⊂ B
(e) C ⊂ C
(f) C ⊂ B
belongs to ⊂ sign is used if an element belongs to the given set and vice versa.
The complete question is:
Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the resulting statements true.
(a) B __ A
(b) C __ A
(c) B __ C
(d) ∅ __ B
(e) C __ C
(f) C __ B
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In the the diagram to the right, sphere O with radius 5 cm is intersected by a plane 4 cm from center O. Find the radiusof the cross section O A
Answers
Since a right triangle is formed, the radius of the cross-section is the missing side of the triangle.
Apply the Pythagorean theorem:
C^2 = a^2 + b^2
Where:
c = hypotenuse = 5
a & b = the other 2 legs of the triangle = 4 and x
Replacing:
5^2 = 4^2 + x^2
solve for x ( radius of the cross-section)
25 = 16 + x^2
25-16 = x^2
9 = x^2
√9 = x
x = 3 cm
. BUILD PERSEVERANCE Factor the algebraic
expression 7.2x²y-0.9xy².
Answers
3. Jamie's grade has increased 42 points over the last 6 weeks because he
has turned in homework and done a few retakes. If his grade increased the
same amount each week, what integer represents his change in grade?
Answers
Answer:
7
Step-by-step explanation:
(x = increase each week)
(6=weeks)
(42= total Grade Change)
Linear equation:
42=6x
Solved:
x=7
A clerk spent his 35-hour workweek as follows: 1/5 of his time in sorting mail; 1/2 of his time in filing letters; and 1/7 of his time in reception work. The rest of his time was devoted to messenger work. The percentage of time spent on messenger work by the clerk during the week was most nearly:
A 6%
B 14%
C 10%
D 16%
Answers
So , the percentage of time spent on messenger work by the clerk during the week was most nearly is 16%.
How to find percentage?From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.
35 h * 1 / 5 = 7 h
35 h * 1 / 2 = 17.5 h
35 h * 1 / 7 = 5 h
7 h + 17.5 h + 5 h
= 29.5 h
The rest of his time = 35 - 29.5
= 5.5 h
5.5 / 35 = 0.15714
= 15 .714 %
Approx. 16 %
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sixty and four hundredths in decimal form
Answers
60 + 0.04 = 60.04
The answer is 60.04
What is the range of this data set?{5, 12, 15, 11, 15, 7, 15, 10, 13}8101215
Answers
We are asked to find the range of the following data
{5, 12, 15, 11, 15, 7, 15, 10, 13}
First, we need to sort the data in ascending order (least to greatest)
{5, 7, 10, 11, 12, 13, 15, 15, 15}
The range is given by
[tex]Range=\max -\min [/tex]The maximum value in the data set is 15
The minimum value in the data set is 5
So, the range is
[tex]\begin{gathered} Range=\max -\min \\ Range=15-5 \\ Range=10 \end{gathered}[/tex]Therefore, the range of the given data set is 10
anne took a test in chemistry she scored 20 markes out of 50 work out her percentge mark
Answers
Answer:
40%
Step-by-step explanation:
to change a fraction to a percentage multiply by 100% , that is
[tex]\frac{20}{50}[/tex] × 100% = 0.4 × 100% = 40%
Answer:
40%
Step-by-step explanation:
Total Mark = 50Mark obtained = 20Percentage = (Mark obtained/Total mark) x 100(20/50) x 100(2/5) x 1002 x 2040%
Solve the following formula for t.
Q=M + Mrt
t= (Simplify your answer.)
Answers
Mathematical objects other than numbers can be used in operations. Here, t can be expressed as [tex]\frac{Q-M}{r}[/tex].
What are mathematical operations?Binary and unary operations are the two most popular forms of operations. Trigonometric functions and negation are examples of unary operations that use only one value. Contrarily, binary operations, which include addition, subtraction, multiplication, division, and exponentiation, only accept two values.
Mathematical objects other than numbers can be used in operations. Logic operations like and, or, and not can be used to combine the logical values true and false. It is possible to add and subtract vectors. Utilizing the function composition operation, it is possible to combine rotations by first performing the first rotation and then the second. The binary operations union and intersection as well as the unary operation of complementation are operations on sets. Composition and convolution are two operations on functions.
Solving for t,
Q = M + Mrt
t = [tex]\frac{Q-M}{r}[/tex]
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i need help with this please check work when you finish answering
Answers
ANSWER :
The answer is A. 2π
EXPLANATION :
Period can be determine by getting the measurement of one complete cycle.
From the graph.
One complete cycle is the blue mark.
Therefore, the period is 2π
3(x + 2) = 3x + 2
Show your work
Answers
3x=2=3x+2
3x=2-3x=3x+2-3x
the answer is
-3x+3x=2=2
i don't know how to setup the equation and neither getting the answer, please help, i only need question 4 btw
Answers
The sum of exterior angles of a regular polygon is 360 degree.
Determine the measure of last exterior angle of a regular pentagon.
[tex]\begin{gathered} 52+87+90+43+x=360 \\ x=360-272 \\ =88 \end{gathered}[/tex]So measure of last angle of a regular pentagon is 88 degree.
. G(x) is the function defined by the following graph. The graph window is: [-3,5,1] by [-60,80,10]
Answers
We are given a function and we are asked the following questions:
Part 1. Evaluate G(-1). The value of G(-1) is the value of the independent variable, that is the vertical axis when the dependent variable is -1, that is the horizontal axis. To find the value we draw a vertical line perpendicular to the horizontal at the value -1, until we intercept the graph, from there we draw a vertical line until we intercept the vertical axis. From the graph we see that:
[tex]G(-1)=20[/tex]Part 2. Evaluate G(2). This is the value of the independent variable when the dependent variable is 2. From the graph we see:
[tex]G(2)=-10[/tex]Part 3. Determine:
[tex]\frac{G(-1)^3-G(2)^2+4G(-1)}{10}[/tex]Replacing the known values:
[tex]\frac{(20)^3-(-10)^2+4(20)}{10}[/tex]Solving the operations:
[tex]\frac{8000-100+80}{10}=\frac{7980}{10}=798[/tex]Stella has 35 rocks in her rock collection. Each month she will add 15 rocks to the collection. Which equation can be used to find y, the total number of rocks in Stella's collection after x months? A) y = 35x + 15 B) y = 15x - 35 c) y = 35x - 15 D) y = 15x +35
Answers
Answer:
A
Step-by-step explanation:
y = 35 + 15x
A
:]
please helppppppppppppppppppppppppppppppp!
Answers
Answer:
(9 x 27) x 5
Step-by-step explanation:
First we have to figure out the powers. 3 To the power of 2 is 9 and 3 to the power of 3 is 27 so we first multiply that and later multiply 5
And so it’s 3^8 • 3^10
And the you add the exponents together so it’s 3^8+10
So then it would be 3^18
But simplified would be 387420489
what is 3 +(-4) on a number line
Answers
a committee on community relations in a college town plans to survey local businesses about the importance
Answers
The most appropriate choice for population and sample will be given by-
Second option is correct
44% is the percentage of non response
What is population and sample?
Population is the entire set of items from where the data is drawn for statistical study
A random selection of members of the population is known as sample.
Here
Number of business chosen at random = 50
Number of questionnaire returned by mail = 28
Number of non responses = 50 - 28
= 22
Since the committee plans to survey local businesses about the importance of students as customers, the population is all about local business.
Since the specific group from the population are 50 local businesses chosen by the committee, sample is the 50 to whom the questionnaire was sent
Percentage of non response = [tex]\frac{22}{50} \times 100[/tex]
= [tex]44[/tex] %
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Complete Question
A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 50 businesses at random. Of these, 28 return the questionnaire mailed by the committee.
Identify the population and the sample for this study.
a)The population is all students in the college town and the sample is the 50 local businesses to whom the questionnaire was sent.
b)The population is all local businesses and the sample is the 50 to whom the questionnaire was sent.
c) The population is the 28 businesses who responded to the questionnaire and the sample is all local businesses.
d)The population is the 50 local businesses to whom the questionnaire was sent and the sample is the 28 who responded.
What is the rate (percent) of nonresponse?
(Use decimal notation. Give your answer as an exact number.)
Consider the function given by the graph. What are
these values?
f(-2)=
f(0) =
f(4) =
Answers
The values of the function given by the graph are:
f(-2 ) = 2
f(0) = 3
f(4) = -1
The graph depicts an inequality equation with discontinuities. Points of discontinuity are breaks in the graph caused by an undefined point when the f(x) function is substituted with an x point that is not part of the solution. Looking at the graph of the provided function f(x), we can clearly see that the function f(x) increases in the interval (-∞ ,0] and subsequently decreases in the interval (0,∞).Furthermore, the function terminates at x=0.
(Because there is a gap in the graph and the function's left and right-hand limits are not equal at x=0)
So from the graph, we can determine the values of the functions as,
f(-2 ) =2
f(0) = 3
f(4) = -1
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Answer:
f(–2 ) = 2
f(0) = 3
f(4) = -1
Step-by-step explanation: i hope this helps :)
POSSIBLE PC14. A bag contains:5 red marbles6 blue marbles3 green marbles4 black marbles2 yellow marblesA marble will be drawn from the bag and replaced 100 times.What is a reasonable prediction for the number of times agreen or black marble will be drawn?P (green or black)P=/100P=(write the whole ratio)P(green and red) without replacement
Answers
Solution
We have
5 red marbles
6 blue marbles
3 green marbles
4 black marbles
2 yellow marbles
For a total of 5+6+3+4+2 = 20 marbles
And we want to find the following probability:
p(green or black) = P(green) + P(black) - P(green and black) = 3/20 + 4/20 - 0/20 = 7/20
Equivalent to : 7/20 * 5/5 = 35/100
p(green and red) without replacement = 0/100
| Log Out Which function has a y-intercept that is equivalent to the y intercept of 3x - 4y = 16? A y = 4x + 1 B y = - 4x + 16 © y = 3x + 4 D y = 2x - 4
Answers
The slope-intercept form of a line is given by:
y = mx + b
where:
m = slope
b = y-intercept
From:
[tex]\begin{gathered} 3x-4y=16 \\ 4y=3x-16 \\ y=\frac{3}{4}x-4 \end{gathered}[/tex]Therefore, the y-intercept of this line is -4.
Hence, the correct option is:
[tex]y=2x-4[/tex]a circle has a radius 6 in in a central age of 60 what is the measure of the arc length is associated with this angle a 2pie b pie c 6pie d 3 pie
Answers
Formula for arc length when the angle is in degrees:
[tex]\text{Arc length = }\frac{\theta}{360}\times2\pi r[/tex]r = radius = 6 in
θ= 60 degrees
[tex]\begin{gathered} \text{Arc length = }\frac{60}{360}\times2\times\pi\times6 \\ \text{arc length = }2\pi\text{ in ches (option A)} \end{gathered}[/tex]PLEASE HURRY ASAP
Which of the following could be an algebraic expression for the total cost of dinner, less a $10 coupon, divided by 4 people?
(x − 10) ÷ 4
4x − 10
10 − 4x
4x(10)
Answers
Answer:
(x − 10) ÷ 4
Step-by-step explanation:
So, the equation is trying to figure out how much each person is paying. x = the whole dinner. Then, you take away $10 from the total cost. Then, with that discounted cost, you're dividing by 4 people to figure out how much each person is paying.
What is the value of 6x² - 4 when x = 5?
Answers
146
Step-by-step explanation:= 6x^2 - 4
= x = 5
= 6 x 5^2 - 4
= 5^2 = 25
= 6 x 25 - 4
= 150 - 4
= 146
Answer:
[tex]\underline{146}[/tex]Step-by-step explanation:
Plug in the value of x into the expression [tex]6x^2-4[/tex].
- You will obtain this: [tex]6(5)^2-4[/tex].
Then all you need to do is use the correct Order of operations to evaluate.
- For example, you need to square 5 first: [tex]6\cdot25-4[/tex].
Then, you need to multiply: [tex]150-4[/tex].
Then, you should subtract: [tex]146[/tex]
↣ I hope I could help!
- Rosaliayes I am having problems learning about equations
Answers
If we have a function [Equation] it would look something like this:
3x+y=4
In order to solve for both values and graph it [If that's what you are trying to do], you solve for y and then replace values [Of your own choosing, or they are given to be studyed] in x, after we replace the values in x, we are going to have the respective value of y.
From our previous example, it would be:
y = -3x+4
So, when we start replacing the values of X, we will get the respective values for Y, let's try doing it from -3 to 3.
x = -3 => y = -3(-3)+4 => y = 13
x = -2 => y = -3(-2)+4 => y = 10
x = -1 => y = -3(-1)+4 ) => y = 7
x = 0 => y = -3(0)+4 => y = 4
x = 1 => y = -3(1)+4 => y = 1
x = 2 => y = -3(2)+4 => y = -2
x = 2 => y = -3(3)+4 => y = -5
From this, we would end up with the following points:
(-3, 13)
(-2, 10)
(-1, 7)
(0, 4)
(1, 1)
(2,
I'll give brainliest!
Answers
Answer:
The side length, s, of the square is 18
Step-by-step explanation:
The sides can be found by taking the square root of the area.
(Area)^1/2=s, where s = side.
(324)^1/2=18
I need help with this question for my computer class
Answers
SOLUTION:
Case: Spreadsheet calculations
Method:
Some common signs
'+' does sum
'-' does difference
'*' does the product
'/' does division
Hence
C7-B6 does the difference for cells C7 and B6
Final answer: Option (D)
C7-B6
A circle in the xy-plane has a center at G 3 1 42 3 and a radius that is units long. Which of the 15 following is an equation of the circle?
Answers
We are asked to find the equation of a circle on the xy-plane, with center (3/4 , 1/2) and a radius of 3/5 units. For doing so, we remember the general equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) represents the center of the circunference, and r its radius.
In our example, we obtain that,
[tex]\text{Center}=(\frac{3}{4},\frac{1}{2})[/tex]And so,
[tex]\begin{gathered} h=\frac{3}{4},k=\frac{1}{2} \\ r=\frac{3}{5} \end{gathered}[/tex]Applying the above formula, we get that the equation of the circle will be:
[tex](x-\frac{3}{4})^2+(y-\frac{1}{2})^2=(\frac{3}{5})^2[/tex]This is:
[tex]\mleft(x-\frac{3}{4}\mright)^2+\mleft(y-\frac{1}{2}\mright)^2=\frac{9}{25}[/tex]Find the volume of the cylinder. Either enter an exact answer in terms of or use 3.14 for 4 units 3 Stuck? Watch a video or use a hint.
Answers
the volume of a cilinder is:
[tex]V=\pi r^2h[/tex]So we can replace the radius and the high so:
[tex]\begin{gathered} V=\pi6^24 \\ V=36\cdot4\cdot\pi \\ V=144\pi \end{gathered}[/tex]Now we can replace pi by 3.14 so:
[tex]undefined[/tex]Nicholas earned $2,000.00 working over the summer and wants to put the money into a savings account. A savings account at bank A earns 5% simple interest and a savings account at bank B earns 4% interest compounded quarterly. If Nicholas plans to deposit the $2,000.00 and leave it in the account for 4 years, at which bank would he earn more interest? A. The interest earned cannot be calculated from the given information. B. The interest earned at both banks will be the same. C. bank A D. bank B
Answers
Answer:
Choice C
==> Bank A
Step-by-step explanation:
Principal P = $2000
Bank A calculation
Simple Interest at 5% for 4 years = Prt = 2000 x 5/100 x 4 = $400
Bank B Calculation
At 4% interest compounded quarterly, the accrued value(Principal + Interest) is given by the formula:
[tex]A = P(1 + r/n)^{nt}[/tex]
where
P = principal
r = annual interest rate as percentage
n = number of compounding per year
t = number of years
We have r = 4/ 100 = 0.04
n = 4 since interest is computed quarterly or 4 times a year
t = 4 years
[tex]A = 2000 ( 1 + 0.04/4)^{(4) \cdot (4)}\\\\A = 2000 (1.01)^{16} = \$2,345.16\\\\\text{Interest } = 2345.16 - 2000 = $345.16[/tex]
Since interest earned at bank A (400) > interest earned at bank B(345.16), the answer would be C. ==> Bank A
Zan took her dog, Simba, to the dog park on Saturday afternoon. There were more than 20 dogs running around the park when they arrived. Determine which inequality describes the dogs at the park. d < 20 d > 20 d ≥ 20 d ≤ 20
Answers
Answer:
Number 2 is the answer to this question.
The inequality to represent the given scenario is d>20. Therefore, option B is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, there were more than 20 dogs running around the park when they arrived.
Let the number of dogs be d.
So, the inequality is d>20
Therefore, option B is the correct answer.
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