From the options given in the problem statement the values of f(x) and g(x) that satisfy equation (2) i.e. y = f(g(x)) = (10)/(√(2x + 9))are:f(x) = 10/√(x) and g(x) = 1/(2x + 9)
What is function ?
Function can be defined in which it relates an input to the output.
In this problem y is called a composite function of f(x) and g(x). So in the options given in the problem statement which option will satisfy y = f(g(x)) is to be found out.
Let f(x) be defined as some function then if ‘x’ is replaced by g(x) in f(x) i.e. f(g(x)) then its value will be y. Hence we can write:
y = f(g(x)) --- (1)
We are also given that
y = (10)/(√(2x + 9))
Let us consider each of the cases given under options, one by one. We have to find out the nature of the function f(x) as well as g(x) so that we substitute g(x) for x in f(x) we have:
y = (10)/(√(2x + 9))
(i) Consider f(x) = 10 and g(x) = √(2x + 9)
Here f(x) cannot take g(x) as its inputs.
(ii) Consider f(x) = 10/√(x) , g(x) = 2x + 9
Here we determine that f(g(x)) = (10)/(√(2x + 9))
(iii) Consider f(x) =10/x , g(x) = 2x + 9
Here f(g(x) = 10/(2x+9)
(iv) Consider f(x)= √(2x + 9) , g(x) = 10
f(g(x) = f(10) = √(2(10) + 9) = √29
Hence, From the options given in the problem statement the values of f(x) and g(x) that satisfy equation (2) i.e. y = f(g(x)) = (10)/(√(2x + 9))are:
f(x) = 10/√(x) and g(x) = 1/(2x + 9)
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Joe invested $600 in two companies, company A and B. In company B, he invested $40 more than his investment in company A. Fill in the following blanks: (1) If Joe invested x dollars in company A, how much did he invest in company B?
Answer:
If Joe invested x dollars in company A, he invested x + 40 dollars in company B.
Find two solutions of each equation. Give your answers in degrees
(0° ≤ < 360°)
and in radians
(0 ≤ < 2).
Do not use a calculator. (Do not enter your answers with degree symbols. Enter your answers as comma-separated lists.)
(a)
sin() = 1/2
degrees
radians
(b)
sin() = − 1/2
degrees
radians
Answer:
(a) sin() = 1/2
degrees: 30, 150
radians: π/6, 5π/6
(b) sin() = − 1/2
degrees: 210, 330
radians: 7π/6, 11π/6
Note that these solutions are in the interval of 0 to 360 degrees or 0 to 2 radians. Also note that these are the primary solutions, there are infinitely many solutions that can be obtained by adding multiples of 360 degrees or 2π radians to these values.
Task 5
Deductions
Medicare $72.50
$310
S. Security
Fed Tax $500
State Tax $262.50
Health ins. $553
Dental $127
ins.
Steve just got a new job working at a
bank. He makes a gross annual
income of $60,000. He wants to buy a
new suit for his job, but the suit costs
$150. Can he afford it?
1: What is Steve's gross monthly income
2: Based on his deductions, what is Steve's
monthly net income
3: Based on the 5% Spending Guideline for
clothing, can he afford the suit
If Steve just got a new job working at a bank. Steve's gross monthly income is $5,000, Steve's monthly net income is $3,277 and Seve can afford the suit based on the 5% spending guideline for clothing.
How to find the gross monthly income?a. Steve's gross monthly income is
Gross income = $60,000 / 12
Gross income = $5,000
b. Steve's monthly net income
His deductions are:
Medicare: $72.50
Social Security: $310
Federal Tax: $500
State Tax: $262.50
Health insurance: $553
Dental insurance: $127
Total deductions = $72.50 + $310 + $500 + $262.50 + $553 + $127 = $1723.00
Steve's monthly net income = $5,000 - $1,723 = $3,277
c. In order to see if Steve can afford the suit using the 5% spending guideline for clothing, we need to find the 5% of his monthly net income:
5% of $3,277 = $163.85
Since the amount of $150 is less than $163.85, Steve can afford the suit based on the 5% spending guideline for clothing.
Therefore Steve's gross monthly income is $5,000, Steve's monthly net income is $3,277 and Seve can afford the suit based on the 5% spending guideline for clothing.
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Which is the equation of the circle that has a diameter with endpoints located at (5, –3) and (11, 5)?
(x – 5)2 + (y + 3)2 = 25
(x – 7)2 + y2 = 100
(x – 8)2 + (y – 1)2 = 25
(x – 11)2 + (y + 5)2 = 100
The equation of the circle that has a diameter with endpoints located at (5, –3) and (11, 5) is; (x – 8)² + (y – 1)² = 25
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
The midpoint of the diameter of a circle is it's center.
As such; the coordinates of its center are;
x = (5+11)/2
x = 8
y = (-3 + 5)/2
y = 1
The coordinates of the center are then; (8, 1)
The radius of a circle is half the length of the diameter;
Radius, r = d/2
where; d = √(11-5)² + (5-(-3))²
d = √36 + 64
d = √100
d = 10
Therefore, radius, r = 10/2 = 5.
Therefore, the equation of the circle usually takes the form;
(x -f)² + (x -g)² = r²
In this scenario; the equation is;
(x – 8)² + (y – 1)² = 25.
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If 4 is added to the quotient of 24 and -8, what
number results?
Answer:
1
Step-by-step explanation:
Quotient of 24 and -8 gives you -3. Hence, 4 added to -3 is 1, which is the answer.
Can someone help me find the value of y?
Answer:
y = 5
Step-by-step explanation:
The angle formed is a right angle which has a measure of 90 degrees. This means that the sum of the two angles is 90 degrees. Using this information we can set up an equation and solve for y
Set up equation
7y + 8 + 8y + 7 = 90
==> combine like terms
15y + 15 = 90
==> subtract 15 from both sides
15y = 75
==> divide both sides by 15
y = 5
On average, the number of electric guitars sold in Ohio each year is equivalent to seven times the average number sold yearly in Montana. If, on average, there are 49,525 electric guitars sold each year in Ohio, how many are sold in Montana?
The number of guitars sold each year in Montana is given as follows:
7075 guitars.
How to obtain the number of guitars sold per year in Montana?The number of guitars sold per year in Montana is obtained applying the proportions in the context of this problem.
Ohio's average is seven times Montana's average, hence Montana's amount is obtained dividing Ohio's amount by 7.
Ohio's amount is given as follows:
49525 guitars.
Hence Montana's amount is obtained as follows:
49525/7 = 7075 guitars.
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Please assist with the math question in the picture
The function graphed above is:
Answer:
Step-by-step explanation:
check the image
Yolanda, Kareem, and Jose served a total of 82 orders Monday at the school cafeteria. Kareem served 2 times as many orders as Jose. Yolanda served 6 fewer orders than Jose. How many orders did they each serve?
Answer:
Yolanda served 13 times , Kareem served 38 times and Jose served 19 times.
Step-by-step explanation:
No of orders served by Yolanda = x
No of orders served by Kareem = y
No of orders served by Jose = z
x + y + z = 82 ------------- (1)
y = 2z ------------ (2)
x = z - 6 ---------(3)
substituting (2) and (3) in (1) :-
z - 6 + 2z + z = 82
4z - 6 = 82
4z = 76
z = 19
y = 2(19)
y = 38
x = 19 - 6
x = 13
Express the following 10√3 as a Single surds
Answer:
The expression 10√3 can be written as a single surd as (10√3) = (10 √3/1) = (10 √3)¹/¹ = (10√3)^(1/1) = 10√3.
HELP ASAP, I PROMISE I WILL GIVE YOU BRAINLIST IF YOU ANSWER RN
Answer:
Step-by-step explanation:
Answer is A
Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and
visitor activity (Orlando Sentinel, May 19, 2018). Hotel occupancy data for February in two consecutive years are as follows.
Occupied Rooms
Total Rooms
Current Year Previous Year
1,505
1,750
c. Conduct a hypothesis test. What is the p-value (to 4 decimals)?
What is the 95% confidence interval estimate of the change in occupancy for the one year period? To 4 decimals
The 95% confidence interval estimate of the change in occupancy for the one year period is given as follows:
(0.1441, 0.1815).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The percent change is given by the change divided by the initial value, hence the parameters are given as follows:
[tex]n = 1505, \pi = \frac{1750 - 1505}{1505} = 0.1628[/tex]
Hence the lower bound of the interval is of:
[tex]0.1628 - 1.96\sqrt{\frac{0.1628(0.8372)}{1505}} = 0.1441[/tex]
The upper bound of the interval is of:
[tex]0.1628 + 1.96\sqrt{\frac{0.1628(0.8372)}{1505}} = 0.1815[/tex]
Missing InformationOnly the confidence interval can be calculated as the remainder of the problem is incomplete
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Write the equation of the quadratic function that contains the point (1,1) and has the same shape as f(x)=2x. The vertex is on the y-axis.
The equation of the quadratic function that contains the point (1,1) is
y = 2x² - 1.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree. A quadratic function must contain at least one term of the second degree.
Given the quadratic function that contains the point (1,1)
x = 1 and y = f(x) = 1
the shape of the equation is the same as f(x) = 2x²
a quadratic equation is given by
y = a(x - k)² + h
here (k, h) is the vertex of the function
given vertex is on the y-axis,
so k = 0
y = ax² + h
and a = 2 from f(x) = 2x²
y = 2x² + h
substitute x= 1 and y = 1
1 = 2 + h
h = 1 - 2 = -1
equation of function is y = 2x² - 1
Hence equation of the function is y = 2x² - 1.
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someone please help !! :)
geometry : angles of polygons & parallelograms (unit 7)
Q : find the value of x
Answer:
x = 13
Step-by-step explanation:
the sum of the exterior angles of a polygon is 360°
sum the 6 exterior angles and equate to 360
3x + 6 + 41 + 6x - 5 + 4x + 7 + 62 + 7x - 11 = 360
20x + 100 = 360 ( subtract 100 from both sides )
20x = 260 ( divide both sides by 20 )
x = 13
for which of the following values does the function intersect the x axis at 2 different points
The values that, the function intersect the x axis at 2 different points is -4 < b < 4. So correct option is D.
A function in mathematics is a relationship between a set of inputs (also known as independent variables or arguments) and a set of outputs (also known as dependent variables or values). The output of a function is determined by the inputs, and the function assigns exactly one output value to each input value.
A function can be represented in many ways, including a formula, a table, or a graph. The formula of a function defines the relationship between the inputs and outputs, and can be used to calculate the output for a given input. A table lists input and output values, and a graph represents the function by plotting the input and output values.
Functions are a fundamental concept in mathematics and are used in many areas, including algebra, calculus, and other branches of mathematics, as well as in science, engineering, and other fields. Functions can be simple, such as linear functions, or complex, such as exponential functions or trigonometric functions.
For the function f(x) = x^2 + bx + 4 to intersect the z-axis at two different points, it must have two real roots. This means that the discriminant of the quadratic equation must be greater than 0. The discriminant of the quadratic equation is given by b^2 - 4(1)(4). Hence, b^2 - 16 > 0, or b^2 > 16, which simplifies to -4 < b < 4.
Therefore, the answer is D: -4 < b < 4.
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what is the x and y intercept of 4x + y + 43
Answer:
The x intercept is going to be (-43/4) and the y intercept is going to be (0,-43)
Step-by-step explanation:
hope this helped
129.938 + 46.07 + 38
What is the answer
Answer: 214.008
Step-by-step explanation: hope this helped :)
prove that, given a nonnegative integer , there is a unique nonnegative integer such that m^2 < sqrt n < (m 1)^2
It is proved that m = √n.
To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:
m^2 ≤ n < (m + 1)^2.
So, after taking the square root, it will be:
m ≤ √n < m + 1
From that we can see m = √n is the unique m.
What is a nonnegative integer?A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.
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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.
88 1
2
3
81°
4
5
64%
m/1 =
m/2 =
m23 =
m/4 =
m25 =
Answer:
92°24°64°35°81°Step-by-step explanation:
You want the measures of 5 marked angles in the figure showing two transversals crossing parallel lines.
Angle 1Angle 1 forms a linear pair with the angle marked 88°, so is supplementary to it.
Angle 1 = 180° -88°
Angle 1 = 92°
Angle 3Angle 3 is a corresponding angle to the one marked 64° where the horizontal transversal crosses the parallel lines. Corresponding angles are congruent.
Angle 3 = 64°
Angle 2Angles 2 and 3 are "remote interior angles" with respect to the exterior angle marked 88°. Hence their sum is 88°.
Angle 2 = 88° -Angle 3 = 88° -64°
Angle 2 = 24°
Angle 4Angles 3, 4, and 81° combine to form a straight angle of 180°.
Angle 4 = 180° -64° -81°
Angle 4 = 35°
Angle 5Angle 5 is an alternate interior angle with respect to the one marked 81° where the downward-sloping transversal crosses the parallel lines. Alternate interior angles are congruent.
Angle 5 = 81°
EASY POINTS!
An art dealer earns a 12% commission for every painting she sells. How much commission does the art dealer earn from selling 3 paintings for $750 each?
$1,020
$180
$270
$90
Answer: $270
Step-by-step explanation: You multiply 3*750, then multiply the product by 0.12 because 0.12 = 12%.
¿En qué carrera es más probable que aplique conceptos de geometría?
Find the equation of the linear function represented by the table below in slope-intercept form. x y -2 -2 2 6 6 14 10 22
The equation of the linear function represented by the table in slope intercept form is f(x) = 2x + 2.
What is Linear Function?
A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.
Equation of the linear function in slope intercept form can be represented as y = mx + d, where m is the slope and d is the y intercept.
Slope is the change in y coordinates divided by the change in x coordinates.
y intercept is the point on the line where the line touches the Y axis.
Given points are (-2, -2), (2, 6), (6, 14) and (10, 22).
Consider the points (-2, -2) and (2, 6).
Slope, m = (6 - -2) / (2 - -2) = 8 / 4 = 2
So the equation becomes y = 2x + d
Substituting one of the points (2, 6) in the above equation,
6 = (2 × 2) + d
d = 2
So the equation is y = 2x + 2.
Hence the given linear function can be represented as f(x) = 2x + 2.
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the southern leaves Chicago, IL at 5:00pm arrives in Kansas City, MO at 12:30am. the distance is 565 Miles. there are no time changes. Find the average speed.
The average speed is 75.33 miles per hour.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Distance = 565 miles
Time.
= 5:00 pm t0 12:30 am
= 7.5 hours
Now,
Average speed.
= 565 / 7.5
= 75.33
Thus,
75.33 miles per hour is the average speed.
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-(x − 1) + 10 = -3(x - 2)
According to the question, the solution to the equation is x = -7.
What is the equation ?The equation is a representation of a mathematical relation between two or more variables. It is usually expressed as an equation, where one side of the equation is equal to the other. For example, the equation y=mx+b is a linear equation with two variables, m and b, which are known as the slope and the y-intercept, respectively.
To solve this equation, we must first combine like terms on both sides of the equals sign.
-3x + 3 - x + 10 = -3x + 6
Next, we can subtract 3 from both sides of the equation to isolate the x-term.
-4x + 13 = -3x + 6
Finally, we can subtract -3x from both sides of the equation to isolate the constant term.
-7x = 7
We can then divide both sides of the equation by -7 to solve for x.
x = -7
Therefore, the solution to the equation is x = -7.
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Finding unknown measures in similar triangles
- i need help with this im trying to understand
The unknown measures in similar triangles in which x is 24 in.
What is a similar triangle?
Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.
We have given,
ΔABC ≈ ΔXYZ
In ΔABC
AC = 36 in, BC = 18 in and AB = x in
In ΔXYZ
XY = 16in, ZY = 12in and XZ = 24in
We know that,
the side and angles of a similar triangle are in proportion to each other.
AC / XZ = 36 / 24 = 3/2
BC / ZY = 18 / 12 = 3/2
AB / XY = x / 16
AC / XZ = BC / ZY = AB / XY --------(similar triangle)
x / 16 = 3/2
x = 3/2 * 16
x = 3 * 8
x = 24
hence, the unknown measures in similar triangles in which x is 24 in.
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Show that a = n, where n is an integer.
What is the value of n?
Answer:
n = 30
Step-by-step explanation:
Since it is not a right-angle triangle, you will need to use sine or cosine rule;
We have two side lengths and the angle between, this means you need to use the cosine rule:
a² = b² + c² - 2bc.cosA
[tex]{a}^{2} = ({4 \sqrt{3} })^{2} + {( \sqrt{6} )}^{2} - 2( 4\sqrt{3})( \sqrt{6} ). \cos(45) \\ {a}^{2} = 48 + 6 - 8 \sqrt{18}(0.707...) \\ {a}^{2} = 54 - 24 \\ {a}^{2} = 30 \\ a = \sqrt{30}[/tex]
Answer:
n = 30
Step-by-step explanation:
For this question, use the cosine law formula:
[tex]a=\sqrt{c^2+b^2-2cb*cosA} \\a=\sqrt{(\sqrt{6})^2+(4\sqrt{3})^2-2(\sqrt{6})(4\sqrt{3})*cos45 }\\a =\sqrt{6+48-(8\sqrt{18})*\frac{\sqrt{2} }{2} }\\a=\sqrt{54-\frac{8\sqrt{36} }{2} }\\a=\sqrt{54-24}\\a=\sqrt{30}[/tex]
If a = [tex]\sqrt{n}[/tex], then n must be 30
What is the domain of function h? h(x)=square root of x-7 +5
The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
h(x) = √(x - 7) + 5
The value inside the square root should be greater than or equal to zero. Then we have
x - 7 ≥ 0
x ≥ 7
The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).
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The table represents the relationship between the number of employees scheduled per estimated customer at a clothing store. The graph represents the relationship between the number of employees scheduled per estimated customer at a coffee shop.
At the clothing store, the number of customers that one employee can help is 4 customers.
At the coffee shop, the number of customers that one employee can help is 6 customers.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the points.Next, we would determine the linear equation representing the clothing shop with these points (2, 4) and (3, 6) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 4 = (6 - 4)/(3 - 2)(x - 2)
y - 4 = 2(x - 2)
y = 2x + 2
When x = 1, we have:
y = 2(1) + 2
y = 4 customers.
Furthermore, a linear equation which models the coffee shop is given by:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.k = y/x
k = 6/1
Therefore, the required linear equation which models the coffee shop is y = 6x.
When x = 1, we have:
y = 6(1)
y = 6 customers.
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-16 subtracted from a number equals 7
Answer:
23
Step-by-step explanation:
If x-16=7
Then X= 23
Let me know I’d this answer is incorrect
