The following equation represents the function g in function notation,
g(x) = 3x - 14 [Option (A)]
Definition of a Function
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.
Given equation is,
y -3x = -14
⇒ y = -14 + 3x
or y = 3x - 14
Here, y stands for or represents the function g(x) which is a function of independent variable x.
Thus, the correct function notation is as follows,
g(x) = 3x - 14
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A punch recipe calls for mixing 2 parts of cranberry juice with 5 parts of apple juice
The proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 parts of cranberry juice and 5 parts of lemon juice.
According to the question,
A punch recipe calls for mixing 2 parts of cranberry juice with 5 parts of apple juice.
84/2 = 42
5*42=210
Hence, the proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 part of cranberry juice and 5 parts of lemon juice.
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equivalent to -8.2 - 5−8.2
The equivalent value of the given expression is -21.4
Difference of decimalsDecimals are values that include decimal points. Given the expression below
-8.2 - 5−8.2
Collect like terms
-8.2 −8.2 - 5
Convert to fractions
-82/10- 82/10 - 5
-164/10 - 5
-16.4 - 5
Take the sum
-21.4
Hence the equivalent value of the given expression is -21.4
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Pls send proper answer , urgent
A 1. What is the function in the following graph?
The rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).
What is the rational function behind the graph seen in the picture?
Herein we have the graph of a rational function of the form f(x) = p(x)/q(x) . The domain of these kind of functions is all real numbers except those values of x such that q(x) = 0. Graphically speaking, there is a vertical asymptote when a discontinuity exists and an horizontal asymptote for x → ± ∞.
In accordance with the picture, there are one horizontal asymptote and one vertical asymptote. As the horizontal asymptote of the function is distinct of 0, then the grade of p(x) is the same grade of q(x). Therefore, we have a rational function of the form:
f(x) = (2 · x + k)/(x + 3) (1)
If we know that x = 0 and y = 2.4, then the value of k is:
2.4 = (2 · 0 + k)/(0 + 3)
2.4 = k/3
k = 7.2
Therefore, the rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).
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Write an absolute value inequality for each of the following. Then graph the
solution set on a number line.
all numbers less than 7and greater than -7
An absolute value inequality for "all numbers less than 7 and greater than -7" is given by |x| < 7.
How to write an absolute value inequality?Based on the information provided, we can logically deduce that the statement describes an intersection of set because the word "and" was used.
This ultimately implies that, we would use the less than (<) symbol to write an absolute value inequality for the given statement:
|x| < 7
Therefore, this can be translated as follows:
-7 < x < 7 or x < 7 and x > -7.
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hellooo please i need help on these question
( f - g )(x) = 10x - 17 and ( f ° g)(-6) = 60. The answers are option D and B
There are different type of FunctionDifferent types of function demands different ways of solving them. Different types are simple function, function by substitution and function of function.
Given that
f(x) = [tex]x^{2}[/tex] + 9x - 14 and g(x) = [tex]x^{2}[/tex] - x + 3
( f - g )(x) will be the difference between f(x) and g(x)
( f - g )(x) = [tex]x^{2}[/tex] + 9x - 14 - ( [tex]x^{2}[/tex] - x + 3)
( f - g )(x) = [tex]x^{2}[/tex] + 9x - 14 - [tex]x^{2}[/tex] + x - 3
( f - g )(x) = 10x - 17
Also, if f(x) = [tex]3x^{2}[/tex] - 15 and g(x) = 1 - 2/3 x
( f ° g)(-6) means that we will evaluate g at -6, then evaluate f at the result of g(-6)
g(-6) = 1 - 2/3 (-6)
g(-6) = 1 + 4
g(-6) = 5
f(g(-6)) = 3([tex]5^{2}[/tex]) - 15
f(g(-6)) = 3 x 25 - 15
f(g(-6)) = 75 - 15
f(g(-6)) = 60
Therefore, ( f - g )(x) = 10x - 17 and ( f ° g)(-6) = 60
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-2(3x+2)-6x≥
-4What are the solutions of the inequality?
The solution of the inequality -2(3x + 2) - 6x ≥ -4 is undefined
Inequality-2(3x + 2) - 6x ≥ -4
open the parenthesis-6x - 4 - 6x ≥ -4
-12x ≥ - 4 + 4
-12x ≥ 0
x ≥ 0 / -12
x is undefined
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what are the domain and range of the graph below.
O domain: [0,00)
range: (-00,00)
O domain: [0,00)
range: (-0,4]
domain: (0,4)
range:
(-00,00)
domain: (-∞,4]
range: [0,00)
Answer:
Domain: [0,∞)
Range: (-∞, 4]
Step-by-step explanation:
The required domain and range of the function shown in the graph are,
Domain = (0, ∞)
Range = (-∞, 4)
To calculate the domain and range of a function from its graph, you can follow these steps:
Identify the x-coordinates of all the points on the graph. The set of all possible x-coordinates is the domain of the function.Write the domain as an interval or as a set of values, depending on the format of the original problem. For example, if the graph is defined for all real numbers, the domain would be written as (-∞, ∞).Identify the y-coordinates of all the points on the graph. The set of all possible y-coordinates is the range of the function.Write the range as an interval or as a set of values, depending on the format of the original problem.So, from the above definition, from the graph we have,
Domain = (0, ∞)
Range = (-∞, 4)
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There are 16 ounces in 1 pound juan is mailing a package that weighs 10 pounds
to know the weight of the package in ounces.
ounces
pounds
complete the statement to describe how to convert pounds to ounces
to find the weight in ounces multiply
the number of pounds by the unit rate
ounces per pound
160 ounces is the answer
16 ounces per pound
16x10=160
First put to find the weight in ounces, *multiply* the number of pounds by the unit rate, 16 ounces per pound. Then put 10 pounds = *160 ounces.*
An ounce is the designation of several different units of mass, weight, or volume, and is largely unchanged from the ancient Roman unit of measurement, uncia. Avoirdupois ounces are 1⁄16 Avoirdupois pounds. This is a US standard and an ounce of the British Empire.
oz [Ouns] n. A unit of weight in the US customary unit, an avoirdupois unit equal to 437.5 grains or 28.35 grams. A pharmacist's weight unit is equivalent to 480 grains or 31.10 grams.
oz, equivalent to 1/16 pound (437 1/2 grain) on the Avoirdupois system and 480 grains or 1/12 pound on the Troy and pharmacist system. Avoirdupois ounces are equivalent to 28.35 grams and pharmacist ounces are equivalent to 31.103 grams.
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Instructions: Find the surface area of the figure below. Round your answers to the nearest tenth, if necessary.
The surface area of the cone is calculated to the nearest tenth as: 173.4 cm².
What is the Surface Area of a Cone?Surface area of a cone = πr(r + l),
Given the following:
Radius (r) = 4 cmSlant height (l) = 9.8 cmPlug in the values
Surface area of the cone = π × 4(4 + 9.8)
Surface area of the cone = 173.4 cm²
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Find the area of a triangle who's side lengths are 13, 14, and 15. (The questions doesn't tell the type of triangle.)
Answer:
84 square units.
Step-by-step explanation:
Area of scalene triangle:[tex]\sf \boxed{\bf Area = \sqrt{s*(s-a)(s-b)*(s-c)}}[/tex]
Here, a, b and c are the sides of the triangle. s is the semi perimeter.
a = 13
b = 14
c = 15
[tex]\sf s= \dfrac{a+b+c}{2}\\\\ =\dfrac{13+14+15}{2}\\\\=\dfrac{42}{2}\\\\s = 21[/tex]
s -a = 21 - 13 = 8
s -b = 21 - 14 = 7
s - c = 21 - 15 = 6
[tex]\sf Area = \sqrt{21*8*7*6}[/tex]
[tex]= \sqrt{ 7* 3 * 2 * 2 * 2 * 7 * 2 * 3}\\\\=7 * 3 *2*2\\\\= 84 \ square \ units[/tex]
Find the coefficient of t to the 4th power in the expansion of (-9t-9) to the 7th power select one: a. -25,515 b. -100,442,349 c. -167,403, 915 d. -4,782, 969
The coefficient of t to the 4th power in the given expansion is -167403915.
Option (c) is the correct answer.
What is an expansion?An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.
Given expansion=[tex](-9t-9)^{7}[/tex]
Coefficient of the 4th power of t in the expansion,
=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]
=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]
=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]
=[tex]35t^{4}(-9)^{7} \\[/tex]
=[tex]35t^{4}(4782969)[/tex]
= -167403915[tex]t^{4}[/tex]
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Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
A cone is a 3-dimensional shape that consists of a circular or flat surface and a curved side. Thus the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]
A cone is a 3-dimensional shape that consists of a circular or flat surface and curved side. Its volume can be determined by;
The volume of a cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius of its flat surface, and h is its height.
From the given question, we have to determine the value of h using the Pythagoras theorem.
Such that;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]4^{2}[/tex] = [tex]h^{2}[/tex] + [tex]1^{2}[/tex]
16 = [tex]h^{2}[/tex] + 1
[tex]h^{2}[/tex] = 15
h = [tex]\sqrt{15}[/tex]
Thus the volume of the cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\frac{1}{3}[/tex]x [tex]\frac{22}{7}[/tex] x [tex]1^{2}[/tex]x [tex]\sqrt{15}[/tex]
= 4.0574
Therefore the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]
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Volume=
Help me please thanks so much :)
The volume of the oblique cylinder is 6867.18 cubic units
How to determine the volume?The given parameters are:
Height = 27
Radius = 9
The volume is calculated as:
[tex]V = \pi r^2 h[/tex]
So, we have:
[tex]V = 3.14 * 9^2 * 27[/tex]
Evaluate
V = 6867.18
Hence, the volume of the oblique cylinder is 6867.18 cubic units
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One pen is chosen without looking from a bag that has 3 blue pens, 6 red pens, and 3 green pens.
Find the probability of choosing a green pen.
The probability of choosing. a green pen is 0.25
What is probability?Probability is the likelihood or chance that an event will occur. Mathematically;
Probability = Expected/Total outcome
If a bag has 3 blue pens, 6 red pens, and 3 green pens, then;
Total pen = 3+6+3
Total pen = 12
If a green pen is chosen, then
Pr(choosing a green pen) = 3/12
Pr(choosing a green pen) = 0.25
Hence the probability of choosing. a green pen is 0.25
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how to solve for x in graphic sketch
12.5% of a number is 25, find the number
Answer:
200
Step-by-step explanation:
Let's call the number x :
12.5% of x = 25
Changing 12.5% into decimal would be 0.125
Now we have the equation :
0.125x = 25
Divide both sides by 0.125 to make x the subject :
x = 25 ÷ 0.125
x = 200
To check we can substitute this value into the question :
12.5% of 200 = 25
Hope this helped and have a good day
Louis is very hungry when he spots a hot dog stand. The stand sells soft drinks for $1.25 each and hot dogs for $2.50 each. Louis has $21 in his pocket and he really wants to buy one soft drink and as many hot dogs as he can purchase. How many hot dogs can he buy?
Answer:
7 hot dogs
Step-by-step explanation:
Set up an equation:
2.5x + 1.25 = 21
2.5x = 19.75
x = 7.9
You cannot buy .9 of a hot dog, so the answer is 7
Graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane.
What is the solution to the equation f(x)=g(x) ?
Answer:
x = 2
Step-by-step explanation:
To solve the equation, you need to set both functions equal to each other and simplify to find the value of "x".
f(x) = 2x + 1
g(x) = -x + 7
f(x) = g(x) <----- Given equation
2x + 1 = -x + 7 <----- Insert functions
3x + 1 = 7 <----- Add "x" to both sides
3x = 6 <----- Subtract 1 from both sides
x = 2 <----- Divide both sides by 3
What is the slope of a line passing through (-5, 5) and
(-4, 10)?
Answer:
5
Step-by-step explanation:
Formula for finding slope:
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
Slope of line passing through (-5,5) and (-4,10)
=
[tex] \frac{5 - 10}{ - 5 - ( - 4)} \\ = \frac{ - 5}{ - 5 + 4} \\ = \frac{ - 5}{ - 1} \\ = 5[/tex]
Answer:
Slope = 5
Step-by-step explanation:
Slope:(-5,5) ; x₁ = -5 & y₁ = 5
(-4, 10) ; x₂ = -4 & y₂ = 10
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{10-5}{-4-[-5]}\\\\ =\dfrac{10-5}{-4+5}\\\\=\dfrac{5}{1}\\\\= 5[/tex]
The width of a window on a house is 48 inches. The house is shown in a scale drawing. The width of the window in the drawing is 20% of its actual width What is the window’s width in the drawing?
please help!
The windows width in the drawing according to the task content is; 9.6inches.
What is the windows width in the drawing?According to the task content, the window's actual width on the house is given as; 48 inches.
Hence, since, the window's width on the drawing is 20% of the actual width, it follows that;
Windows drawing width = 20% × 48 = 9.6 inches.
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The monthly income of a government servant is Rs 77,280 and he gets the festival expense of one month's salary, what is his taxable income?
I don't think this question is complete but here's ur answer
The average weight of 3 men a, b and c is 84 kg. another man d joins the group and the average now becomes 80 kg. if another man e whose weight is 3 kg more than that of d, replaces a then the average weight of b, c, d and e becomes 79 kg. what is the weight of a?
The weight of A is 75kg.
How to calculate the weight?Total weight of A + B + C = 84 x 3 = 252kg
Total weight of A + B + C + D = 80 x 4 =.320 kg
Weight of D = 320 - 252 = 68 kg
Given, E = D + 3 = (68 + 3) kg = 71 kg
Total weight of B + C + D + E = (79 x 4) = 316 kg
Weight of B + C = 316 kg - 71 kg - 68 kg = 177 kg
Weight of A only will be:
= 320 kg - 177 kg - 68 kg
= 75 kg
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Identify the sets of congruent angles. Explain your conclusions.
Answer:CB,CH,AE,AB
Step-by-step explanation:
Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of cosines, what is the measure of angle A? Round your answer to the nearest whole number, if necessary.
a = 10 cm
b = 17 cm
c = 11 cm
Answers
45°
127°
87°
34°
The angle A of the triangle ABC has a measure of approximately 34°. (Right choice: D)
How to find the missing angle of a triangle by the law of cosine
To determine the missing angle of a triangle by the law of the cosine, we must know the lengths of the three sides of the figure. Please notice that angle A is opposite to the side a in accordance with the law of the cosine. Then:
[tex]\cos \theta = \frac{(10\,cm)^{2}-(17\,cm)^{2}-(11\,cm)^{2}}{-2\cdot (17\,cm)\cdot (11\,cm)}[/tex]
θ ≈ 34.016°
The angle A of the triangle ABC has a measure of approximately 34°. (Right choice: D)
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honestly don’t know this ?
1 ) 6
2) 6
3) -2
4) 2
5) -2
6) 2
Find the length of BC¯¯¯¯¯¯¯¯
Answer:
B
Step-by-step explanation:
I love trig lol,
Assuming you know trig, Cos(17)=BC/42
Cos(17)*42=BC
Cos(17)~0.956
0.956*42=40.152=BC
Since this is a approximation, B is the closest to our estimate.
How to find the answer?
i) The number of students that come to school by motorcycle only = 8
ii) The number of students that did not take all the three types of transportation = 9
iii) Number of students that did not come to school by car = 28
Solving questions on venn diagramThe total number of students = 40
The number of students that come to school by car alone = 9
The number of students that come to school by motorcycle only = 8
The number of students that come to school by car only = 11
The number of students that come to school by both car and motorcycle = 3
Number of students that did not take all the three types of transportation = 40 - (9 + 8 + 3 + 11)
= 40 - 31
Number of students that did not take all the three types of transportation = 9
Total students that come to school by car = 9+3 = 12
The total number of students that did not come to school by car = 40 - 12 = 28
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Will make BRAINLIEST!!
Complete the congruence statement for the figure below.
x+2/3 - x+1/5 = x-3/4 - 1
Answer:
x = 157/60
Step-by-step explanation:
x + 2/3 - x + 1/5 = x - 3/4 - 1
x - x - x = -2/3 - 1/5 - 3/4 - 1
-60x/60 = -40/60 - 12/60 - 45/60 - 60/0
-60x = -40 - 12 - 45 - 60
-60x = -157
x = -157/-60
x = 157/60
157/60 + 2/3 - 157/60 + 1/5 = 157/60 - 3/4 - 1
2/3 + 1/5 = 157/60 - 3/4 - 1
40/60 + 12/60 = 157-60 - 45/60 - 60/60
40 + 12 = 157 - 45 - 60
52 = 157 - 105