step by step explanations for the following
g(x)=4x-5
f(x)= -2x-3
find (f•g) (-8)
and problems on the paper numbers 5-8 please
Answers
Answer:
5. [tex]\bold{(g \circ f)(-3) = 16}}[/tex]
6. [tex]\bold{h(h(-3x)) = -12x + 15 }}[/tex]
7. [tex]{\bold{f\left(g\left(x-3\right)\right):\quad 3x-21}}[/tex]
8. [tex]\bold{\text \bold g(f(-3x)) = -36x + 15}}[/tex]
Step-by-step explanation:
These are examples of composite functions.
What is a composite function?
A function by definition is a process that takes a collection of inputs and produces a corresponding collection of outputs in such a way that the process produces one and only one output value for any single input value.
Since we consider a function a process it makes sense to think of two functions acting in sequence to produce a single output. The output from one function is fed into the second function.
A composite function can be written as:[tex](f \circ g)(x)[/tex]The above can also be written as [tex]f(g(x)[/tex]This means the output of function [tex]g[/tex] is fed as input to function [tex]f[/tex]We refer to g as the inner function and f as the outer functionThe evaluation goes from inner to outer so first [tex]g(x)[/tex] is evaluated and the result fed to [tex]f(x)[/tex] as input which produces the composite result
Note that we can have [tex]f[/tex][tex]g[/tex] as the outer function, in which case the notation will be [tex](g \circ f)(x)[/tex] or [tex]g(f(x))[/tex]
Problem Solution
5. [tex]g(x) = x + 3 \;\text and\; f(x) = 3x + 4[/tex]
Find [tex](g \circ f)(-3) = g(f(-3))[/tex]
⇒ 3(3) + 4 = 9 + 4 = 13
Then use this value for [tex]x[/tex] in [tex]g(x) = x + 3[/tex]
⇒ 13 + 3 = 16
[tex]{\boxed{\bold{(g \circ f)(-3) = 16}}[/tex]
6. [tex]h(x) = 2x + 5[/tex]
Find [tex]h(h(-3x))[/tex]
Substitute -3x wherever you see an x
=> 2 (-3x) + 5 => -6x + 5Feed this into h again
h((-3x)) = h(-6x + 5)
= 2(-6x + 5) + 5
= -12x +10 + 5
= -12x + 15
[tex]\\\boxed{\bold{h(h(-3x)) = -12x + 15 }}[/tex]
[tex]7.\;\;\;g\left(x\right)\:=\:x-\:3,\:f\left(x\right)\:=\:3x\:-\:3\\\\\text{Find } \:f\left(g\left(x-3\right)\right)[/tex]
[tex]\mathrm{For}\:g=x-3\:\mathrm{substitute}\:x\:\mathrm{with}\:x-3[/tex][tex]=x-3-3 = x - 6[/tex]
[tex]\mathrm{For}\:f=3x-3\:\mathrm{substitute}\:x\:\mathrm{with}\:x-6[/tex]
[tex]=3\left(x-6\right)-3[/tex]
Simplify to get
[tex]3x-21[/tex]
[tex]\boxed{\bold{f\left(g\left(x-3\right)\right):\quad 3x-21}}[/tex]
.[tex]\bold{8.\;\;g(x) = 3x + 3, f(x) = 4x + 4}\\\\\bold{\text{Find } g(f(-3x))}[/tex]
[tex]\text {For}\:f(x) =4x+4\:\mathrm{substitute}\:x\:\mathrm{with}\:-3x}[/tex][tex]=4\left(-3x\right)+4 =-12x+4[/tex] [tex]\mathrm{For}\:g=3x+3\:\mathrm{substitute}\:x\:\mathrm{with}\:-12x+4[/tex]
[tex]=3\left(-12x+4\right)+3 = -36x+12 + 3 = -36x + 15[/tex]
[tex]\boxed{\bold{\text g(f(-3x)) = -36x + 15}}[/tex]
Related Questions
Balloon
1 reached
a height of X meters.
Balloon
2 reached a height of 7 times balloon 1.
Balloon 3 reached a height of half that of balloon 1.
Balloon 4 reached a height of 30 metres more than balloon 1.
The total height reached by all the balloons was 550 metres.
(a)
Formulate an algebraic expression to model the heights reached by balloons 2, 3
(b)
Find the heights reached by balloons 1, 2, 3 and 4.
Answers
Algebraic expression for Height of Balloon 2 = 7x and Height of Balloon 3 = x/2.
Heights reached by balloons 1, 2, 3 and 4 will be 54.73, 383.11, 27.36, 84.73 respectively.
We have the following given information as per the question
Balloon 1 reaches x m.
Balloon 2 reaches a height of 7 times balloon 1
∴ Balloon 2 reaches 7x m.
Balloon 3 reaches a height of half that of balloon 1.
∴ Balloon 3 reaches [tex] \frac{x}{2} [/tex] m.
Balloon 4 reaches a height of 30 meters more than balloon 1.
∴ Balloon 4 reaches ( x + 30 ) m.
Now As given The total height reached by all the balloons was 550 meters.
∴ Height of Balloon 1 + Height of Balloon 2 + Height of Balloon 3 + Height of Balloon 4 = 550 meter
∴ x + 7x + [tex] \frac{x}{2} [/tex] + (x + 30 ) =550
∴ 9.5x + 30 = 550
∴ 9.5x = 550 - 30
∴ 9.5x = 520
∴ x = 520/9.5
∴ x = 54.73 meter
(a) Algebraic expression to model the heights reached by balloons 2, 3 will be
Height of Balloon 2 = 7x = 7(54.73) = 383.11 meter
Height of Balloon 3 = x/2 = 54.73 / 2 = 27.36 meter
(b) The heights reached by balloons 1, 2, 3 and 4 will be as follows
Height of Balloon 1 = x = 54.73 meter.
Height of Balloon 2 = 7x = 7(54.73) = 383.11 meter
Height of Balloon 3 = x/2 = 54.73 / 2 = 27.36 meter
Height of Balloon 4 = x + 30 = 54.73 + 30 = 84.73 meter
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Miguel pays $68 biweekly for health insurance which is 14% of the total cost his employer pays the rest what is the total annual cost to the nearest dollar of Miguel's health insurance
Answers
Cost of the health insurance is $11657.14
What is cost?
A cost is the worth of money that has been used up to create something or supply a service and is thus no longer accessible for use in production, research, retail, or accounting. In business, the cost might be one of acquisition, in which case the money spent to obtain it is recognized as cost. In this situation, money is the input that is used to purchase the item. This acquisition cost might be the total of the original producer's production expenses and the acquirer's additional transaction costs over and above the amount paid to the producer. Typically, the price includes a profit margin above the cost of manufacture.
14% of x = 68
x = 68 x 100/14
= $485.71
Total cost = $485.71 x 24 months = $11657.14
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = -x + 7.
X
0
3
6
9
y
5
6
7
8
X
-6
-3
0
3
y
9
8
7
6
The equation that represents the other equation is y=
The solution of the system is (
)
4
X +
Reset
Next
Answers
y = 1 / 3 x + 5 is the linear equation for the first table.
The system of equations' answer is (3, 6).
Linear Equation: What Is It?A linear equation is an algebraic equation of the form y= mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."
based on the available facts;
Equation of a point slope:
y = mx + b,
where m = slope and b = y-intercept
As a result, the equation for the second table is y = - 1 /3 x + 7.
With the help of the table's (0, 5)(3, 6) values, the equation for the first table may be solved. Therefore,
m = 6 - 5 / 3 - 0 = 1 / 3
let's find b using (0, 5)
5 = 1 / 3(0) + b
b = 5
Therefore, the equation of the first table is as follows:
y = 1 / 3 x + 5
The solution to the system of equation can be calculated as follows:
y + 1 /3 x = 7
y - 1 / 3 x = 5
2y = 12
y = 12 / 2
y = 6
6 - 1 / 3 x = 5
- 1 / 3 x = 5 - 6
- 1 / 3 x = - 1
x = 3
Therefore, the solution to the system of equation is (3, 6)
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Brian is working his way through school. He works two part-time jobs for a total of 22 hours a week. Job A pays $6.10 per hour, and Job B pays $7.30 per hour. How many hours did he work at each job the week that he made $148.60.
Answers
Let a be the number of hours that Brian works at Job A in one week and b be the number of hours that he works at Job B .in one week
Since Brian worked 22 hours per week and he made $148.60, we can set the following system of equations:
[tex]\begin{gathered} a+b=22, \\ 6.10a+7.30b=148.60. \end{gathered}[/tex]Subtracting b from the first equation we get:
[tex]\begin{gathered} a+b-b=22-b, \\ a=22-b\text{.} \end{gathered}[/tex]Substituting the above equation in the second one we get:
[tex]6.10(22-b)+7.30b=148.60.[/tex]Applying the distributive property we get:
[tex]\begin{gathered} 6.10\times22-6.10\times b+7.30b=148.60, \\ 134.20+1.20b=148.60. \end{gathered}[/tex]Subtracting 134.20 from the above equation we get:
[tex]\begin{gathered} 134.20+1.20b-134.20=148.60-134.20, \\ 1.20b=14.40. \end{gathered}[/tex]Dividing the above equation by 1.20 we get:
[tex]\begin{gathered} \frac{1.20b}{1.20}=\frac{14.40}{1.20}, \\ b=12. \end{gathered}[/tex]Substituting b=12 in a=22-b we get:
[tex]a=22-12=10.[/tex]Answer:
Mom and Dad have decided to put themselves on a strict budget so that the family can save money to go onvacation. For breakfast, the family decides to spend no more than $20.00 for the week.Each day, the family eats 1/3 of a pound of granola and drinks 2/7 of a liter of milk for breakfast.Milk costs $4,49 per liter, but different types of granola have different prices.If the family only buys one type of granola for the week, what is the price per pound of the most expensivegranola they can afford?Explain your solution using logic, tables, graphs, and/or algebraic reasoning.
Answers
For breakfast, the family decides to spend no more than $20.00 for the week.
Each day, the family drinks 2/7 of a liter of milk for breakfast.
For the entire week, the amount of milk consumed is
[tex]7\times\frac{2}{7}=2\; \text{liters}[/tex]Milk costs $4,49 per liter, so the cost of the total amount of milk consumed is
[tex]2\times\$4.49=\$8.98[/tex]So, the amount left for the granola is
[tex]\$20.00-\$8.98=\$11.02[/tex]Each day, the family eats 1/3 of a pound of granola for breakfast.
For the entire week, the amount of granola consumed is
[tex]7\times\frac{1}{3}=\frac{7}{3}\; \text{pounds}[/tex]Let x be the price per pound of the most expensive granola they can afford.
[tex]\begin{gathered} \frac{7}{3}\cdot x=\$11.02 \\ x=\$11.02\cdot\frac{3}{7} \\ x=\$4.72 \end{gathered}[/tex]Therefore, the most expensive granola they can afford is $4.72
Gabe is paid semi monthly and contributes 9% of the total cost of his individual healthcare coverage he pays $48.47 per paycheck towards this contribution what is the total value of Gabes healthcare coverage for the year
Answers
Cost of the health insurance is $12925.33
What is cost?
A cost is the worth of cash that has been used up to create it or supply a function and is thus no longer accessible for use in manufacturing, research, commerce, or bookkeeping. In business, the cost might be one of procurement, in which case the money being spent to obtain it is recognized as cost. In this situation, money is the input that is used to purchase the item. This acquisition cost might be the total of the original producer's production expenses and the acquirer's direct capital costs above and beyond the amount paid to the producer. Typically, the package includes a gross margin above the cost of manufacture.
9% of x = 48.47
x = 48.47 x 100/9
= $538.55
Total cost = $538.55 x 24 months = $12925.33
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The product of two irrational numbers is an irrational number
a.True
b.False
Answers
False, The product of two irritational numbers is either rational or irrational numbers.
A rational number is a number expressed in the form of p/q where p and q are integers and q should not be zero. Example: 2/5, 24
Whereas an irrational number is a number that is not rational in nature means it neither be expressed in the form of p/q nor in ratio terms. Example: √12, √3
Product of two irrational numbers: √2* √2 = 4 (which is a rational number)
Product of again two irrational numbers: √2*√3= √6 ( which is an irrational number)
Therefore, the product of two irrational numbers can be rational or irrational numbers.
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The product of two irrational numbers is an irrational number is false because it is either a rational or irrational number.
What is a rational number?A rational number is defined as a numerical representation of a part of a whole that represents a fraction number.
It can be a/b of two integers, a numerator a, and a non-zero denominator b.
The product of two irrational numbers √3 ×√3 = 3
This is a rational number.
Again, the product of two irrational numbers: √5 ×√3 = √15
This is an irrational number.
As a result, the product of two irrational integers can be both rational and irrational.
Thus, the product of two irrational numbers is an irrational number is false because it is either a rational or irrational number.
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Urgenttt!!!!!!!!!!!!!
Which of the following expressions is accurate for angle 8 that intersects the unit circle at point (-0.949, 0.314).
Answers
Cos(0) = - 0.949 this expression is accurate for the unit circle which is intersected at point by angle 8 according at point (-0.949, 0.314).
What is circle ?An elliptical plane figure is a circle. From a fixed location known as the circle's center, each point on the circle is equally distant. It has a two-dimensional (2D) shape and a radius value. The Latin word "circulus" (which means little ring) is the root of the English word "circle."A circle is a two-dimensional shape that is made up of a collection of points that are spaced out from the center of the circle (its fixed point) on the plane by a fixed or constant distance (radius). The radius of a circle is the fixed distance between points that is fixed from the fixed point, which is known as the origin or center of the circle.
The terminal side of angle 0 intersects the unit circle at point P(- 0.949, 0.314) That means, OQ = 0.949 and PQ = 0.314
Here, OP is the radius of the unit circle. So, OP = 1
In respect of angle 0, the adjacent side is OQ and the hypotenuse is OP.
We know that,
cos= [tex]\frac{adjacent}{hpotenusey}[/tex]
So,
cos(0) = - [tex]\frac{OQ}{OP}[/tex] [As the angle is in quadrant II, so cos is negative]
cos(0) = - [tex]\frac{-0.949}{1}[/tex]
cos(0) = - 0.949
Cos(0) = - 0.949 this expression is accurate for the unit circle which is intersected at point by angle 8 according at point (-0.949, 0.314).
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factorise 3^2-16x +5
Answers
Answer:
3²- 16x +5
9-16x+5
-16x+9+5
-16x + 14
Step-by-step explanation:
I hope this will be helpful for you.
Tickets for the monster truck rally cost $12 for children and $20 for adults. Last
night 400 total tickets were sold for a total of $6000. Use c for the child tickets and
a for adult tickets. If one of the equations for this system is a + c = 400, write
the second equation for this system below.
Answers
Answer:
20a + 12c = 6000
Step-by-step explanation:
a = adult tickets
c = child tickets
$20 for adults, $12 for children, for a total of $6000
20a + 12c = 6000
a + c = 400
QUESTION DOWN BELOW PLEASE HELP!! ITS DUE SOON!
Answers
The unknown angles of the triangle and trapezium are as follows:
∠1 = 110°, ∠2 = 40°∠1 = 120°, ∠2 = 60°How to find angles in a triangle and trapezium?A triangle is a polygon with three sides.
The sum of angles in a triangle is 180 degrees.
Therefore, angle 1 can be found as follows:
∠1 = 180 - 40 - 30
∠1 = 180 - 70
∠1 = 110 degrees.
Therefore, angle 2 can be found as follows:
∠2 = 180 - 40 - 40 - 30 - 30
∠2 = 180 - 80 - 60
∠2 = 180 - 140
∠2 = 40 degrees.
A quadrilateral is a polygon with 4 sides. The sum of angles in a quadrilateral is 360 degrees.
Therefore, the triangle in the trapezium is an isosceles triangle. The base angles are equal.
Hence,
∠1 = 180 - 30 - 30
∠1 = 180 - 60
∠1 = 120 degrees
Sum of angles in the same transversal is supplementary.
Therefore,
90 + 30 + ∠2 = 180
∠2 = 180 - 120
∠2 = 60 degrees
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Use substitution to find the solution to the system ofequation.-4x + y = 6-5x – y = 21
Answers
Let:
[tex]\begin{gathered} -4x+y=6_{\text{ }}(1) \\ -5x-y=21_{\text{ }}(2) \end{gathered}[/tex]From (1), solve for y:
[tex]y=6+4x_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} -5x-(6+4x)=21 \\ -5x-6-4x=21 \\ -9x-6=21 \\ -9x=21+6 \\ -9x=27 \\ x=\frac{27}{-9} \\ x=-3 \end{gathered}[/tex]Replace the value of x into (3):
[tex]\begin{gathered} y=6+4(-3) \\ y=6-12 \\ y=-6 \end{gathered}[/tex]Circle whether the point is a solution to the inequality. Show work to support the answer.y ≤ 1/3x + 4 is (-6,2) a solution?Yes/No
Answers
Answer:Explanation:
Yes
The point is a solution if it satisfies the inequality.
In this case, the inequality is y ≤ (1/3)x + 4, so replacing (x, y) = (-6, 2), we get:
y ≤ (1/3)x + 4
2 (1/3)(-6) + 4≤
2 ≤ -2 + 4
2 ≤ 2
Since 2 is equal to 2, the inequality is satisfied and (-6, 2) is a solution.
So, the answer is Yes.
I need help on this question please and thank you
Answers
It is proved that the line c is parallel to line d.
What is defined as the supplement angles?If two angles add up to 180 degrees, they are described as supplementary angles. When supplementary angles are combined, they establish a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Supplementary angles can be either adjacent or not. As a result, there are two kinds of supplementary angles. Every one of these kinds of supplementary angles is discussed further below.supplementary angles adjacentNon-contiguous supplementary anglesFor the given question;
Angle 2 and angle 3 are supplement;
∠2 + ∠3 = 180 ......eq 1
See from figure.
∠4 = ∠3 (vertically opposite angles)
Thus, replacing ∠3 with ∠4 in eq 1.
∠2 + ∠4 = 180 (linear pair)
As ∠2 and ∠4 form the linear pair. Thus, line c is parallel to line d.
Therefore, line c proved to be parallel to line d.
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assume that each of the n trails
Answers
Given,
The value of n is 8.
The value of x is 0.
The value of p is 0.6.
The binomial expression is,
[tex]P(X=x)=^nC_x\times(p)^x\times(1-p)^{n-x}[/tex]Subsituting the values then,
[tex]\begin{gathered} P(X=0)=^8C_0\times(0.6)^0\times(1-0.6)^{8-0} \\ P(X=0)=\frac{8!}{0!\times8!}\times1\times(0.4)^8 \\ P(X=0)=1\times1\times(0.4)^8 \\ P(X=0)=0.000655 \\ P(X=0)=0.0007 \end{gathered}[/tex]ence, the probability is 0.0007.
how do you solve this?
Answers
According to the given values, the length of the arc is 1 cm approx.
What is an arc?An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. A graph arc is an ordered pair of adjacent vertices in a graph. An arc is specifically any section of a circle's circumference (other than the entire curve).So, the formula to find the length of the arc:
Arc Length = θ × (π/180) × rNow, substitute the values in the formula as follows:
Arc Length = θ × (π/180) × rArc Length = 8π/9 × (π/180) × 16.5Arc Length = 8π/9 × π/180 × 16.5Arc Length = 2π/9 × π/45 × 16.5Arc Length = 2π × π/45 × 1.8Arc Length = 6.28 × 3.14/45 × 1.8 (π = 3.14)Arc Length = 11.304 × 3.14/45Arc Length = 1.256 × 3.14/5Arc Length = 3.94384/5Arc Length = 0.788768Rounding off: 1.00 cmTherefore, according to the given values, the length of the arc is 1 cm approx.
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Four friend must give a 7 minute presentation.each friend must speak for an equal amount of time. How long will each friend speak?
Answers
Answer:
1 minute and 75 seconds
Step-by-step explanation:
you take 4 and divide it by 7 minutes there for getting 1.75
What is the correct evaluation of 3x - x + 2, when x is equal to -4?
Answers
Answer:
When x = -4, the equation's answer is -6.
Hope this helps!
Step-by-step explanation:
3(-4) - ( -4 ) + 2
-12 - (-4) +2 ( negative times negative is positive )
-12 + 4 + 2
-8 + 2 or -12 + 6
is -6
Chef Kim baked his famous casseroles for a company holiday party. The casseroles had different shapes and different delicious fillings. Spinach Cheese Rectangle 3 8 Circle 3 4 What is the probability that a randomly selected casserole is shaped like a rectangle giver that the casserole is filled with spinach? Simplify any fractions.
Answers
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
[tex]P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]then
Step 1
Let
rectangle filled with spinach= favorable outcomes=3
total outcomes= total casseroles= 3+8+3+4=18
Now, replace.
[tex]\begin{gathered} P=\frac{favorable\text{ outcomes}}{\text{total outcomes}} \\ P=\frac{3}{18} \\ P=0.1666 \\ \text{rounded} \\ P=0.17 \end{gathered}[/tex]therefore, the answer is 0.17
I hope this helps you
6. The following observations are arranged in ascending order. The median of the data is 25 find the value of x. 17, x, 24, x + 7, 35, 36, 46 (3 Points)
Answers
The value of x = 18.
What is median?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Median = [tex]\frac{n+1}{2} ^{th}[/tex] term
Given that,
The median of the data is 25.
The observations are 17, x, 24, x+7, 35, 36, 46.
Here, n = 7
Median = 25
Median = [tex]\frac{7+1}{2} ^{th}[/tex] term
Median = [tex]\frac{8}{2}^{th}[/tex] term
Median = 4[tex]^{th}[/tex] term
Median = x+7
25 = x+7
X = 25-7
X = 18
Here, x+7
X+7 = 18+7
X+7 = 25.
Therefore, the value of x is 18.
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On a coordinate plane, a graph curves up through (negative 2, negative 5) to inflection point (0, 1), and then curves up through (1, 4). Consider the graph shown. Which ordered pairs are on the inverse of the function? Check all that apply.
Answers
The ordered pairs are on the inverse function are (-5, -2) and (4, 1)
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the ordered pairs on the inverse of the function?From the question, we have the following coordinate points
Point (negative 2, negative 5)Inflection point (0, 1)Curves up through (1, 4)Rewrite the points as:
Point (-2, -5)Inflection point (0, 1)Curves up through (1, 4)Remove the inflection point.
So, we have
Point (-2, -5)Curves up through (1, 4)The next step is to switch/swap the positions of x and y in the above equation ordered pairs
So, the points become:
Inverse point (-5, -2)Another inverse point (4, 1)Hence, the ordered pairs that are on the inverse function of the function are (-5, -2) and (4, 1)
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Answer:
its
A(-5,-2),
B(0,-1),
E(1,0),
F(4,1).
Step-by-step explanation:
i took one for the team
Find the area of a rectangle that is 2 7/9 m long and 4 4/5 m wide. Enter your answer as a mixed number and reduce if possible.
Answers
Answer:
13 ⅓.
Step-by-step explanation:
The area of a rectangle is given by
Area = Length × Breadth
Length = 2 7/9 = 25/9 and breadth = 4 4/5 = 24/5
.: Area = 25/9 × 24/5 = 600/45 (15 can go to both the numerator and denominator)
We have 40/3 but to convert it to a mixed fraction we get 13 ⅓ as your area.
6.07 X 10^7 in standard form
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6.07 \times 10^7}\\\mathsf{= 6.07(10^7)}\\\mathsf{= 6.07(10\times10\times10\times10\times10\times10\times10)}\\\mathsf{= 6.07(100\times100\times100\times10)}}\\\mathsf{= 6.07(10,000\times1,000)}\\\mathsf{= 6.07(10,000,000)}\\\mathsf{= 60,700,000 \rightarrow 6.07\times 10^7}\\\\\huge\text{Therefore, your answer should be: }\boxed{\mathsf{60,700,000}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The mean of the values in a data set is b. If each of the values in the data set
were multiplied by 8, what would be the mean of the resulting data?
A. 9b
B. 7b
C. b
D. 8b
Answers
Answer:
The answer is D.
Step-by-step explanation:
I hope 'm not too late answer your question good luck.
find two rational numbers lying between 1 and 1.2
Answers
Answer:
1.1 and 1.12
Step-by-step explanation:
a rational number is any number that can be written as a fraction or a decimal that does not go on forever (unless it is a repeating decimal, ex: 3.454545..)
so any decimal that can be written as a fraction that is between 1 and 1.2 works
Write in all missing angles.
Answers
Answer:
The answers are all there. 50° + 22°= 77°
180° - 77° = 103°
Step-by-step explanation:
All the rest is just mirrored.
[tex]\sqrt{6} +2\sqrt{3} +\sqrt{12}[/tex]
Answers
[tex] = \sqrt{6} + \sqrt{12} + \sqrt{12} \\ \\ = \sqrt{6} + 2 \sqrt{12} \\ = \sqrt{6} + 2 \sqrt{4 \times 3} \\ = \sqrt{6} + 2 \times \sqrt{4} \times \sqrt{3} \\ = \sqrt{6} + 2 \times 2 \sqrt{3} \\ = \sqrt{6} + 4 \sqrt{3} [/tex]
ATTACHED IS THE SOLUTION
Find the midpoint of the segment with the following endpoints.
(9, 2) and (5,5)
Answers
Answer:
(7,3.5)
Step-by-step explanation:
Midpoints
x = (x1 + x2)/2 = (9 + 5)/2 = 14/2 = 7
y = (y1 + y2)/2 = (2 + 5)/2 = 7/2 = 3.5
Use Gaussian elimination or Gauss-Jordan elimination.
Mike works a total of 58 hr per week at his two jobs. He makes $7 per hour at job A and $8 per hour at job B. If his total
pay for one week is $424 before taxes, then how many hours does he work at each job?
Answers
Mike works 40 hours at job A and 18 hours at job B.
What are simultaneous equations?Simultaneous equations are two or more algebraic equations that share the same unknown variables and have the same solution for each of them. This suggests that the equations are simultaneous and have a single solution.
Given:
Mike makes $7 per hour at job A and $8 per hour at job B.
Let x be the number of hours Mike spends working at job A and y be the number of hours he spends working at job B.
Since he works a total of 58 hours per week,
x + y = 58
His total pay for one week is $424.
7x + 8y = 424
Solving both equations simultaneously we get,
From the first equation, we have, y = 58 - x
Putting the value of y in the second equation,
7x + 8(58 - x) = 424
7x + 464 - 8x = 424
8x - 7x = 464 - 424
x = 40
So, now calculate y = 58 - 40 = 18
Therefore, Mike spends 40 hours working at job A and 18 hours working at job B.
To learn more about simultaneous equations visit:
https://brainly.com/question/12647791
#SPJ9
The graph of a 3rd degree polynomial is shown below. Use the Fundamental Theorem of Algebra to determine the number of real and imaginary zeros.
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\texttt{real roots : 2 }[/tex]
[tex]\qquad \tt \rightarrow \: imaginary \: \: roots = 1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given polynomial is a 3rd degree polynomial so it has a total of three roots.
And we know, where the curve (of polynomial) cuts the x - axis is its real root. so, from the graph we can infer that the given polynomial has 2 real roots [ as it cuts the x - axis at two points, i.e x = -2 and x = 1 ]
Hence, Number of real roots = 2
Number of imaginary roots = total roots - real roots
i.e 3 - 2 = 1
So, number of imaginary roots = 1
Answered by : ❝ AǫᴜᴀWɪᴢ ❞