Looking at f(x) and g(x), we can see that g(x) is made by f(x) multiplied by -6.
Since the function was multiplied by a negative value, that means we had a reflection over the x-axis.
Also, if the function was multiplied by a constant value, that means we had a vertical stretch by a factor equal to the absolute value of the constant.
Therefore the correct options are A and D.
I'll be there tomorrow thank you so very sweet for the reminder of my day
we are told to complete the tables using the same ratio. To do that we need to multiply each number in the upper row by the same number to get the number in the lower row. Or divide the same number in the lower row to get the number in the upper row. In the case of table 4 we have that in the first column the numbers:
[tex]\begin{gathered} 1 \\ 9 \end{gathered}[/tex]Therefore, we need to multiply the number in the first row by 9, to get the number in the lower row. Therefore, for the second column we have:
[tex]\begin{gathered} 3 \\ 27 \end{gathered}[/tex]Since 9x3 = 27. In the third column:
[tex]\begin{gathered} 5 \\ 45 \end{gathered}[/tex]Since 9x5 = 45. In the fourth row:
[tex]\begin{gathered} 7 \\ 63 \end{gathered}[/tex]Since 9x7=63. In the final row:
[tex]\begin{gathered} 9 \\ 81 \end{gathered}[/tex]Since 9x9 = 81. And thus we complete the table.
The complete table would be:
[tex]\begin{bmatrix}{1} & 3 & {5} \\ {9} & {27} & {45} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{7} & {9} & {} \\ {63} & {81} & {} \\ {} & {} & {}\end{bmatrix}[/tex]
An ice cream shop owner's business assets and liabilities are listed below. Owned Inventory $32,500 Cash $75,420 Building Mortgage $154,265 Savings Account $25,000 Owned Equipment $15,670 Small Business Loan $15,652 Other Debt $1,235 Accounts Receivable $12,540 Property Value $125,768 What is the total value of the ice cream shop owner's business assets? $125,768 $171,152 $274,358 $286,898
The total value of the ice cream shop owner's business assets is D. $286,898.
What are business assets?Business assets are the value of the assets of the Ice Cream Shop.
Business assets are distinct from the owner's assets.
The business assets consist of liabilities (amounts owed outsiders) and equity (the difference between assets and liabilities).
Business Assets:Owned Inventory $32,500
Cash $75,420
Savings Account $25,000
Owned Equipment $15,670
Accounts Receivable $12,540
Property Value $125,768
Total assets = $286,898
Business Liabilities:Small Business Loan $15,652
Other Debt $1,235
Building Mortgage $154,265
Total liabilities = $171,152
Equity = $115,746 ($286,898 - $171,152)
Thus, the business assets for this ice cream shop are worth Option D.
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For which intervals is the function negative?Select each correct answer. (4,∞)(−1.5,4.2)(1,4)(−2.5,2.5)(−3,1)(−∞,−3)
Answer:
(−∞,−3)
(1,4)
Explanation:
To find the interval where the function is negative, we would look at the regions on the graph where the values of y are negative. The required intervals are the values of x in those regions. Looking at the graph,
On the left, the values of y are negative between x = - infinity and x = - 3
On the right, the values of y are negative between x = 1 and x = 4
Thus, the correct options are
(−∞,−3)
(1,4)
Answer:
(−3, 1) and (4, ∞)
Step-by-step explanation:
your grade must be at least 64 to pass this class g least 64 g least or equal to 64 g greater 64 g greater equal 64
The given statement is your grade must be at least 64 to pass this class.
The inequality that represents this situation is
[tex]g\ge64[/tex]order the fractions from greatest to least 4/5,2/3,13/15,7/9
The fractions arranged from greatest to least are- 13/15, 4/5, 7/9, 30/45
Here, we are given 4 fractions- 4/5, 2/3, 13/15, 7/9
In order to compare them, let us equalize their denominators.
The denominators are- 5, 3, 15 and 9
The LCM of 5, 3, 15 and 9 is 45
Thus, we can write the fractions as-
4/5 = (9*4)/(5*9) = 36/45
2/3 = (2*15)/(3*15) = 30/45
13/15 = (13*3)/(15*3) = 39/45
7/9 = (7*5)/(9*5) = 35/45
Now, we can easily compare the fractions by comparing their numerators.
We see that-
39 > 36 > 35 > 30
Thus, 13/15 > 4/5 > 7/9 > 30/45
Hence, the fractions arranged from greatest to least are- 13/15, 4/5, 7/9, 30/45
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Which number line
represents the solution to 5+8x < 3(2x+4)
Answer:
x < 3 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I cannot see a number line, but the solution can be found by:
5 + 8x < 3(2x+4) Distribute the 3
5 + 8x < 6x + 12 Subtract 6x from both sides
5 + 2x < 12 Subtract 5 from both sides
2x < 7 Divide both sides by 2
x < [tex]\frac{7}{2}[/tex]
or
x < 3[tex]\frac{1}{2}[/tex] This means that all of the numbers less than 3 1/2 are answers.
I need help with something
Answer:
S'(-2, 6)
Explanation:
Translating a point to the right, meaning adding to the x-coordinate
Rearrange x = 3g + 2 to make g the subject.
g = 1/3 x - 2/3 is a function of g .
In the simplest terms, what is a function?
A relationship between a group of inputs and one output each is referred to as a function. A function, expressed simply, is an association between inputs where each input is connected to one and only one output. A domain, codomain, or range exists for every function.x =3g + 2
Switch sides:
3g + 2 = x
Take away 2 from both sides:
3g = x - 2
Divide both sides by 3:
g = 1/3 x - 2/3
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Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the button on your calculator to solve. 8 mi. 5 mi. Volume of the cylinder = mi3
Write out the volume of a cylinder shown below
Formula
[tex]\begin{gathered} \text{Volume of a cylinder = }\Pi r^2\text{ h} \\ where\text{ radius = 5mi , height = 8mi , }\Pi\text{ = 3.142} \\ \text{Volume of a cylinder = }3.142x(5)^2x8 \\ V=628.4mi^3 \\ ThereforeVolumeofthecylinder=628.4mi^3\text{ (nearest tenth)} \end{gathered}[/tex]Hence the volume of the figure = 628.4mi³
Consider functions f and g.
The correct option regarding the multiplication of the functions f(x) and g(x) is given by:
C. [tex](f \times g)(x) = \frac{x^2 + 6x + 8}{x^2 + 2x - 15}, x \neq -5, x \neq 3[/tex]
Multiplication of functionsTo multiply two rational functions, we multiply the numerators of each function and the denominator of each function to generate the rational functions.
In the context of this problem, before multiplying the functions, we can simplify them.
Function f(x) is given by:
[tex]f(x) = \frac{x^2 - 16}{x^2 + 3x - 10}[/tex]
The numerator and the denominator can be simplified as follows:
Numerator: (x + 4)(x - 4): applying subtraction of perfect squares.Denominator: (x + 5)(x - 2): due to it's roots.Function g(x) is given by:
[tex]g(x) = \frac{x^2 - 4}{x^2 - 7x + 12}[/tex]
The numerator and the denominator can be simplified as follows:
Numerator: (x + 2)(x - 2): applying subtraction of perfect squares.Denominator: (x - 3)(x - 4): due to it's roots.Then the multiplication function is:
[tex](f \times g)(x) = \frac{(x + 4)(x - 4)}{(x + 5)(x - 2)} \times \frac{(x + 2)(x - 2)}{(x - 3)(x - 4)}[/tex]
The common terms (x - 4) and (x - 2) are simplified, hence the function is given by:
[tex](f \times g)(x) = \frac{x + 4}{x + 5} \times \frac{x + 2}{x - 3} = \frac{x^2 + 6x + 8}{x^2 + 2x - 15}[/tex]
Hence option C is correct, with x = -5 and x = 3 being removed from the function due to the fact that they are the zeros of the denominator.
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What is the image point of (-2,-3) after a translation right 2 units and up 4 units?
Marsha buys 3 pounds of cheddar cheese and some Swiss cheese Both cheeses cost $450 per pound. The total cost is $24.75. How many pounds of Swiss cheese did Marsha buy?
Let x represent the number of pounds of Swiss cheese that Marsha bought.
We were told that Marsha buys 3 pounds of cheddar cheese and some Swiss cheese Both cheeses cost $450 per pound. This means that the cost of 3 pounds of cheddar cheese is 3 * 4.50 = 13.5
Also, the cost of x pounds of Swiss cheese is 4.5 * x = 4.5x
If the total cost is $24.75, it means that
4.5x + 13.5 = 24.75
The equation is
4.5x + 13.5 = 24.75
We would solve for x. Thus,
4.5x = 24.75 - 13.5
4.5x = 11.25
x = 11.25/4.5
x = 2.5
Thus, she bought 2.5 pounds of Swiss cheese
How many terms are inthe followingexpression?3x + 4 + a + 6y
When talking about algebraic expressions, each term is limited by + or - signs. It means a term is located between two addition or substraction signs, except for the first and the last ones.
In the given expression there are 4 terms:
3x
4
a
6y
Each one is separated from another for + signs.
Hi guys.I was sick today and I’m still not feeling good.I missed out on class and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
x = 11
Step-by-step explanation:
(9x - 5) + (6x + 20) = 180
15x + 15 = 180
15x + 15 -15 = 180 -15
15x = 165
15x/15 = 165/15
x = 11
Help me out please please
The statement that the graph y = 2x² - 4x - 2 has a y-intercept of (0, 2) is false.
How to find y-intercept of a graph?The y-intercept is the point where a graph crosses the y-axis.
In simple terms, it is the value of y when x = 0.
Therefore, the graph is express as follows:
y = 2x² - 4x - 2
Let's check when x = 0
Therefore,
y = 2x² - 4x - 2
y = 2(0)² - 4(0) - 2
y = 2(0) - 4(0) - 2
Therefore,
y = 0 - 2
y = -2
The statement is false that the y-intercept of the graph is (0, 2)
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For f(x) = -6x-2, find the rate of change on the interval [-2, 4].
The most appropriate choice for rate of change will be given by -
Rate of change of f(x) = -6x -2 on the interval [-2, 4] = -6
What is rate of change of a function?
Rate of change of a function represents the rate at which the value of one quantity changes with change in the value of other quantity.
Here,
f(x) = -6x - 2
[tex]f^{'} (x) = \frac{d}{dx}(-6x - 2)\\[/tex]
[tex]= -6[/tex]
[tex]f^{'} (x)[/tex] represents rate of change
Rate of change of f(x) = -6x -2 on the interval [-2, 4] = -6
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What is the slope of the following equation? -3y-x=0
Given the equation
[tex]-3y-x=0[/tex]To determine the slope, first write the equation in slope-intercept form (y=mx+b)
[tex]\begin{gathered} -3y-x=0 \\ -3y=x \\ y=-\frac{1}{3}x \end{gathered}[/tex]The slope corresponds to the coefficient multiplying x.
For this equation the slope is equal to -1/3.
Does someone mind helping me please?
The proportion used to find the missing side is RS/QS = RO/PQ, the value of y = 12ft
First we need to see whether triangle RQS is similar with triangle RPO
Angle QRS = Angle PRQ (common angle)
Angle RSQ = ROP (Given, that they are right angles)
So, triangle RQS is similar with triangle RPO
Now the sides of one triangle is in proportion with the other
RS/RO = RQ/RP = QS/PQ
RS/RO = QS/PQ
RS/QS = RO/PQ
9/12 = y/16
3/4 = y/16
3/y = 4/16
3/y = 1/4
y = 4 x 3
y = 12
To find the missing side the proportion used is RS/QS = RO/PQ, the value of y = 12ft
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Hi guys.I was sick on Friday and I don’t understand the work.I watched all my teachers videos and still don’t understand.I’ll be giving out 10 points to whoever helps.
What is the sum of the polynomials?(8x2-9y2-4x)+(x2-3y2–7x)7x2 - 6y2 + 3x9x2 - 6y2+3x9x2 - 12y2 + 3x9x2 - 12/2 - 11x
Let's simplify the following expression:
[tex]\text{ (8x}^2-9y^2-4x)+(x^2-3y^2-7x)[/tex]We get,
[tex]\text{ (8x}^2-9y^2-4x)+(x^2-3y^2-7x)[/tex][tex]\text{ 8x}^2-9y^2-4x+x^2-3y^2-7x[/tex]Let's put like terms beside each other and proceed with the operation:
[tex]\text{ 8x}^2-9y^2-4x+x^2-3y^2-7x[/tex][tex]\text{ 8x}^2+x^2-9y^2-3y^2-7x-4x[/tex][tex]\text{ (8x}^2+x^2)+(-9y^2-3y^2)+(-7x-4x)[/tex][tex]\text{ (9x}^2^{})+(-12y^2)+(-11x)[/tex][tex]\text{ 9x}^2-12y^2-11x[/tex]Therefore, the sum of the given polynomials (8x^2-9y^2-4x)+(x^2-3y^2–7x) is 9x^2 - 12y^2 - 11x.
The answer is letter D.
Which of the following equations below is a linear inequality?
Inequality occurs when a non-equal comparison is made between two mathematical expressions or two numbers.
Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1.
Of the options, the only one that represents a linear inequality is:
[tex]yThe FIRST OPTION is correct.the first answer is correct
What is 24 divided by 1200 in long division
Answer:
50
Step-by-step explanation:
First you'll want to start off with the 3 main numbers "120" so divide that by 24 and you'll get 5 after bringing that up you want to multiply 5 by 25 and you'll get 120 then you want to minus the original 120 by it and you'll get 0 which after that you'll want to bring the other 0 down that you did nothing to and divide it by 24 which will get you 0 and bring that up and then you got your answer
Right triangle GEO has right angle E.The length of segment EO is 10 and the length of segment OG is 15.Find the measure of angle G.
Solution
- The sketch of the triangle is given below:
- To solve for the angle [tex]\begin{gathered} \sin\angle G=\frac{Opposite}{Hypotenuse}=\frac{10}{15} \\ \\ \angle G=\sin^{-1}(\frac{10}{15}) \\ \\ \\ \angle G=41.81031489...\approx41.81\degree \end{gathered}[/tex]
Final Answer
The answer is 41.81
2. Solve each problem in two different ways as modeled in the example,Example; } x 6 = ?---&*6=zmedena. x 164x 16Kb. x12fx 12
Let's begin by listing out the given information:
[tex]\begin{gathered} \frac{2}{3}\cdot6=\frac{2\cdot6}{3}=\frac{12}{3}=4 \\ \frac{2}{3}\cdot6=2\cdot\frac{6}{3}=2\cdot2=4 \\ \\ \frac{3}{4}\cdot16=\frac{3\cdot16}{4}=\frac{48}{4}=12 \\ \frac{3}{4}\cdot16=3\cdot\frac{16}{4}=3\cdot4=12 \\ \\ \frac{4}{3}\cdot12=\frac{4\cdot12}{3}=\frac{48}{3}=16 \\ \frac{4}{3}\cdot12=4\cdot\frac{12}{3}=4\cdot4=16 \end{gathered}[/tex]I need help putting these from greatest to least 20.22.00220.0220
EXPLANATION:
The correct order is as follows:
2.002
20.2
20.02
20
The previous order is due precisely to the location it would have on the number line, in the case of whole numbers with decimals, the decimals that immediately follow the whole number must be compared to know which is the greater of the two.
This is a two part question just need help figuring out what exactly it is I need to mark up for the first section up on top and also on the second part of it I need help figuring out if both triangles are congruent and if they are need help stating the congruency
Given the triangles CDE and JLM
For the triangles we have the following:
1) CD = JL
2) CE = JM
3) DE = LM
So, there 3 pairs of congruent sides
So, the triangles are congrurent by S.S.S ( Side-Side-Side) postulate
C is corresponding to J
D is corresponding to L
E is corresponding to M
So,
[tex]\triangle\text{CDE}\cong\triangle\text{JLM}[/tex]For marking the triangles, see the following figure:
Find the missing value. X 5 3 3 6 equal
Similar triangles
The image provided with the question shows 3 similar triangles. The lines of length a, m, and 5 are parallel, so the lengths are proportional
The proportionality can be written as:
[tex]\frac{3}{2}=\frac{3+6}{2+4}=\frac{3+6+3}{x+4+2}[/tex]Operating:
[tex]\frac{3}{2}=\frac{9}{6}=\frac{12}{x+6}[/tex]The first two parts of the equalities are the same fraction (when simplified). We can use the last and the first one to find x:
[tex]\frac{3}{2}=\frac{12}{x+6}[/tex]Cross-multiplying:
3(x + 6) = 2*12
Dividing by 3:
x + 6 = 8
Subtracting 6:
x = 2
I need help with my scale project is there anyway you could make me two similar figures with this and it also has the proportions.
To make a similar figure, we measure the lengths of each component of the figure - for example, the leg of the figure is 2 units - and then multiply each measured length by a number. This number could be any number - could be 2, 3, 4 ... but we will choose a small enough number that will give us a figure that can fit inside the graph.
Now here are the measurements of the figure.
The legs = 1 units
bottom = 2 units
top = 2 units
sides = 2 units
nose = 0 units (it is a point)
eyes - 0.5 units
Now let's multiply the measurements above by 3, which gives
The legs = 3 units
bottom = 6 units
top = 6 units
sides = 6 units
nose = 0 units (it is a point)
eyes - 1.5 units.
Finally, we draw a figure with these measurements.
The function h is defined as follows.
h(x)=3x²+2
Since functions are frequently composed of two smaller functions to create new functions, this definition of function is sometimes used.
What is the domain and range of f/x )= 3x 2?The graph of the function will be a straight line with no discontinuities when the equation f(x) = 3x - 2 is used.
The domain of this expression is all real integers.
The expression f(x) = 3x - 2 has as its domain "x | x is a real number," which can be written as (-,","") for any x > R.
F (x) = 3 x f (x) = 3 x f (x) = 3 x is the given function.
The domain of f f f is R mathbbR R since 3 x 3x 3x is defined for any x R x in mathbbR xR (where R mathbbR R is the set of all real numbers).
Consider the function y = f(x),
which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
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Solve for z-p(d + z) = -2+59
Answer
[tex]z=-(\frac{57}{p}+d)[/tex]Explanation
The question ask us to solve for z in the equation
-p (d + z) = -2 + 59
-p (d + z) = 57
Divide both sides by -p
[tex]\begin{gathered} \frac{-p(d+z)}{-p}=\frac{57}{-p} \\ d+z=\frac{-57}{p} \\ \text{Subtract d from both sides} \\ d+z-d=\frac{-57}{p}-d \\ z=\frac{-57}{p}-d \\ z=-(\frac{57}{p}+d) \end{gathered}[/tex]Hope this Helps!!!
