Translate left 12 units, stretch by a factor of 4, and reflect over the x-axis. Then state the vertex. g(x)= vertex:
Using the transformation concepts, it is found that:
The rule for g is: [tex]g(x) = -4x^{2}[/tex]
The vertex is: (0,0).
Stretching a function f(x) vertically by a factor of b is given by:
[tex]g(x) - bf(x)[/tex]
Reflecting a function over the x-axis is the equivalent of:
g(x) = -f(x)
The original function is: [tex]f(x) = x^{2}[/tex]
Stretching by a factor of 4 means that the function is multiplied by 4, thus: [tex]g(x) = 4x^{2}[/tex]
Reflecting over the x-axis, that is, multiplying by -1, we have that: [tex]g(x) = -4x^{2}[/tex], which is the rule for g.
From the above equation, added at the end of this answer, the vertex is at (0,0).
Hence the answer is the vertex is at (0,0)
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x + 5.5 = 0
State whether these statements are true or false.
a. 2(x+3) <= -5
b. 3 - 2x > 12
c. x square + x < 24.75
Only option 'a' is true
What is equation?Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some components of an equation. The "=" sign and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation. Without these, one can still form an equation, such as 5 + 10 = 15. There are no variables in the equation below. An equation with variables, on the other hand, is an algebraic equation.Calculation
Given, x + 5.5 = 0
x = -5.5
a. 2(x+3) ≤ -5
2(-5.5+3) ≤ -5
2*(-2.5) ≤ -5
-5 ≤ -5
Hence, it is true
b. 3 – 2x > 12
3 – 2(-5.5) > 12
3 – 11 > 12
-8 > 12
Hence, it is false
c.[tex]x^{2}[/tex] +(-5.5) < 24.75
[tex]-5.5^{2}[/tex] + (-5.5) < 24.75
30.25 <24.75
Hence, it is false
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Two subscription services offer deliveries of boxes of nutritious, organic snack foods each month. For how many months of deliveries will the two plans corset the same?
At 4 months of subscription, both plans will cost the same.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Two subscription services offer deliveries of boxes of nutritious, organic snack foods each month.
Snacks 4 U has 4$ for 3 months and from then $14 a month and Healthy times has 1 month of free subscription and then $10 months.
Assuming no. of months required that two plans will cost the same is x.
∴ 12 + 14x = 10x
4x = 12
x = 3 and + 1 for the free months.
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Consider a sequence whose first five terms are: 3, 8, 15, 24, 35
Which function (with domain all integers n
1) could be used to define and continue this sequence?
The following number in the series is 48.
Arithmetic Progression (AP) is a number sequence in which the difference between any two consecutive numbers is a constant value.
Given first five terms of a sequence are 3,8, 15, 24, 35
On examining the series we see:
3 - 0 = 3
8 - 3 = 5
15 - 8 = 7
24 - 15 = 9
35 - 24 = 11
The increments are an arithmetic progression with the first term being 3 and the difference being 2.
The next term (sixth term) is 13.
Hence the next number of the series 3, 8, 15, 24, and 35 is 35 + 13 = 48
Therefore the next number in the series is 48
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Valley spa purchased $7,800 in plumbing components from tubman company. Valley spa signed a 60-day, 10% promissory note for $7,800. If the note is dishonored, what is the amount due on the note? (use 360 days a year. ).
The amount due on the note with the cost of $7800 , 10% promissory note for 60 days is equal to $7930.
As given in the question,
Cost of purchase a plumbing components = $7,800
Valley spa signed promissory note for 60 day
Percentage of promissory note = 10%
Condition: For the note is dishonored :
Amount due,
Due Interest on the note
= 7800 × (10 /100) × ( 60 /360)
= 78 × 10 × ( 1/6)
= 13 × 10
= $130
Total amount due
= original cost + interest
= $(7800 + 130)
= $7930
Therefore, for the dishonored note the amount due on the note is $7930.
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Elizabeth has a mask collection of 420 masks. She keeps 65% of the masks on her wall. How many masks does she keep on her wall?
The number of masks Elizabeth kept on the wall is 273.
How to find the number of mask she keeps on the wall?Elizabeth has a mask collection of 420 masks. She keeps 65 percent of the masks on her wall.
The number of mask she keeps on the wall can be calculated as follows:
Therefore,
number of mask she keeps on the wall = 65 percent of total mask collection
number of mask she keeps on the wall = 65% of 420
number of mask she keeps on the wall = 65 / 100 × 420
number of mask she keeps on the wall = 27300 / 100
Therefore,
number of mask she keeps on the wall = 273
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Write an equation in point-slope form that passes through the points (-4,7) and (8,3)
Answer:EMD
Step-by-step explanation:
Answer:
Since there are two points there are two equations that can written.
1. [tex]y-7=-\frac{1}{3} (x+4)[/tex]
2. [tex]y-3=-\frac{1}{3} (x-8)[/tex]
Step-by-step explanation:
Step 1: Point Slope Form
[tex]y-y_{1} =m(x-x_{1})[/tex]Step 2: Find the slope of the two points
Slope = m[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]Points: (-4,7) and (8,3)y₂ = 3y₁ = 7x₂ = 8x₁ = -4[tex]m=\frac{3-7}{8-(-4)}=\frac{-4}{8+4} =\frac{-4}{12} =\frac{-1}{3}[/tex]Step 3: Write the equation
[tex]y-y_{1} =m(x-x_{1})[/tex][tex]m=-\frac{1}{3}[/tex]Points: (-4,7) and (8,3)Using the point (-4,7):[tex]y-7=-\frac{1}{3} (x+4)[/tex]Using the point (8,3):[tex]y-3=-\frac{1}{3} (x-8)[/tex]Solve using linear combination. 2x – 3y = – 9 x + 3y = 18
a. (27, 9)
b. (3, 27)
c. (9, 3)
d. (3, 5)
The solution to the equation by linear combination is (d) (3, 5)
How to determine the solution to the equation?From the question, we have the following system of equations
2x – 3y = – 9
x + 3y = 18
By linear combination, we start by eliminating one of the variables
This is done by adding the equations
So, we have
2x + x -3y + 3y = -9 + 18
Evaluate the like terms
3x = 9
Divide both sides
x = 3
Substitute x = 3 in x + 3y = 18
3 + 3y = 18
So, we have
3y = 15
Divide
y = 5
Hence, the solution is (d) (3, 5)
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The complete table of values is:
x -2 -1 0 1 2
y 1/9 1/3 1 3 9
How to complete the table of values?From the question, we have the following equation:
f(x) = 3ˣ
From the table of values, we have the following x values
x = -2, -1, 0, 1 and 2
Substitute x = -2, -1, 0, 1 and 2 in the equation f(x) = 3ˣ
When x = -2
f(-2) = 3⁻² = 1/9
When x = -1
f(-1) = 3⁻¹ = 1/3
When x = 0
f(-1) = 3⁰ = 1
When x = 1
f(1) = 3¹ = 3
When x = 2
f(2) = 3² = 9
Hence, the complete table of values is:
x -2 -1 0 1 2
y 1/9 1/3 1 3 9
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Maya accepted a new job at a company with a contract guaranteeing annual raises. Let SS represent Maya's salary after working for nn years at the company. The table below has select values showing the linear relationship between nn and S.S. Determine Maya's salary when hired.
well, we know that the relationship of "n" and "s" is linear, so hmmm let's get their equation first.
to get the equation of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{68000})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{76000}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{76000}-\stackrel{y1}{68000}}}{\underset{run} {\underset{x_2}{9}-\underset{x_1}{7}}} \implies \cfrac{ 8000 }{ 2 } \implies 4000[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{68000}=\stackrel{m}{ 4000}(x-\stackrel{x_1}{7}) \\\\\\ ~\hfill {\Large \begin{array}{llll} s-68000=4000(n-7) \end{array}} ~\hfill[/tex]
now, when she was hired, well that was when there were no years, namely at year 0, so we can say that's when n = 0
[tex]s-68000=4000(n-7)\implies s-68000=4000(\stackrel{n}{0}-7) \\\\\\ s-68000=4000(-7)\implies s-68000=-28000 \\\\\\ s=-28000+68000\implies {\Large \begin{array}{llll} s=40000 \end{array}}[/tex]
Sally is making necklaces and bracelets for the craft fair. a necklace uses 16 beads, and a bracelet uses 27 beads. sally wants to make twice as many bracelets as necklaces, and she wants to use up all of her 910 beads. how many of each should she make?
Answer:
Sally can make 26 bracelets and 13 necklaces.
Step-by-step explanation:
necklace = 16 beads
bracelet = 27
(twice as many bracelets as necklaces)
total = 910 beads
27*26 = 702 beads (26 bracelets)
16*13 = 208 beads (13 necklaces)
702+208 = 910
write as many three-digit numbers as you can. your answers can only use the digits 0, 2, and 5, but you can repeat digits.
The numbers 0, 2, and 5 can be repeated any number of times to create 16 three-digit numbers.
Given that,
As many three-digit numbers as you can must be written. Only the numerals 0, 2, and 5 may be used in your replies, although you may repeat digits.
This is a problem on Permutations
Permutation is the different ways that a set of elements can be arranged, either all at once or part of them at a time. There are two alternative arrangements, AB and BA, for instance, if we have two elements, A and B.
Repeating number permutation
= 3³ - 11(as one of the digit is Zero "0")
= 3 × 3 × 3 - 11
= 16
Let me list each result one by one.
222, 205, 250, 255, 225, 252, 220, 202.
502, 520, 552, 525, 555, 522, 550, 505.
Thus, there are 16 three-digit integers that may be constructed by the numbers 0,2, and 5 with any digit repeated.
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if sue will only buy apples if the price decreases because each apple yields a smaller amount of additional satisfaction, she is exemplifying the law of .
Sue is an example of the law for "diminishing marginal utility" if she only buys apples if the price drops because each apple produces less additional satisfaction.
Explain the term diminishing marginal utility?The phenomenon known as diminishing marginal utility describes how each extra unit of gain results in an ever-smaller rise in subjective value.
For instance, three bites of sweets are preferable to two, but the pleasure does not improve significantly after the nineteenth mouthful.One typical good having diminishing marginal value is food. Consider an apple as an illustration. An apple is pretty valuable if you're famished. However, as you consume more apples, you become less hungry, decreasing the value of each new apple.Thus, Sue is an example of the law for "diminishing marginal utility" if she only buys apples if the price drops because each apple produces less additional satisfaction.
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please answer this question
It's really important
for #3:
a) 0.9
b) 0.4
c) 0.7
d) 0.08
e) 3.9
f) 1.6
g) 5.5
h) 12.4
And for #4:
The answer is $131.63
Nathan earns 9.75 dollars in one hour, and you want to figure out how many he makes in thirteen and a half hours. To do this, just multiply 9.75 by 13.5.
9.75*13.5 is 131.625. However, money only goes to the hundredths place, which means there are only 2 decimal places. This means you should round 131.625 to the hundredths place, which makes 131.63.
I'm going to do a short answer so here:
a) 0.9
b) 0.4
c) 0.7
d) 0.8
e) 0.39
f) 1.6
g) 5.5
h) 12.4
All of these can be solved by doing this (example_:
2.7/3=
(27/3)/10
(9)/10= 0.9
essentially, just recognize that they are similar to their whole number counterparts.
4. $9.75*13.5= ~131.63 (technically 131.625, but that doesn't exist in monetary values)
in a function, each input is related to multiple outputs.
In a function, each input is related to multiple outputs is False.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
Function of function, as the name suggests, are functions applied over functions themselves. This is also called function composition.
A function can be defined as a relationship between an output value, y, and an input value x; where each input value of x has one and only one output value of y.
This means that each output value of a function can have multiple inputs (for example, quadratic functions have 2 inputs for each output except the vertex), but no input can have multiple outputs.
Therefore, In a function, each input is related to multiple outputs is False.
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Once Isabel rented the warehouse space, she decided to post ads on several social media sites to advertise her online bookstore. Let x represent the number of months the ads have been posted. Isabel finds that the function below describes the number of books sold as a function of the number of months her ads have been posted.
f(x) = 1000 + 1000
⦁ How many books were sold after 8 months
Graph the function.
Answer: 3000 thousand books were sold
Step-by-step explanation:
help please this is due on friday
If four digit numbers are made using the digits 0 to 6, the number of even digits formed without repeatetion is 204.
For an even number the last digit can be either zero or 2,4, 6 and each digit can be used only once
If the 4th digit is 0, then that leaves 5 possible numbers for the 1st digit, 4 for the 2nd, and 3 for the 3rd. 5 x 4 x 3 = 60 possible 4-digit even numbers.
If the 4th digit is 2,4 or 6, that leaves 4 possible numbers for the 1st digit (as 1st digit can’t be 0), 4 for the 2nd digit, and 3 for the 3rd digit. 4 x 4 x 3 x 3 = 144 possible 4-digit even numbers.
total possible even digits is = 60 + 144 = 204
Therefore, if four digit numbers are made using the digits 0 to 6, the number of even digits formed without repeatetion is 204.
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2. Perform the operation.
(8x² + 8x - 9) + (3x² + 5x)
Answer:
here is the, ans hope it helps :)
x = -13 ± (√ 565) / 22 is the solution to the operation
(8x² + 8x - 9) + (3x² + 5x) = 0.
∴ (8x² + 8x - 9) + (3x² + 5x) = 0
=> 8x² + 8x - 9 + 3x² + 5x = 0
=> 11x² + 13x -9 = 0
After obtaining the standard form a, b and c are identified from the original equation and are placed into the quadratic formula.
∴ x = (-b±√(b²-4ac))/(2a)
11x² + 13x -9 = 0
where,
a = 11, b = 13, c = -9
=> x = (-13 ± √(13² - 4×11(-9)) )/ (2×11)
=> x =( -13 ± (√ 565) )/ (22).
So, the solution to (8x² + 8x - 9) + (3x² + 5x) = 0 is x = -13 ± (√ 565) / 22.
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The complete question is -
Perform the operation:
(8x² + 8x - 9) + (3x² + 5x) = 0
At a local print shop, 12 copies can be made for $6. At this rate, how how many copies could be made for $27?
Answer: 54 copies
Step-by-step explanation:
12 copies for $6
1 copy for $0.5
x copies for $27
27/0.5 = 54
1(54) = 54 copies
19 is what percent of 95
Answer:
20%
Step-by-step explanation:
19 of 95 can be written as:
19/25
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
19/25 x 100/100
= (19 x 100/95) x 1/100 = 20/100
Therefore, the answer is 20%
If you are using a calculator, simply enter 19÷95×100 which will give you 20 as the answer.
Hope this helped!
Which graph represents the solution set of 4x - y ≤ - 6?
None of the graphs shows the solution set for the given inequality, so it may be written incorrectly or maybe there are some graphs not shown in the image.
Which graph represents the solution set for the inequality?Here we have the inequality:
4x - y ≤ - 6
If we isolate the variable y, we get:
4x + 6 ≤ y
First, because of the symbol "≤" we know that we will have a solid line (the points on the line are also solutions).
We also can see that we have a positive slope
y ≥ 4x + 6
Also we can see that the y-intercept is 6, now the problem is that none of the graphs meets the 3 conditions.
Solid line.Positive slopey-intercept at y = 6So there is no correct option, which means that there may be a mistake in the inequality you wrote.
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if the null hypothesis is 'french people do not differ from english people in height', what will be the alternative hypothesis?
The alternative hypothesis will be French people differ from English people in height.
A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables.
In statistical hypothesis testing, null and alternate hypotheses are applied. The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.
Given
Null hypothesis- French people do not differ from English people in height.
Therefore, the Alternative hypothesis for the given statement is - French people differ from English people in height.
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How do I do this???
I need to find it out, but it is comlicated
Answer:
x=3
Step-by-step explanation:
The equation for perimeter of a rectangle is 2(l)+2(w)
So, 2(x+2)+2(2x-1)=
2x+4+4x-2=20
You then combine like terms
6x+2=20, then subtract 2 from both sides
6x=18, then divide 6 by both sides
x=3
I need help please so I'm supposed to find x but when I find it I have to put in in the problem and then it has to equal 25 or might just be wrong overall I don't know
Answer:
x=-12.5
Step-by-step explanation:
The corresponding angles theorem shows that -6x+80 is supplementary to 25.
So -6x+80+25=180
-6x+80=155
-6x=75
-6x/-6=75/-6
x=-12.5
3 3/8 x 7 1/4 with explanation
Step-by-step explanation:
3 3/8 = 27/8
7 1/4 = 29/4
29/4 X 27/8 = 783/32 = 24 15/32
Line p passes through points (18, 11) and (-17, 22). Line q passes through points (2, 37) and (-9, 72). Are line p and line q parallel or perpendicular?
The lines p and q are perpendicular lines.
According to the question,
We have the following information:
Line p passes through points (18, 11) and (-17, 22). Line q passes through points (2, 37) and (-9, 72).
We will find the slope of both the lines to check whether they are perpendicular or parallel. If their slope is equal then they are parallel and if their slope is not equal or inverse of the other one then they are perpendicular.
(Slope is denoted by m.)
m = (y2-y1)/(x2-x1)
For line p:
x1 = 18, y1 = 11, x2 = -17 and y2 = 22
m = (22-11)/(-17-18)
m = -11/35
For line q:
x1 = 2, y1 = 37, x2 = -9 and y2 = 72
m = (72-37)/(-9-2)
m = -35/11
Now, the slope is inverse.
Hence, the lines p and q are perpendicular lines.
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determine whether or not the distribution is a discrete probability distribution and select the reason why or why not.
The given probability distribution is a discrete probability distribution.
Given,
x: 3 4 7
P(X=x): 0.19 0.3 0.51
Discrete probability distribution property;
∑P[tex](x_{i} )[/tex] = 1
Discrete probability distribution;
The outcomes of events that can be counted or are finite are included in a discrete probability distribution. This differs from a continuous distribution, in which results can occur anywhere along a continuum. The binomial, Poisson, and Bernoulli distributions are typical examples of discrete distributions.
That is,
∑P[tex](x_{i} )[/tex]
= 0.19 + 0.3 + 0.51
= 1
The property for a discrete probability distribution is thus satisfied.
So, the probability distribution that is being presented is a discrete probability distribution.
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The given question is incomplete. Completed question is given below;
Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not. x −3 4 7 P(X=x) 0.19 0.3 0.51 Answer First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision.
due now pls help me :P
Answer:
B
Step-by-step explanation:
y intercept is whenever x is 0 or in this case when they haven’t been on any rides
Here Jamie starts off with 24 tickets before going on any rides
Hopes this helps
PLEASE HELP ASAP. are these functions?????
The figure shown in 2 and 4 are the functions. Options B and D are correct.
Given that,
A number of graphs have been shown, to determine which graph is a function,
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Graph 1,
Is not function because it is a scatter plot,
Graph 2
Is line, which is a function,
Graph 3
Is a circle with a curve that is not functional,
Graph 4
Is parabola and quadratic function,
Thus, the figure shown in 2 and 4 are the functions. Options B and D are correct.
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Word Problem. A lacrosse player throws a ball in the air from an initial height of 7 feet. The ball has an initial
vertical velocity of 90 feet per second. Another player catches the ball when it is 3 feet above the ground. How
long is the ball in the air?
The ball hits the ground after 3.39 seconds.
What is initial velocity?A physical system's behavior in terms of its motion is described using equations of motion. The equations of motion are relationships between different terms and quantities. There are primarily three equations of motion, often known as the laws of constant acceleration, that apply when there is uniform acceleration.Any item subject to forces will accelerate. The object's velocity changes as a result of this acceleration. As a result, the initial velocity is the object's speed before the change brought on by acceleration. The velocity will be the final velocity after the object has been accelerating for a while.acc to our question-
The following quadratic equation can be used to calculate the height of the ball after t seconds while accounting for gravity.
is the initial velocity. is the initial height.In this problem:Height of 8 feet, thus .Initial velocity of 32 feet per second, The equation is:We want the positive value, so:The ball hits the ground after 3.39 seconds.learn more about initial velocity click here:
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If possible please show work
Not exactly sure what this is but by a glance theyre asking what do you do to days to get the total?
Therefore if you have in the D column 1-5 the process is always multiplying by 250 so 1 day gives 1 * 250 = $250
2 days gives 2*250 = $500
That means the equation must be
T =250D
