Sketch a graph y = |x – 3| – 2 and describe the translations.
Answers
Answer:
Shifted horizontally to the right 3 units, and shifted vertically down 2 units
Step-by-step explanation:
The parent graph of this equation is y = |x|
There are 2 translations to this graph for the equation y = |x - 3| - 2
The "x - 3" part shifts the graph to the right 3 units
The -2 shifts the graph vertically down 2 units
See below for the parent graph, and the graph of the equation we are working with
The graph of function y = |x - 3| - 2 is shown in figure.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The equation is,
⇒ y = |x - 3| - 2
Now,
Since, The equation is,
⇒ y = |x - 3| - 2
Clearly, The equation y = |x - 3| - 2 is the translation of y = |x| with 3 units right and 2 units up.
Thus, The graph of function y = |x - 3| - 2 is shown in figure with 3 units right and 2 units up translation of y = |x|.
Learn more about the translation visit:
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Related Questions
Ivan wants to ship a box that is 6 in. Tall, 4 in. Wide, and 5 in. Long to his cousin, and used the calculation below. What was his error, and what is the correct volume?
Answers
Answer:
sample response He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.
Answer:
He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.
That is the correct answer
Step-by-step explanation:
a. The ratio of boys to girls in a class is 6 to 5 . What is the ratio of girl s to all the students in the class? b. If the ratio of boys to girls in a class is m:n, what is the ratio of girl s to all the students in the class? c. If five elevenths of the class are girls, what is the ratio of girls to boys? a. The ratio, in simplest form, of the number of girl s to the total number of students is 5 :11 . b. The ratio, in simplest form, of girl s to all the students in the class is nothing :nothing . c. The ratio, in simplest form, of girls to boys is nothing :nothing.
Answers
Answer:
a. Ratio of girls to all students 5:11
b. Ratio of girls to all students n:m+n
c. Ratio of girls to boys 5:6
Step-by-step explanation:
In order to find each of these, we simply need to look at these as a comparison of two data points.
a. In this example, we are looking for girls to all students. We already who there would be 5 girls in the comparison. Then we need to find the whole amount, which is girls + boys (6 + 5 = 11)
5:11
b. In this example, we are looking for girls to all students. We already who there would be n girls in the comparison. Then we need to find the whole amount, which is girls + boys (m + n)
n:m+n
c. In this example, we are looking for girls to boys. We already who there would be 5 girls in the comparison. Then we need to find the boys amount, which is whole - girls (11 - 5 = 6)
5:6
Final answer:
The ratio of girls to all students in a class with a boy-girl ratio of 6 to 5 is 5 to 11. The general ratio of girls to all students with a boy-girl ratio expressed as m:n is n:(m+n). Lastly, if five elevenths of the class are girls, then the ratio of girls to boys is 5 to 6.
Explanation:
Understanding Ratios in a Classroom Setting
The ratio of boys to girls in a class is initially given as 6 to 5. To find the ratio of girls to all the students in the class, the sum of the parts of the ratio must first be calculated, which is 6 (boys) + 5 (girls) = 11 (total students).
Therefore, the ratio of girls to the total number of students is 5 to 11. This is because for every 11 students, 5 are girls. If the ratio of boys to girls is expressed as m:n, then the ratio of girls to all students will be n:(m + n).
For a scenario where five elevenths of the class are girls, the ratio of girls to boys needs to be determined. As five elevenths represent the girls, six elevenths must represent the boys, since they sum up to the whole, which is one (or 11/11). Therefore, the ratio of girls to boys is 5:6.
For every pizza Eric's family ate, eric ate2 of the 8 pieces. If Eric's family bought 2 pizzas, write the ratio of the total number of pieces Eric ateto the total number of pieces the family ate.
Answers
Answer:
4 over sixteen, or 4/16 is your answer.
Step-by-step explanation:
There are 2 pizzas, each of which contain 8 pieces. So, in all, there were 8 pieces. Eric ate two pieces from each pizza. So, 2+2=4. Thus, he ate four out of the 16 pieces. That brings us to our answer, 4/16.
I hope this helps you, have a wonderful day!
Final answer:
The ratio of the total number of pieces Eric ate to the total number of pieces eaten by his family when they bought 2 pizzas, is 1:4, meaning Eric eats 1 out of every 4 pieces.
Explanation:
For every pizza Eric's family ate, Eric ate 2 of the 8 pieces. If Eric's family bought 2 pizzas, to find the ratio of the total number of pieces Eric ate to the total number of pieces the family ate, we start by calculating the total pieces in 2 pizzas and the pieces Eric ate.
Each pizza has 8 pieces, so 2 pizzas have 8 * 2 = 16 pieces in total.
Since Eric eats 2 pieces per pizza, for 2 pizzas, he would eat 2 * 2 = 4 pieces in total.
Therefore, the ratio of the pieces Eric ate to the total pieces is:
4 (pieces Eric ate) : 16 (total pieces), which simplifies to 1:4.
This ratio means that for every piece of pizza Eric eats, there are 4 pieces total, indicating Eric eats 1 out of every 4 pieces.
David sold 6 apple trees. He sold 5 of the apple trees to max. What fraction of the apple trees did david sell to max
Answers
Answer:
wouldn't it be 6/5 or 5/6 or 1.2
Step-by-step explanation:
A jar contains 38 marbles. It has 10 red, 22 black and 6 green marbles. Two marbles are drawn, the first is not returned before the second one is drawn. What is the probability that both marbles are black?
P(Both Black) = 11 / 19
P(Both Black) = 231 / 703
P(Both Black) = 231 / 722
P(Both Black) = 121 / 361
Answers
Answer:
The correct answer option is 231 / 703
Step-by-step explanation:
We are given that a jar has 38 marbles, out of which 10 are red, 22 are black and 6 are green. Two marbles are drawn and the first marble is not returned when the second one is drawn.
We are to find the probability that both marbles are black.
1st draw: P (black) = [tex]\frac{22}{38} =\frac{11}{19}[/tex]
2nd draw: P (black) = [tex]\frac{21}{37} [/tex]
P (Both Black) = [tex]\frac{11}{19} \times \frac{21}{37}[/tex] = 231 / 703
A party store sells large plates in packs of 12 and small plates in packs of eight. In order to have an equal number of both, what is the least amount of large plaate packs that would have to be purchased?
Answers
Answer:
The least amount of large plate packs that would have to be purchased is 24.
Step-by-step explanation:
To do this we have to find first multiplication of 8 that is equally divided by 12.
A person can buy large packs of plates in multiple of 12 only.
A person can buy {1,2,3,4,5,6,7,8,...}packs of plates and will purchase
{12,24,36 ,48,60,72,84,96,...}large plates.
A person can buy small packs of plates in multiple of 8 only.
A person can buy {1,2,3,4,5,6,7,8,9,10,11,12...}packs of plates and will purchase..
{8,16,24,32,40,48,56,64,72,80,88,96,...}small plates
Now we have to keep in mind that one has to purchase equal amount of plates..
A person can buy {24,48,72,96} plates and hence least amount of large plate packs that would have to be purchased is 24....
Please help me if you can!
Answers
Here is your answer
[tex]<b>z= 20 degrees</b>[/tex]
REASON:
[tex]<font color="blue" size=5>Concept used</font>[/tex]: The sum of adjacent angles of a parallelogram is 180 degrees.
So, in above given figure
[tex] 2z+16+124=180 [/tex] (measures of adjacent angles)
[tex]2z+140=180 [/tex]
[tex] 2z=180-140 [/tex]
[tex]2z=40 [/tex]
[tex]z= 40/2 [/tex]
[tex]z= 20 [/tex]
HOPE IT IS USEFUL
True or false (Picture provided)
Answers
The answer is: True.
Why?A counterexample is a way that we can prove that something is not true about a mathematical equation or expression, it's also considered as an exception to a rule.
So:
[tex]sec^{2}x-1=\frac{cosx}{cscx}\\\\tg^{2}x=\frac{cosx}{\frac{1}{sinx}}\\\\\frac{1-cos2x}{1+cos2x}=cosxsinx[/tex]
Then, evaluating we have:
[tex]\frac{1-cos(2*45)}{1+cos(2*45)}=cos(45)*sin(45)\\\\\frac{1-0}{1+0}=\frac{\sqrt{2} }{2}*\frac{\sqrt{2}}{2}\\\\1=\frac{(\sqrt{2})^{2} }{4}\\\\1=\frac{2}{4}\\\\1=\frac{1}{2}[/tex]
Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for [tex]sec^{2}x-1=\frac{cosx}{cscx}[/tex] and the answer is true.
Have a nice day!
At what x-values do the graphs of the functions y=cos 2x and y=1-sin^2x intersect over the interval 0 < x < pi
_ _
Answers
Answer:
No solution.
Step-by-step explanation:
The given functions are
[tex]y=\cos2x[/tex] and [tex]y=1-\sin^2x[/tex].
To find the point of intersections of the graphs of the two functions: we equate them and solve for [tex]x[/tex].
[tex]\cos2x=1-\sin^2x[/tex]
Recall the double angle identity; [tex]\cos2x=cos^2x-sin^2x[/tex]
Apply this identity to obtain;
[tex]cos^2x-sin^2x=1-\sin^2x[/tex]
[tex]\Rightarrow cos^2x=1[/tex]
[tex]\cos x=\pm1[/tex]
[tex]x=0\:or\:x=\pi[/tex]
if the interval is [tex]0\le x\le \pi[/tex], then the two graphs intersect at [tex]x=0\:or\:x=\pi[/tex]
But [tex]x=0\:and\:x=\pi[/tex] does not belong to the open interval [tex]0\:<\:x\:<\:\pi[/tex]
No point of intersection.
Lisa purchased groceries worth $34 for a party. A gallon of milk costs $2.50, a gallon of ice cream costs $7.50, and a gallon of lemonade costs $3.00
If Lisa bought 4 gallons of milk, and 2 gallons of ice cream, how many gallons of lemonade did she buy?
Answer 1: 5
Answer 2: 3
Answer 3: 2
Answer 4: 4
Answers
Answer 2 she bought 3 gallons of lemonade
4x2.50=10
2x7.50=15
10+15=25
34-25=9
9 divided by 3=3
Answer:
Answer 2 is right.
Step-by-step explanation:
Given that Lisa purchased groceries worth $34 for a party.
A gallon of milk costs $2.50
No of gallons bought - 4
Cost of milk = [tex]2.50*4 =10[/tex]
a gallon of ice cream costs $7.50
Cost of ice creams = [tex]2*7.50 = 15[/tex]
, and a gallon of lemonade costs $3.00
Let lemonade purchased be x
Then total cost = [tex]10+15+3x[/tex]
This equals 34
[tex]25+3x =34\\3x=9\\x=3[/tex]
No of gallons of lemonade purchased =3
Answer 2 is right
A pyramid has a cross-sectional shapes, taken parallel to its base, that are _____ to one another
Answers
Answer: similar
Step-by-step explanation: apex
Answer:
The fill in the blank is the word similar.
Step-by-step explanation:
A pyramid has a cross-sectional shapes, taken parallel to its base, that are similar to one another.
When we do the cross-section of a pyramid parallel to its base, the cross-section formed will be in the same shape like the base.
Whenever a cross section is done parallel to the base of any pyramid, the resulting shape will be same like the base. As we move up in the pyramid and cross section it, the shape formed will be like the base but with smaller dimensions. But the shape will be the same as the base.
Bethany sells roses and petunias. The expression 3r+2.5p3r+2.5p3, r, plus, 2, point, 5, p gives the cost (in dollars) of r roses and p petunias. What is the cost of 7 roses and 8 petunias?
Answers
What is the equation of the horizontal asymptote? f(x)=4⋅2^x−5
Question options:
y=0
y=4
y=−5
y=2
Answers
ANSWER
[tex]y = - 5[/tex]
EXPLANATION
The horizontal asymptote of a general exponential function,
[tex]f(x) = a {(b)}^{x} + c[/tex]
is y=c.
The given exponential function is
[tex]f(x) = 4{(2)}^{x} - 5[/tex]
By comparing the given function to
[tex]f(x) = a {(b)}^{x} + c[/tex]
we have c=-5, therefore the horizontal asymptote is
[tex]y = - 5[/tex]
After 2 years, $600 deposited in a savings account with simple interest had earned $120 in interest. What was the interest rate?
Answers
Answer:
300%
Step-by-step explanation:
600 / 120 = 300
What is the m∠N ? Can someone help me :)
Answers
Answer:
61°Step-by-step explanation:
Use the sine law:
[tex]\dfrac{MO}{\sin(\angle N)}=\dfrac{NM}{\sin(\angle O)}[/tex]
We have:
[tex]MO=18\\\\NM=6\\\\m\angle O=17^o\to\sin17^o\approx0.2924[/tex]
Substitute:
[tex]\dfrac{18}{\sin(\angle N)}=\dfrac{6}{0.2924}[/tex] cross multiply
[tex]6\sin(\angle N)=(18)(0.2924)[/tex]
[tex]6\sin(\angle N)=5.2632[/tex] divide both sides by 6
[tex]\sin(\angle N)=0.8772\to m\angle N\approx61^o[/tex]
Choose Yes or No to tell if the fraction 4 9 49 will make each equation true. 63 × □ = 28 63×□=28 18 × □ = 8 18×□=8 96 × □ = 42 96×□=42 36 × □ = 16 36×□=16
Answers
Answer:
YES
YES
NO
YES
Step-by-step explanation:
Assuming that the value is [tex]\dfrac{4}{9}[/tex].
Let's take each of the equations and check if the fraction makes the equation true.
When multiplying a whole number to a fraction, it is the same as multiplying the whole number to the numerator and dividing the total by the denominator.
[tex]63*\dfrac{4}{9}=28[/tex]
[tex]\dfrac{63*4}{9}=28[/tex]
[tex]\dfrac{252}{9}=28[/tex]
[tex]28=28[/tex] YES
[tex]18*\dfrac{4}{9}=8[/tex]
[tex]\dfrac{18*4}{9}=8[/tex]
[tex]\dfrac{72}{9}=8[/tex]
[tex]8=8[/tex] YES
[tex]96*\dfrac{4}{9}=42[/tex]
[tex]\dfrac{96*4}{9}=42[/tex]
[tex]\dfrac{384}{9}=42[/tex]
[tex]42.67=42[/tex] NO
[tex]36*\dfrac{4}{9}=16[/tex]
[tex]\dfrac{36*4}{9}=16[/tex]
[tex]\dfrac{144}{9}=16[/tex]
[tex]16=16[/tex] YES
Answer:
yes
yes
no
yes
hope this helps!!
Solve: 3x(x + 4) + 3(x + 4) = 0 A) 0 and -4 B) -1 and 4 C) -1 and -4 Eliminate D) 1 and 4
Answers
Answer:
The answer is C) -1 and -4
Step-by-step explanation:
Sorry i don't have the step by step explanation but that's the answer
what is the value of the constant in the equation that relates the height and width of this rectangle?
would appreciate any help i could get :)
Answers
Answer:
Option C. [tex]2.5[/tex]
Step-by-step explanation:
we know that
In the rectangle of the figure
[tex]\frac{H}{W}=\frac{25}{10}=2.5[/tex]
so
[tex]H(W)=2.5W[/tex]
The constant is equal to [tex]2.5[/tex]
Answer:
2.5
Step-by-step explanation:
You have a job as a teacher with a starting salary of $37,185. You will receive a 6% raise every year. How much will you salary be after 5 year?
Answers
if it is asking for compound interest your answer should be 49761.9
Simplify the expression (4x − 3)(x + 5).
A. 4x2 − 17x + 15
B. 4x2 − 17x − 15
C. 4x2 + 17x + 15
D. 4x2 + 17x − 15
Answers
D using the foil method
Answer: [tex]4x^2+17x-15[/tex]
Step-by-step explanation:
To simplify the given expression we need to apply the distributive property in algebra.
The distributive property is given by :
[tex]a(b+c)=ab+ac[/tex]
The given expression:
[tex](4x- 3)(x + 5)\\\\=(4x-3)x+(4x-3)5\ \ \ \ \text{By distributive property}\\\\=4x^2-3x+20x-15\\\\=4x^2+(-3+20)x-15\ \ \ \text{Combining like terms}\\\\=4x^2+17x-15[/tex]
Describe the translation of f(x) = |x|.
4 1\2 left, 1\2 unit down
1\2 unit left, 4 1\2 up
1\2unit left, 4 1\2units down
4 1\2 units left, 1\2 unit up
Answers
Answer:
the correct answer would be choice C
it went left 1/2 units and went down 4 1/2 units
Answer:
It's the third option.
Step-by-step explanation:
f(x) = |x| is shaped like a V with the vertex at the point (0, 0).
The translation is 1/2 unit to the left, 4 1/2 units down.
Solve the equation (linear equation)
[tex]8^{2x+7} = (\frac{1}{32})^{3x}[/tex]
Answers
Answer: [tex]x=-1[/tex]
Step-by-step explanation:
By the negative exponent rule, you have that:
[tex](\frac{1}{a})^n=a^{-n}[/tex]
By the exponents properties, you know that:
[tex](m^n)^l=m^{(nl)}[/tex]
Therefore, you can rewrite the left side of the equation has following:
[tex](\frac{1}{8})^{-(2x+7)}=(\frac{1}{32})^{3x}[/tex]
Descompose 32 and 8 into its prime factors:
[tex]32=2*2*2*2*2=2^5\\8=2*2*2=2^3[/tex]
Rewrite:
[tex](\frac{1}{2^3})^{-(2x+7)}=(\frac{1}{2^5})^{3x}[/tex]
Then:
[tex](\frac{1}{2})^{-3(2x+7)}=(\frac{1}{2})^{5(3x)}[/tex]
As the base are equal, then:
[tex]-3(2x+7)=5(3x)[/tex]
Solve for x:
[tex]-6x-21=15x\\-21=15x+6x\\-21=21x\\x=-1[/tex]
Find the area of a parallelogram that has a base of 24 feet and a height of 12 feet
Answers
you're answer would be two hundred eighty eight
Answer:
288
Explanation:
Hope this helps
He model below can be used to find the quotient of one over two divided by one over six. What is the quotient?
Answers
1/2÷1/6
=
1/2*6/1
=
6/2
=
3
Answer:
Quotient would be 3.
Step-by-step explanation:
The model below can be used to find the quotient of one over two dividend by one over six.
We will rewrite the problem :
[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{6}[/tex]
As we know when we divide the two fractions, we must invert the second fraction and put the sign of multiplication in place of division sign and multiply.
So now we can write the problem as :
[tex]\frac{1}{2}[/tex] × [tex]\frac{6}{1}[/tex]
= [tex]\frac{6}{2}[/tex]
= 3
Quotient would be 3.
A 5.5-foot-tall woman walks at 4 ft/s toward a street light that is 27.5 ft above the ground. what is the rate of change of the length of her shadow when she is 16 ft from the street light? at what rate is the tip of her shadow moving?
Answers
The scenario involves differentiating a proportional relationship between the woman's distance from a streetlight and the length of her shadow to determine the rate of change of the shadow's length and the speed of the shadow's tip.
Explanation:The question involves finding the rates of change in the scenario where a woman walks toward a streetlight and the effects on her shadow's length and speed. Let's denote the distance between the woman and the streetlight as x, the length of her shadow as y, and her height as h. The streetlight's height is given as H. Using similar triangles, we can establish the relationship (H - h) / y = H / (x + y). Differentiating both sides with respect to time, t, allows us to calculate the rates of change we're interested in.
To find the rate of change of her shadow's length when she is 16 feet from the streetlight, we can take dh/dt as 0 since her height is constant, dx/dt as -4 ft/s because she is walking towards the light and substitute into the derived equation after differentiating. Similarly, we calculate the rate at which the tip of the shadow is moving by adding the rate of the woman's movement to the rate of change of the shadow's length.
g A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes (P = 0.287). This conclusion implies that the maximum difference in GPAs between male and female scholarship athletes is 0.287. the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287. the GPAs for male and female scholarship athletes are identical, except for 28.7% of the athletes. the chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in GPAs is 0.287
Answers
Answer:
the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287
Step-by-step explanation:
When conducting hypothesis tests, the P value tells you the probability of the results happening by random chance. That's why we usually test against a very low alpha level, usually 1% or 5%.
Here P = 28%, so there is a 28% chance that if we take a sample of athletes, about 1 out of 4 times there won't be a significant difference in GPA between males and females.
PLEASE HELP! I AM NEED IT DESPERATELY!!
Write the equation of the line in point-slope form.
Answers
Answer:
y= -2x/3+8
Step-by-step explanation:
find 2 points: (0,8) and (6,4)
substitute in y=ax+b
8=0a+b
b=8
4=6a+b
4=6a+8
6a=-4
a=-2/3
Given that the points (-5,7), (5,7),(5,1), and (-5,1) are vertices of a rectangle, how much stronger is the width than the length
Answers
Answer:
4 units
Step-by-step explanation:
The sides of the rectangle are parallel to the axes, so it is a simple matter to subtract coordinate values to find the dimensions.
Along the line y=7, the rectangle extends from -5 to 5, so has width 10.
Along the line x=5, the rectangle extends from 1 to 7, so has length 6.
The width is 10 - 6 = 4 units more than the length.
Answer: width=7 length =9
9-7=2
2 is the answer
Jerome solved the equation below by graphing.
log2(x) + log2(x-2) = 3
Which of the following shows the correct system of equations and solution?
Answers
Answer:
B. x = 4
Step-by-step explanation:
I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:
[tex]\log_bm+\log_bn=\log_bmn[/tex]
Using this law, we can combine and rewrite our initial equation as
[tex]\log_2(x\cdot(x-2))=3\\\log_2(x^2-2x)=3[/tex]
Remember that logarithms are simply another way of writing exponents. The logarithm [tex]\log_28=3[/tex] is just another way of writing the fact [tex]2^3=8[/tex]. Keeping that in mind, we can express our logarithm in terms of exponents as
[tex]\log_2(x^2-2x)=3\rightarrow2^3=x^2-2x[/tex]
2³ = 8, so we can replace the left side of our equation with 8 to get
[tex]8 = x^2-2x[/tex]
Moving the 8 to the other side:
[tex]0=x^2-2x-8[/tex]
We can now factor the expression on the right to find solutions for x:
[tex]0=(x-4)(x+2)\\x=4, -2[/tex]
The only option which agrees with our solution is B.
Answer:
The answer is:
[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]
Step-by-step explanation:
We are given a logarithmic expression as:
[tex]\log_2 x+log_2 (x-2)=3[/tex]
As we know that:
[tex]\log_a x=\dfrac{\log x}{\log a}[/tex]
Hence, we get the logarithmic expression as follows:
[tex]\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}=3[/tex]
We know that we can get the system of equations as follows:
[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}[/tex]
and
[tex]y_2=3[/tex]
Hence, when we plot the graph for this system of equations we see that the point of intersection of the graph is: (4,3)
Hence, the solution is the x-value of the point of intersection of the two equations.
Hence, x=4 is the solution.
Hence, the correct option is:
[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]
∠A and ∠B supplementary and vertical angles. What is m∠B
135
90
180
45
Answers
Answer:
90°
Step-by-step explanation:
Supplementary means they add to 180°. Vertical angles are congruent, so they must both be 180°/2 = 90°.
Answer:
90
Step-by-step explanation:
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