Answers
ANSWER:
(a)
(b)
STEP-BY-STEP EXPLANATION:
(a)
We must do the following transformation:
[tex]y=f(x)\rightarrow y=f(-x)[/tex]In this case, reflects f(x) about the y-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(-x,y)[/tex]We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-4.2\mright)\rightarrow(4,2) \\ (0,4)\rightarrow(0,4) \\ (4,6)\rightarrow(-4,6) \end{gathered}[/tex]We graph and we have:
(b)
We must do the following transformation:
[tex]y=g(x)\rightarrow y=-g(x)[/tex]In this case, reflects f(x) about the x-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(x,-y)[/tex]We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-7,-2\mright)\rightarrow\mleft(-7,2\mright) \\ \mleft(-4,-5\mright?)\rightarrow\mleft(-4,5\mright) \\ \mleft(4,-1\mright)\rightarrow\mleft(4,1\mright) \end{gathered}[/tex]We graph and we have:
Related Questions
PLEASE ITS URGENT I NEED HELP!!! I BEG YOU GUYS PLEEAASEEE THANKS..
Answers
Explanation
remember some properties of the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]then, to solve this solve each option and compare
Step 1
[tex]6^{-5}\cdot6^2[/tex]solve
[tex]\begin{gathered} 6^{-5}\cdot6^2=6^{-5+2}=6^{-3} \\ \end{gathered}[/tex]so, this is not an answer
Step 2
[tex](\frac{1}{6^2})^5[/tex]solve
[tex]\begin{gathered} (\frac{1}{6^2})^5=(6^{-2})^5=6^{(-2\cdot5)}=6^{-10} \\ \end{gathered}[/tex]so, this is an answer
Step 3
[tex]\begin{gathered} (6^{-5})^2 \\ \text{solve} \\ (6^{-5})^2=6^{-5\cdot2}=6^{-10} \end{gathered}[/tex]so, this is an answer
Step 4
[tex]\begin{gathered} \frac{6^{-3}}{6^7} \\ \text{solve} \\ \frac{6^{-3}}{6^7}=\frac{1}{6^3\cdot6^7}=\frac{1}{6^{3+7}}=\frac{1}{6^{10}}=6^{-10} \end{gathered}[/tex]so, this is an answer
Step 5
[tex]\begin{gathered} \frac{6^5\cdot6^{-3}}{6^{-8}} \\ \text{solve} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=\frac{6^{5-3}}{6^{-8}}=\frac{6^2}{6^{-8}}=6^2\cdot\frac{1}{6^{-8}}=6^2\cdot6^8=6^{10} \end{gathered}[/tex]so, this is not an answer
I hope this helps you
A triangle has vertices P (4.1), Q (4, 5) and R (7,5) What is the area of ∆PQR? (Area= 1/12 basexheight)
Answers
First, plot the points on a graph and form the triangle:
By looking at the triangle we can see that:
Base: 2
Height: 4
Area : 1/2 x 2 x 4 = 4 units2
For the equation, complete the given table.
Answers
Answer:
Step-by-step explanation:
first row: 4
second: 2
third: 6
fourth: 9
plug in x for x in the equation/plug in y for y in the equation for whichever is given.
Write an equation of variation to represent the situation and solve for the missing information The time needed to travel a certain distance varies inversely with the rate of speed. If ittakes 8 hours to travel a certain distance at 36 miles per hour, how long will it take to travelthe same distance at 60 miles per hour?
Answers
The time needed to travel a certain distance varies inversely with the rate of speed, so:
[tex]\begin{gathered} let\colon \\ t=\text{time} \\ v=\text{rate of speed} \\ t\propto\frac{1}{v} \end{gathered}[/tex]8hours----------------------------->36mi/h
xhours----------------------------->60mi/h
[tex]\begin{gathered} \frac{8}{x}=\frac{36}{60} \\ \text{ Since the it varies inversely:} \\ \frac{8}{x}=(\frac{36}{60})^{-1} \\ \frac{8}{x}=\frac{5}{3} \\ \text{solve for x:} \\ x=\frac{3\cdot8}{5} \\ x=4.8h \end{gathered}[/tex]4.8 hours or 4 hours and 48 minutes
What is the measure of the angle at the bottom of home plate?
Answers
We will ave the following:
*First: We will determine the sum of all internal angles of the polygon:
[tex](n-2)\cdot180\Rightarrow(5-2)\cdot180=3\cdot180[/tex][tex]=540[/tex]*Second: Now, that we know that the sum of all internal angles will be 540°, the following is true:
[tex]90+90+135+135+\alpha=540[/tex]Now, we solve for alpha [The angle]:
[tex]\Rightarrow\alpha=540-135-135-90-90\Rightarrow\alpha=90[/tex]So, the measure of the angle at the bottom is 90°.
Examine the graph and write a statement about the data. Use specific information from the graph.
Answers
This bar graph represents the percentage of the public's trust in the Federal Government from year 1960 to 2015. The public trust was highest in year 1960 at 74% and it was at its lowest in 2015 at 18%.
identify the equation
Answers
SOLUTION
We want to identify the equation that represents the data in the table.
Let's put the first values for x and y from the table, that is x = -2 and y = 11 and see if it works for the first option
[tex]y=x+5[/tex]This becomes
[tex]\begin{gathered} y=x+5 \\ y=-2+5 \\ y=3 \end{gathered}[/tex]Since we didn't get y = 11, but we got y = 3, then the first option is wrong.
Let's try the next one
[tex]y=-3x+5[/tex]This becomes
[tex]\begin{gathered} y=-3x+5 \\ y=-3(-2)+5 \\ y=6+5 \\ y=11 \end{gathered}[/tex]So, we got y = 11, this option should be the correct answer, but let us confirm with the next values of x and y which are (0, 5).
So we will put x = 0, if we get y = 5, then the option is correct, so
[tex]\begin{gathered} y=-3x+5 \\ y=-3(0)+5 \\ y=0+5 \\ y=5 \end{gathered}[/tex]Since we got y = 5, this option is correct.
Hence, the answer is the 2nd option.
[tex]y=-3x+5[/tex]Rewrite the following equation in slope-intercept form. x - 7y = 20 Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
x - 7y = 20
slope-intercept form = ?
Step 02:
Slope-intercept form of the line
y = mx + b
x - 7y = 20
x = 20 + 7y
x - 20 = 7y
7y = x - 20
[tex]y\text{ = }\frac{x}{7}\text{ - }\frac{20}{7}[/tex]The answer is:
y = x/7 - 20/7
i have questions on a math problem. i can send when the chats open
Answers
The random sample is determined as the simplest forms of collecting data from the total population.
Under random sampling, each member of the subset carries an equal opportunity of being chosen as a part of the sampling process.
So according to the question given
Assign each person of the population a number. Put all the numbers into bowl and choose ten numbers.
is the random sample because every person carries an equal opportunity of being chosen from the total population.
Hence the correct option is A.
What is the equation in slope-intercept form of the line that passes through the point (1,5) and is parallel to the line represented by 3x-y=4?
Answers
Answer:
[tex]3x - 14[/tex]
Step-by-step explanation:
-y= -3x+4
-1 because de y no have a number in front
-1y÷-1= -3x÷-1 4÷-1
15. The new county park is one mile square. What would be the length of a road around its boundaries?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
County park:
area = 1 mile²
Step 02:
length of a road around:
area = side²
1 mile ² = s²
[tex]\begin{gathered} s^2=1 \\ s=\sqrt[]{1}=\text{ 1 } \end{gathered}[/tex]s = 1 mile
perimeter = 4 s = 4 * 1 mile = 4 miles
The answer is:
the length of a road around its boundaries is 4 miles
If a projectile is fired straight upward from the ground with an initial speed of 224 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2.+224t Find the maximum height of the projectile.
Answers
The height reached by the projectile is 784 feet.
What is the maximum height of the projectile?
The projectile experiments an uniformly accelerated motion due to gravity, whose height is represented by the quadratic equation:
h(t) = - 16 · t² + 224 · t
Where t is the time, in seconds.
In this problem we need to find the maximum height reached by the projectile, which can be found by finding the vertex form of the quadratic equation:
h(t) = - 16 · (t² - 14 · t)
h(t) - 16 · 49 = - 16 · (t² - 14 · t + 49)
h(t) - 784 = - 16 · (t - 7)²
The maximum height of the projectile is 784 feet.
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The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Equation 1
Equation 2
Equation 1 is modeled for the percentage of never-married American adults, y, x years after 1970 and Equation 2 is modeled for the percentage of married
American adults, y, x years after 1970. Use these models to complete parts a and b.
a. Determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For
that year, approximately what percentage of Americans, rounded to the nearest percent, will belong to each group?
In year
the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately % percentage of
Americans will belong to each group.
Answers
After 4 years the percentage of never-married adults will be the same as the percentage of married adults.
The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Multiply the second equation with 3
-3x + 10y = 160 .....equation 1
3x + 6y = 492........equation 2
adding equation 1 and 2
16y = 652
y = 40.75
x + 2y = 164
x = 164 - 2 (40.75)
x = 82.5
Let the number of years be t
-3x+10y x t = x+2y
t = 4x - 8y
t = 330 - 326
t = 4 years
Therefore, after 4 years the percentage of never-married adults will be the same as the percentage of married adults.
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Which information will prove a quadrilateral is a square?O All 4 sides are congruentO All 4 sides are congruent and all 4 angles are right anglesO All 4 angles are right anglesO Both pairs of opposite sides are parallel
Answers
Answer
All 4 sides are congruent and all 4 angles are right angles
Step-by-step explanation
In a square, all the four sides measure the same (they are congruent). And the four angles are right angles, that is, they measure 90°
Identify the domain and range of the relation. Is the relation a function? Why or why not?
{(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
Answers
Domain={-3, 0, 1, 2}, Range={1,2,5,4} and the relation is not a function.
What is a function?A relation is a function if it has only one y-value for each x-value.
The given relation is {(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
The domain is the set of all the first numbers of the ordered pairs.
In other words, the domain is all of the x-values.
Domain={-3, 0, 1, 2}
The Range is the set of all the second numbers of the ordered pairs.
In other words, the range is all of the y-values.
Range={1,2,5,4}
The given relation is not a function because there are two values of y for one value of x. It means 4 and 1 are values of 2.
Hence Domain={-3, 0, 1, 2}, Range={1,2,5,4} and the relation is not a function.
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Bc is included between
Answers
Answer:
A. angle B and angle C
Step-by-step explanation:
Line segments are named after the two points where they begin and end.
Evaluate (3√2-1) (3√2+1)
Answers
Answer:
9√3 converted is 15.58845727
Which statement is true for all real values of θ? sin2θ − cos2θ = 1 cos2θ − sin2θ = 1 cos2θ = sin2θ − 1 cos2θ = 1 − sin2θ
Answers
The statement holds true for all true values of is cos²θ = 1 − sin²θ
What is meant by trigonometric identities?Trigonometric Identities are equalities that involve trigonometry functions and hold true for all variables in the equation. There are numerous trigonometric identities involving the side length and angle of a triangle. Trigonometry identities are trigonometry equations that are always true, and they are frequently used to solve trigonometry and geometry problems as well as understand various mathematical properties. Knowing key trig identities aids in the retention and comprehension of important mathematical principles as well as the solution of numerous math problems. Convert everything to sine and cosine terms. When possible, use the identities. Begin by simplifying the left side of the equation, then move on to the right side if you get stuck.To learn more about trigonometric identities, refer to:
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X 즈 - + 3 = 15 -4someone help me confused
Answers
First we have to transfer the number 3 the other side of equal sign as follows,
[tex]\begin{gathered} \frac{x}{-4}=15-3 \\ \frac{x}{-4}=12 \end{gathered}[/tex]Now, we need to transfer (-4) to the other side of the equal side by multiplying with the number 12.
[tex]\begin{gathered} \frac{x}{-4}=12 \\ x=12\ast(-4) \\ x=-48 \end{gathered}[/tex]Thus, the answer of the x is (-48).
Which of the following correctly identifies the vertices that lie on the major axis of the conic section shown below? (x - 2) 3-2*) (y+5) = 1 4 9 O A. (2,-2) and (2,-8) O B. (-5,5) and (-5,-1) O C. (5,5) and (-1,-5) O D. (0,-5) and (4,-5)
Answers
General equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]where (h,k) is the center, and a and b are some constants.
If b² is greater than a², then the y-axis is the major axis.
In this case, the ellipse is defined by the next equation:
[tex]\frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1[/tex]This means that:
[tex]\begin{gathered} b^2=9 \\ b=\sqrt[]{9} \\ b=3 \end{gathered}[/tex]And, h = 2, k = -5
The vertices on the major axis are computed as follows:
(h, k+b) and (h, k-b)
Substituting with h = 2, k = -5, and b = 3, the vertices are:
(2, -5+3) and (2, -5-3)
(2, -2) and (2, -8)
which fraction remains in the quotient when 4,028 is divided by 32
Answers
We get that
[tex]\frac{4028}{32}=\frac{1007}{8}=\frac{1000}{8}+\frac{7}{8}=125+\frac{7}{8}[/tex]so the fractions that remains is 7/8
I need help with my math
Answers
Answer:
The fourth choice: y+3 = 1(x+2); y= x-1
Explanation:
The point slope form of a linear equation is
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point on the line and m is the slope.
Now we first calculate the slope.
[tex]m=\frac{3-(-3)}{4-(-2)}=\frac{6}{6}=1[/tex]therefore, we have
[tex]y-y_0=1(x-x_0)[/tex]Now we use (x0, y0) = (-2, -3) and get
[tex]y-(-3)_{}=1(x-(-2))[/tex][tex]\boxed{y+3=1\mleft(x+2\mright)}[/tex]which is our equation in point-slope form.
Now, we convert the equation above into the slope-intercept form.
Subtracting 3 from both sides gives
[tex]y+3-3=x+2-3[/tex][tex]\boxed{y=x-1}[/tex]which is the equation in slope-intercept form.
Hence, the answer to the question is
[tex]y+3=1(x+2);y=x-1[/tex]which is the fourth option.
Y.11 Multi-step problems with customary uni You have prizes to reveal! Go to your Tracy decides to take her puppy for a walk. After 90 feet, they stop to smell some roses. Then, Tracy runs into a friend 200 yards up the road. They start talking, and soon it's time for Tracy to go home. So, she and her puppy head back to her house. How many feet long was Tracy's walk? feet Submit
Answers
Given:
The distance travelled by Tracy till she stopped to smell roses, x=90 feet.
The distance from roses to the friend, y=200 yards.
The distance travelled by Tracy one side,
[tex]\begin{gathered} D=x+y \\ =90\text{ f}eet+200\times3feet \\ =90\text{ f}eet+600\text{ f}eet \\ =690\text{ f}eet \end{gathered}[/tex](1 yard=3 feet).
Now, the total distance travelled byTracy both sides is,
[tex]\begin{gathered} d=2D \\ =2\times690\text{ f}eet \\ =1380\text{ f}eet \end{gathered}[/tex]Therefore, Tracy walk was 1380 feet long.
If the 10 letters are {aa,aa,aa,aa,bb,bb,cc,cc RR,RR} are available and all 10 of them are to be selected without replacement,what is the number of different permutations?
Answers
In order to calculate the number of permutations, first we start with the factorial of the number of letters.
There are 10 letters, so we start with the factorial of 10.
Then, we need to check the number of repetitions. Each repetition will be a factorial in the denominator:
[tex]x=\frac{10!}{a!\cdot b!\operatorname{\cdot}...}[/tex]We have four repetitions of aa, two repetitions of bb, two repetitions of cc and two repetitions of RR, therefore the final expression for the number of permutations is:
[tex]x=\frac{10!}{4!2!2!2!}[/tex]Calculating this expression, we have:
[tex]x=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5\operatorname{\cdot}4!}{4!\operatorname{\cdot}2\operatorname{\cdot}2\operatorname{\cdot}2}=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5}{8}=18900[/tex]Therefore there are 18900 permutations.
4. Identify the properties that are always true for the given quadrilateral by placing an X in the appropriate box. Property Parallelogram Rectangle Rhombus Square Isosceles Trapezoid Kite a. Opposite sides are parallel. b. Only one pair of opposite sides is parallel C. Opposite sides are congruent Side Relationships d. Only one pair of opposite sides is congruent e. All sides are congruent. f. 2 pairs of consecutive sides are congruent.
Answers
There is quadrilateral, means it has 4 lines
Is a rhombus
If z = 12.8, what's is the value of 2(z - 4)?
Answers
The given expression is
[tex]2(z-4)[/tex]Let's replace z = 12.8.
[tex]2(12.8-4)=2(8.8)=17.6[/tex]Therefore, the value is 17.6.5. Use a number line to find the product: 5 x (-3)=
Answers
First, we solve the expression.
Since it is a negative number we have to place it 15 places to the left ( from zero)
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y ≥ 3x - 6y < -2x - 1LABEL ALL COORDINATESAnswer
Answers
Answer:
(-3, 2)
Explanation:
Given the system of inequalities:
[tex]\begin{gathered} y\ge3x-6 \\ y<-2x-1 \end{gathered}[/tex]To solve the inequalities graphically, follow the steps below:
Inequality 1
First, find the equation of the boundary line.
[tex]y=3x-6[/tex]Next, determine the intercepts to draw the boundary line.
[tex]\begin{gathered} \text{When }x=0,y=3(0)-6=-6\implies(0,-6) \\ \text{When y}=0,0=3x-6\implies3x=6\implies x=2\implies(2,0) \end{gathered}[/tex]Join the points (0,-6) and (2,0) using a solid line.
Finally, determine the required half-plane using the origin test.
[tex]\begin{gathered} At\text{ (0,0)} \\ y\ge3x-6\implies0\ge-6(T\text{rue)} \end{gathered}[/tex]The side that contains the point (0,0) is the required half-plane.
The graph showing the first inequality is given below:
Inequality 2
First, find the equation of the boundary line.
[tex]y=-2x-1[/tex]Next, determine the intercepts to draw the boundary line.
[tex]\begin{gathered} \text{When }x=0,y=-2(0)-1=-1\implies(0,-1) \\ \text{When y}=0,0=-2x-1\implies-2x=1\implies x=-0.5\implies(-0.5,0) \end{gathered}[/tex]Join the points (0,-1) and (-0.5,0) using a broken line.
Finally, determine the required half-plane using the origin test.
[tex]\begin{gathered} At\text{ (0,0)} \\ y<2x-1\implies0<-1(False\text{)} \end{gathered}[/tex]The side that DOES NOT contain the point (0,0) is the required half-plane.
The graph of the system of inequalities is given below:
A point in the solution set is (-3, 2).
2. What is an algebraic expression for each phrase?a. the product of 9 and a number tb. the difference of a number x and 1/2c. the sum of a number m and 7.1 d. the quotient of 207 and a number n
Answers
The algebraic expression for each phrase would be the following:
a. the product of 9 and a number t would be expressed as:
9*t
b. the difference of a number x and 1/2 would be expressed as:
x - 1/2
c. the sum of a number m and 7.1 would be expressed as:
m + 7.1
d. the quotient of 207 and a number n would be expressed as:
207 / n
Angela bought a calculator on sale for 15% off. Sales tax is 7.5%. If the calculator cost x dollars, which expression represents the total cost of the calculator?A). (x-0.15) (0.075)B). (x-0.15) (1.075)C). (x-0.15x) (0.075)D). (x- .015x) (1.075)
Answers
Original price = x
Price with 15% off = x - 0.15x
Price with 15% off and 7.5% tax = (x - 0.15x)(1.075)
Answer:
Option B: (x - 0.15x)(1.075)
