to rotate 90 degrees counterclockwise we must transform the points like this
[tex](x,y)\longrightarrow(y,-x)[/tex]and then invert the sign of the y-coordinate or the second coordinate of each point, so the total transformation is
[tex](x,y)\longrightarrow(y,x)[/tex]now, transform each point
[tex](0,4)\longrightarrow(4,0)[/tex][tex](0,1)\longrightarrow(1,0)[/tex][tex](2,1)\longrightarrow(1,2)[/tex][tex](2,4)\longrightarrow(4,2)[/tex]Question 5 of 10According to this diagram, what is cos 16°?
Explanation
We are given the following:
We are required to determine the value of cos 16° from the diagram given.
We know that according to the trigonometry ratio rules:
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]So, we have:
[tex]\cos16\degree=\frac{24}{25}[/tex]Hence, the answer is:
[tex]\cos16\operatorname{\degree}=\frac{24}{25}[/tex]Does the equation x = 1 represent a function?How do I know if it represents a function if it doesn't have y axis to show if it is.
A function is a relation between variables y and x,
where theres only a y value for every x value
In this case x=1 . For every value of x = 1 ,there are infinite values for y , it can take any value , negative or positive.
So this is NOT a function
A car travels 120 miles on 10 gallons of gas. At this rate, how many gallons will it need to travel 312 miles?
26 gallons
1) We can write this information setting up a proportion
miles gallons
120 10
312 x
2) Assuming the pace hasn't changed, then we can consider that as proportional:
120x = 312 * 10
120x= 3120
x = 3120/120
x =26
3) So 26 gallons are going to be needed for those 312 miles.
Given the right triangle find the value of sec(90 degree - theta) when a= 12, b= 5, c= 13
Use the next trigonometric identities:
[tex]\begin{gathered} \sec (90º-\theta)=\frac{1}{\cos (90º-\theta)} \\ \\ \cos (90º-\theta)=\sin \theta \end{gathered}[/tex]Then, the sec(90º - θ) is:
[tex]\sec (90º-\theta)=\frac{1}{\sin \theta}[/tex]The sin(θ) is:
[tex]\sin \theta=\frac{opposite}{hypotenuse}=\frac{5}{13}[/tex]Then:
[tex]\sec (90º-\theta)=\frac{1}{\frac{5}{13}}=\frac{13}{5}[/tex]Then, the sec(90º - θ) is 13/5Find the circumference of a circle with a Diameter = 12 m. Use 3.14 for π and round to 2 decimal places. ANS. C= B_____________. m
The circumference of a circle is given by the formula
[tex]s=2\cdot\pi\cdot r[/tex]however we also knos that the diameter can be written as
[tex]D=2\cdot r[/tex]meaning that the formula for the circumference can also be written as
[tex]s=D\cdot\pi[/tex]then the circumference for the given information is:
[tex]\begin{gathered} s=12\cdot3.14 \\ s=37.68 \end{gathered}[/tex]Totsakan enlarged the size of a photo to aheight of 18 in. What is the new width if itwas originally 2 in tall and 1 in wide?
Let's begin by identifying key information given to us:
New size: Height = 18 in, Width = ?
Old size: Height = 2 in, Width = 1 in
We will get the width of the new photo by following the explanation below:
[tex]\begin{gathered} 18\colon2=x\colon1 \\ \Rightarrow\frac{18}{2}=\frac{x}{1} \\ \text{Cross multiply, we have:} \\ 2\cdot x=18\cdot1\Rightarrow2x=18 \\ 2x=18 \\ \text{Divide both sides by ''2'', we have:} \\ x=\frac{18}{2}=9 \\ \therefore x=9in \end{gathered}[/tex]Therefore, the width of the enlarged photo is 9 inches
Completing a race) Ned spent 63 minutes walking 11 while If the ratio of time walking to jogging was 9:1, race? 2 minutes did he spend completing the
While completing the race, Ned spent 63 min walking if the ratio of time walking to jogging was 9:1, how many minutes did he spend completing the race?
Let
x-----> time spent walking
y -----> tiime spent jogging
we have
x/y=9/1
x=9y -----> equation A
we have
x=63 min
substitute in the equation A
63=9y
solve for y
y=7 minutes
therefore
teh answer is
7 minutesThe following scatter plot represents the relationship between a person's weight and the number of calories the person burns in one minute of jump roping. What type of relationship is shown?
The scatter plot shows a positive correlation because the points show a linear-trend describing that when x-values (weight) increases then y-values (calories) also increases.
Hence, the relationship is a Positive correlation.
133/ 12 i need the answer
We will have:
[tex]\frac{133}{12}=11.08333\ldots\approx11[/tex]The fraction is approximately 11.
I just need to know the answer to question 11
Answer:
A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.
Explanation:
Given the compound inequalities:
[tex]x-1\le7\text{ or }2x\ge22[/tex]First, solve both inequalities:
[tex]\begin{gathered} x-1\le7\implies x\le7+1\implies x\le8 \\ 2x\ge22\implies x\ge\frac{22}{2}\implies x\ge11 \end{gathered}[/tex]Thus, the number line should be the one that represents the solution:
[tex]x\le8\text{ or }x\ge11[/tex]• For x≤8, there is a ,closed circle on 8, and ,shading to the left.
,• For x≥11, there is a ,closed circle on 11, and ,shading to the right.
Therefore, the correct description will be:
A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.
The last option is correct.
Part 1: Person A has a car with the average fuel consumption of 20 miles per gallon. Person B has an average fuel consumption of 30 miles per gallon. Person C has an average fuel consumption of 40 miles per gallon. they are trying to work out how much fuel they will each save if they change cars. Person A, " I am going to buy Person B's car." Person B says, " I am going to buy Person C's car." Person C says that each week they will both save the same amount of fuel.Is person C correct? Part 2: Person C wants to buy a new car. Each week, he wants to save the same amount of fuel as person A saved. What average fuel consumption should person C look for in a new car?
Let's assum that each person drives 120 miles per week.
Then for person A we have:
[tex]\begin{gathered} 20mi\rightarrow1\text{gal} \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{20}=6gal \\ x=6\text{gal} \end{gathered}[/tex]for person B we have:
[tex]\begin{gathered} 30mi\rightarrow1gal \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{30}=4gal \\ x=4\text{gal} \end{gathered}[/tex]finally, for person C:
[tex]\begin{gathered} 40mi\rightarrow1gal \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{40}=3gal \\ x=3\text{gal} \end{gathered}[/tex]Then, if person A changes to person B's car, we have that the save is:
[tex]6-4=2[/tex]if person B buys person C's car, then the save is:
[tex]4-3=1[/tex]therefore, the savings on gas will be different for both of them and person C is incorrect.
2)Since person A saved 2 gallons, then the new car for Person C must save 2 gallons for each mile traveled.
Then we have the following equation:
[tex]3-x=2[/tex]where 'x' represents the number of gallons consumed in 120 miles. then, solving for x we have:
[tex]\begin{gathered} 3-x=2 \\ \Rightarrow-x=2-3=-1 \\ \Rightarrow-x=-1 \\ x=1 \end{gathered}[/tex]therefore, person C will need to buy a car that uses 1 gallon for eah 120 miles traveled
write in algebraic expression1) quotient of a number b and 36 2) 45 divided into a number r3) sum of 21 and a number x4) a number z less 19 5) a number f divided by 6
Solution
For this case we can do the following:
1)
[tex]\frac{b}{36}[/tex]2)
[tex]\frac{45}{r}[/tex]3)
[tex]21+x[/tex]4)
[tex]z-19[/tex]5)
[tex]\frac{f}{6}[/tex]4. A farmhouse shelters no more than 12 animals. Some are goats and some are ducks.Altogether there are more than 34 legs. How many of each animal could there be?What are you being asked to find?What are you given?Define your variables.Create & solve a system.Explain your solution(s).
• What are you being asked to find? define your variables
We are being asked to find the number of goats and ducks that there might be in the farmhouse.
• What are you given?
,•
From the information given by the question, we know that there are as many as 12 animals and that they have as many as 34 legs.
• Create & solve a system
from the given information we can write two expressions, one for the total number of animals, which equals 12, and another for the number of legs, let's call x to the number of goats and y to the number of ducks.
We know that there are a total of 12 animals, this is the number of goats plus the number of ducks, then we can write the expression:
goats + ducks = 12
x + y = 12
0.
And we know that there are 34 legs since a duck has 2 legs and a goat has 4, the number of legs of all the ducks would be the number of ducks times 2 and the number of legs of all the goats is 4 times the number of goats, then we can express the equation:
goat's legs + duck's legs = 34
4x + 2y = 34
Then, the system of equations that we have to solve is:
1. x + y = 12
2. 4x + 2y = 34
Now let's solve the system of equations, by following these steps:
Solve for y from the first equation:
x+y=12
x-x+y=12-x
y=12-x
Replace the expression y=12-x into the second equation and find the value of x.
4x + 2y = 34
4x+2(12-x)=34
4x+2*12-2x=34
4x+24-2x=34
2x+24=34
2x+24-24=34-24
2x=10
2x/2=10/2
x=5
Now that we know that x equals 5, let's replace it into the expression y=12-x, to find the value of y:
y=12-x
y=12-5=7
Then, x equals 5 and y equals 7
• Explain your solution
,•
In the farmhouse could there be a total of 5 ducks and 7 goats
Consider parallelogram QRST below.Use the information given in the figure to find m ZR, x, and m ZROS.R.4x1275040°7S
The opposite angles of a parallelogram are equal, therefore:
[tex]\begin{gathered} m\angle R=m\angle T \\ so\colon \\ m\angle R=75 \end{gathered}[/tex]Opposite sides of a parallelogram are parallel and equal so:
[tex]\begin{gathered} QT=RS \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]∠TSQ and ∠RQS are alternate interior angles, therefore:
[tex]\begin{gathered} m\angle RQS=m\angle TSQ \\ so_{}\colon \\ m\angle RQS=40 \end{gathered}[/tex]Find sectheta costheta, and cottheta where theta is the angle show in the figure
We will have the following:
We first determine the missing side of the triangle:
[tex]x=\sqrt{17^2-8{}^2}\Rightarrow x=15[/tex]Now, we determine the expressions:
[tex]\begin{gathered} sec(\theta)=\frac{17}{8} \\ \\ \\ cos(\theta)=\frac{8}{17} \\ \\ \\ cot(\theta)=\frac{8}{15} \end{gathered}[/tex]Is my answer correct? 3/4 + 9/16 = 3/16
Answer:
is not correct because the lcm will be 16 and u will get 21/16
logitechExample 6:Triangle XYZ is graphed below. Draw and label Triangle X'Y'Z' after a dilation using a scale factor oftwo.I.113XWhat will be the coordinates of point Y" after a reflection of polygon X'Y'Z' over the x-axis?Answer
First answer:
Second Answer:
The coordinates of the Y'' after reflection of poligon X'Y'Z' over the x axis: (-2, -4)
Item Price (dollars) $1,400 $2,400 $3,000 $4,400 Sales Tax (dollars) $112 $192 $240 $352 Based on the table, what is the rate of change? O The rate of change for the sales tax is $0.07 per dollar. O The rate of change for the sales tax is $0.08 per dollar. O The rate of change for the sales tax is $0.06 per dollar. The rate of change for the sales tax is $0.125 per dollar.
We know that the rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then
[tex]r\text{ = }\frac{Change\text{ in y}}{\text{Change in x}}\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are points of our model.
So, in this case we have that:
[tex]r\text{ = }\frac{Y2-Y1}{X2-X1_{}}\text{ = }\frac{112-352}{1400-4400}\text{ = }\frac{240}{3000}\text{ = 0.08}[/tex]So, the correct answer is: the rate of change for the sales tax is $0.08 per dollar.
i added the choices for the first box as well.
Looking at the triangles, we see that they have two congruent sides, and the angles between them are congruent too.
Then, the two triangles are related by side-angle-side (SAS), so the triangles are congruent (SAS theorem).
i need help with math
Answer:
x = 33
Step-by-step explanation:
Creating an equation
The angles shown are corresponding angles
Corresponding angles are angles that occupy the same position and are on the same side of the transversal. For a better sense of this, kindly review the attached image.
Corresponding angles are congruent ( equal to each other )
This means that 124 = 4x - 8
Solving for x
124 = 4x - 8
==> add 8 to both sides
132 = 4x
==> divide both sides by 4
33 = x
What is the slope-intercept form of the line with the point (0, 3) and a slope = -2?O A. y = 2x + 3O C. y = -2x + 3D. y = -2x - 3B. y = 2x - 3
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The given equation is
[tex]y=-2x+3[/tex]Compare it with the form above to find m and b
Since the coefficient of x is -2, then
m = -2
Since m is the slope of the line, then
The slope of the line is -2
The answer is B
Simplify the Expression [tex]12g + 3 - g {}^{2} + 2[/tex] g=4
done
Linus leaves his house and walks 7 blocks West to avoid Lucy. He then walks 3 blocks North to visit Charlie Brown. What is the shortest distance between the houses? Round to the nearest tenth.
First, draw a schematic representation of that situation:
The shortest distance between the starting point (Linus's house) and the endpoint (Charlie's house) is a straight line. Since a right triangle is formed with the sides of length 7 blocks and 3 blocks, we can use the Pyhtagorean Theorem to find the length of the hypotenuse:
[tex]\begin{gathered} ?=\sqrt[]{3^2+7^2} \\ =\sqrt[]{9+49} \\ =\sqrt[]{58} \\ \approx7.6 \end{gathered}[/tex]Therefore, the shortest distance between those two points would be 7.6 blocks.
This pentagonal prism is cut by the plane shown. The plane is parallel to the base of the pentagonal prism. What is the shape of the cross-section?
If the plane is parallel to the base, then the cross section has the same shape of the base: a penthagon.
The function h is defined by h (x)=3x² - 4.Find h (3x).
When we have a function f(x) we can evaluate it for different arguments (the value of x) by replacing the argument in the definition of the function.
In this case, we know h(x) and we have to express h(3x). To do this, we replace x in the original function with 3x:
[tex]\begin{gathered} h(x)=3x^2-4 \\ h(3x)=3(3x)^2-4=3\cdot(3^2x^2)-4=3\cdot9x^2-4=27x^2-4 \end{gathered}[/tex]Answer: h(3x) = 27x²-4
3. Find the median, range, and interquartile range for this data set. 21, 31, 26, 24, 28. 26 Median: Range: IQR:
The given data set is 21,31,26,24,28,26.
Arranging the data set in the ascending order,
21,24,26,26,28,31.
The data set contains 6 numbers,
The median can be determined by taking the average of 3rd and 4th term of the data set,
[tex]\begin{gathered} \text{Median}=\frac{26+26}{2} \\ =26 \end{gathered}[/tex]Thus, the required median is 26.
The range can be determined by taking the difference between the highest and the lowest value of the data set,
[tex]\begin{gathered} \text{Range}=31-21 \\ =10 \end{gathered}[/tex]Thus, the range of the data set is 10.
The interquartile range of the data set can be determined by taking the difference of quartile 1 and quartile 3.
[tex]\begin{gathered} \text{IQR}=Q_3-Q_1 \\ =28-24 \\ =4 \end{gathered}[/tex]Thus, the required interquartile range is 4.
Line Segment WV has an endpoint at (5, -7) and the midpoint is at (-3, 2). What are the coordinates of the other endpoint? Write your answer as an ordered pair: (x, y)
Answer:
Step-by-step explanation: it is that
3. The height of a projectile object fired into the air can be modeled by h(t) = -16t² + 48t + 3, where his
height, in feet, and t is time, in seconds. What is the maximum height the projectile will reach?
A. 3 feet
B. 35 feet
C. 39 feet
D. 105 feet
Answer:
C. 39 feet
Step-by-step explanation:
[tex]{ \tt{h(t) = - 16 {t}^{2} + 48t + 3 }}[/tex]
- Let us find the limits of the function
[tex] { \tt{ \frac{d \{h(t) \}}{dt} = - 32t + 48 }} \\ [/tex]
- So, let us differentiate for the second time;
[tex]{ \tt{ \frac{d {}^{2} \{h(t) \} }{dt {}^{2} } = - 32}} \\ [/tex]
- So, at maximum height; d{h(t)}/dt is 0;
[tex]{ \tt{ - 32t + 48 = 0}} \\ { \tt{ - 32t = - 48}} \\ { \tt{t = 1.5 \: seconds}}[/tex]
- Therefore; maximum height is;
[tex]{ \tt{h(t) = - {16t}^{2} + 48t + 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt{h(1.5) = - 16(1.5) {}^{2} + 48(1.5) + 3}} \\ { \tt{h(1.5) = - 36 + 72 + 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt{h(1.5) = 39 \: feet}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
.a. Triangle ABC with coordinates A (3, 4), B (7,7), and C (8, 1) is translated 6 units left and 7 units down.
Triangle ABC with coordinates A (3, 4), B (7,7), and C (8, 1) is translated 6 units left and 7 units down.
we have that
the rule of the translation is
(x,y) -------> (x-6, y-7)
Applying the rule to the coordinates of triangle ABC
A(3,4) ------> A'(3-6,4-7)
A'(-3,-3)
B(7,7) ------> B'(7-6, 7-7)
B'(1,0)
C(8,1) --------> C'(8-6,1-7)
C'(2,-6)
John has 44 quarters.Jan has 100 dimes. Whohas more money?
Note that 10 dimes = $1
Also 4 quarters = $1
That means, 100 dimes equals $10
Also, 44 quarters =