PLAC S(7,-5) K(9, -4) I(8, -7) R(9, -9) T(7,-8) and perform: (1) T(x, y) -> (X-6, y) and label S'KTR'T' (2) Reflect SKIRT over the x-axis and label S"K"I"R"T". Write the rule using the notation. (3) Shift SKIRT 4 units up and 5 units right and label S""K"|""R""T". Write the rule. (4) Write the new coordinates of KV after shifting K"9 units up & 12 left.
Answers
You have the following points:
S(7,-5) K(9,-4) I(8,-7) R(9,-9) T(7,-8)
T(x,y) => (x - 6,y)
S => S'(7-6,-5) = S'(1,-5)
K => K'(9-6,-4) = K'(3,-4)
I => I'(8-6,-7) = I'(2,-7)
R => R'(9-6,-9) = R'(3,-9)
T => T'(7-6,-8) = T'(1,-8)
T(x,y) => (x,-y) reflection around x-axis
S' => S''(1,5)
K' => k''(3,4)
I' => I''(2,7)
R' => R''(3,9)
T' => T''(1,8)
T(x,y) => (x+5,y+4)
S'' => S'''(1+5,5+4) = S'''(6,9)
K'' => K'''(3+5,4+4) = K'''(8,8)
I'' => I'''(2+5,7+4) = I'''(7,11)
R'' => R'''(3+5,9+4) = R'''(8,13)
T'' => T'''(1+5,8+4) = T'''(6,12)
T(x,y) => (x -12,y+9)
S''' => S''''(6-12,9+9) = S''''(-6,18)
K''' => K''''(8-12,8+9) = K''''(-4,17)
I''' => I''''(7-12,11+9) = I''''(-5,20)
R''' => R''''(8-12,13+9) = R''''(-4,22)
T''' => T''''(6-12,12+9) = T''''(-6,21)
The previous result are the final points after all transformations.
A graph of the result is as follow:
the points S,K,I,R
Related Questions
Approximately 33,400 people took a vacation to a state park 15 years ago. Last year 99,500,000 vacationed to the same state park. Approximately how many more people visited the park than 15 years ago?
Answers
99,466,600
Explanations:The approximate number of people that took a vacation to the state park 15 years ago = 33,400
The number of people that vacationed to the state park last year = 99,500,000
The approximate difference between the number of people that visited the state 15 years ago and last year = 99,500,000 - 33,400
The approximate difference between the number of people that visited the state 15 years ago and last year = 99,466,600
Approximately, 99,466,600 more people visited the park last year than 15 years ago
What are the solutions of 12-x2= 0?O x=2,3 and x = -2/3O x=3/5 and x = -3,2O x= 4/3 and x = -4/3O x = 6 and x = -6
Answers
The given equation is
[tex]12-x^2=0[/tex]Let's solve for x.
[tex]\begin{gathered} 12=x^2 \\ x=\pm\sqrt[]{12} \\ x=\pm\sqrt[]{4\cdot3} \\ x=\pm2\sqrt[]{3} \end{gathered}[/tex]Hence, the correct answer is the first answer choice.Germaine measured the height of a plant, H, in centimeters (cm) as a function of days, d, since he planted it in his yard. The following table shows his data. d 0 2 4 6 8 10 12 H(d) 8.2 9.6 11.0 12.4 13.8 15.2 16.6 What is the rate of change of the function?
Answers
The formula for determining the rate of a function is expressed as
rate = (y2 - y1)/(x2 - x1)
In this scenario,
the values of d are the x values and the values of H(d) are the y values. Looking at the table,
When x1 = 0, y1 = 8.2
when x2 = 2, y2 = 9.6
By substituting these values into the formula,
rate of change = (9.6 - 8.2)/(2 - 0)
rate of change = 1.4/2
rate of change = 0.7
Rita correctly answered 9 questions out of 10 on a test. What fraction of the test questions did Rita answer incorrectly? A 9/10 B 9/100 C 1/10 D 1/100
Answers
We need to find the fraction of the test questions that Rita answered incorrectly.
We know that Rita correctly answered 9 questions. Since the test had 10 questions, Rita answered incorrectly 1 question.
So, Rita answered incorrectly 1 out of 10 questions. And we represent this fraction by writing the number of correct questions over the total number of questions::
[tex]\frac{1}{10}[/tex]Therefore, the answer is option C.
explain how properties of equality can be used to determine the pair without having to find the solution set for each.
Answers
If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. Then, in the first case, we can add -7 to both sides and get
[tex]\begin{gathered} 2(x+1)=13-7 \\ 2(x+1)=6 \end{gathered}[/tex]Similarly, in the second case, we can add -14 to both side and get
[tex]\begin{gathered} 4(x+2)=26-14 \\ 4(x+2)=12 \end{gathered}[/tex]We can also divide both sides by the same quantity. In the first case, we can divide by 2 and ger
[tex]\begin{gathered} x+1=\frac{6}{2} \\ x+1=3 \end{gathered}[/tex]in the second case, we can divide by 4 and get
[tex]\begin{gathered} x+2=\frac{12}{4} \\ x+2=3 \end{gathered}[/tex]Finally, in the first case, we can add -1 to both side and get
[tex]\begin{gathered} x=3-1 \\ x=2 \end{gathered}[/tex]Similarly, in the second case, we can add -2 in both sides and get
[tex]\begin{gathered} x=3-2 \\ x=1 \end{gathered}[/tex]Then, in sumarry, you can add, substract, multiply or divide by the same number in both sides in order to remain the equallity of the given equation
I got this question wrong, the answer in the gray box is the correct one but I would like it to be worked through, so I know what I did wrong, thank you!
Answers
see the figure below to better understand the problem
Find out the distance traveled by Andrea after 6 hours
Multiply the speed by the time
so
190*6=1,140 miles
Find out the distance traveled by Carlos after 6 hours
240*6=1,440 miles
For this problem, you must apply the law of cosines, because we know the length sides of two sides of the triangle and the included angle. You need to calculate the length of the third side
Applying the law of cosines
[tex]c^2=a^2+b^2-2(a)(c)\cos (C)[/tex]where
a=1,140 miles
b=1,440 miles
C=130 degrees
substitute
[tex]c^2=1,140^2+1,440^2-2(1,140)(1,440)\cos (130^o)[/tex]c=2,341.7 miles
therefore
The answer is 2,341.7 milesIf c ⊥ b, what is m∠2?A) 98B 99C) Not enough information D) 82
Answers
Answer
C) Not enough information
Step-by-step explanation
Given that lines c and b are perpendicular, then angles 5, 6, 7, and 8 measure 90°.
Since we don't know what is the relationship between lines c and a or between b and a, then we cannot conclude anything about the measure of angles 1, 2, 3, or 4.
It’s homework I been stuck on the problem for 20 mins
Answers
The given transformation is:
[tex]g(x)=6f(8x)+1[/tex]What we do is to express the x in f(x) as a product and 8 and another number.
• 80=8 x 10
,• -56=8 x -7
,• -32 = 8 x -4
,• 8=8 x 1
Therefore:
[tex]\begin{gathered} g(10)=6f(8\times10)+1=6f(80)+1=6(-9)+1=-14 \\ \implies x=10,g(x)=-14 \\ \\ g(-7)=6f(8\times-7)+1=6f(-56)+1=6(-2)+1=-11 \\ \implies x=-7,g(x)=-11 \\ \\ g(-4)=6f(8\times-4)+1=6f(-32)+1=6(5)+1=31 \\ \implies x=-4,g(x)=31 \\ \\ g(1)=6f(8\times1)+1=6f(8)+1=6(7)+1=43 \\ \implies x=1,g(x)=43 \end{gathered}[/tex]The completed table is, therefore:
For Items 5-7, determine the slope of the line that passes through each pair of points.
Answers
slope=-4
Explanation
Step 1
when you have two points of a line, P1 and P2 , the slope is given by:
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ \text{and} \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(-4,11)
P2(1,-9)
Step 2
replace in the formula
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-9-11}{1-(-4)}=\frac{-20}{1+4}=\frac{-20}{5}=-4 \\ \text{slope}=-4 \end{gathered}[/tex]I hope this helps you.
A trapezoid midsegment measures 6. One of the bases measures 10.What is the measure of the other base?
Answers
A trapezoid midsegment measures 6.
One of the bases measures 10.
What is the measure of the other base?
Let
x -----> the measure of the other side
we have that
6=(x+10)/2 -------> by midsegment theorem
solve for x
12=x+10
x=12-10
x=2
answer is 22. A company manufactures a certain item and sells it online. The company has a business model where the cost C, in dollars, to make xitems is given by the equation C=2.5x+21 and the revenue R, in dollars, made by selling xitems is given by the equation R=6x. The break even point is the point where the cost and the revenue intersect. How many items must the company sell to break even?
Answers
Explanation:
6 items
Explanation:
The break-even point is the point when the cost is equal to the revenue, so we can formulate the following equation:
C = R
2.5x + 21 = 6x
Then, we can solve for x, so:
2.5x + 21 - 2.5x = 6x - 2.5x
21 = 3.5x
21/3.5 = 3.5x/3.5
6 = x
Therefore, the company needs to make 6 items to break even.
Three out of 8 skittles are green . which represents the fraction of green skittles in total?
Answers
Let:
Ng = Number of green skittles
N = Total number of skittles
The fraction which represent the fraction of green skittles in total is given by:
[tex]\frac{Ng}{N}=\frac{3}{8}=0.375[/tex]Answer:
0.375
Theoretical Probability - Guided Practice#10 - The bag contains 4 red, 1 yellow, 2 blue, 6 purple, and 3 green marbles. Find theprobability of picking a marble that is not a red marble.O 60%O 45%25%75%
Answers
Answer:
75%
Explanation:
The number of red marbles, n(R) = 4
Total number of marbles, n(S) = 4+1+2+6+3 = 16
The probability of not picking a red marble, P(R'):
[tex]\begin{gathered} P(R^{\prime})=1-P(R) \\ =1-\frac{n(R)}{n(S)} \\ =1-\frac{4}{16} \\ =1-\frac{1}{4} \\ =\frac{3}{4} \\ =0.75 \\ =75\% \end{gathered}[/tex]The probability of picking a marble that is not a red marble is 75%.
Find x when y = 0:2x + 3y = -8x = ?
Answers
Substituting y=0 in the given equation, we get:
[tex]\begin{gathered} 2x+3(0)=-8. \\ \end{gathered}[/tex]Simplifying the above result, we get:
[tex]2x=-8.[/tex]Now, dividing the above equation by 2, we get:
[tex]\frac{2x}{2}=\frac{-8}{2}.[/tex]Therefore:
[tex]x=-4.[/tex]Answer:
[tex]x=-4.[/tex]Can you help me please?The sum of two numbers is 46. The sum of 6 times the larger and 4 times the smaller is 238. What’s the larger number and the smaller number
Answers
We have:
The sum of two numbers is 46: x + y = 46
The sum of 6 times the larger and 4 times the smaller is 238: 6x + 4y = 238
Where
x = the larger number
y = the smaller number
Solve the system of equations:
[tex]\begin{gathered} x+y=46 \\ 6x+4y=238 \end{gathered}[/tex]So:
[tex]\begin{gathered} x+y-x=46-x \\ y=46-x \end{gathered}[/tex]Substitute y in the second equation:
[tex]6x+4(46-x)=238[/tex]Simplify and solve for x:
[tex]\begin{gathered} 6x+184-4x=238 \\ 2x+184=238 \\ 2x+184-184=238-184 \\ 2x=54 \\ \frac{2x}{2}=\frac{54}{2} \\ x=27 \end{gathered}[/tex]Then for y:
[tex]y=46-27=19[/tex]Answer:
larger number: 27
smaller number: 19
Which of the following is the best estimate of the temperature at 11:00 pm if the temperature continues to drop at the same rate?
Answers
In order to calculate the rate, we calculate the variation of temperature and time
[tex]\begin{gathered} \Delta time=8-6 \\ \Delta time=2 \\ \\ \Delta temperature=-17-(-13) \\ \Delta temperature=-17+13 \\ \Delta temperature=-4 \end{gathered}[/tex]then, calculate the rate by dividing the variation of temperature by the variation of time
[tex]\frac{\Delta temperature}{\Delta time}=\frac{-4\degree C}{2h}=-\frac{2\degree C}{h}[/tex]the rate is equal to -2°C per hour, then from 8:00 pm to 11:00 pm, there is a difference of 3 hours.
Multiply the time by the rate:
[tex]-\frac{2\degree C}{h}\times3h=-6\degree C[/tex]The temperature drops another 6°C, then,
[tex]-17\degree C-6\degree C=-23\degree C[/tex]Answer:
The temperature will be about -23°C
Austin mad this histogram showing the number of siblings for each of the students in his swim class. How many more students have 2 or 3 siblings than 4 or 5 siblings?
Answers
Given a histogram, the height of the bars represents the number of students for each corresponding number of siblings.
Students with 2 or 3 siblings: 10 students.
Students with 4 or 5 siblings: 2 students.
Therefore, the difference will be
[tex]10-2=8[/tex]Hence, 8 more students have 2 or 3 siblings than 4 or 5 siblings.
Evaluate the variable expression when a = 4, b = 4, and c = -2.bc = (2a)
Answers
According to the given data we have the following expression:
bc = (2a)
a=4
b=4
c=-2
To evaluate and calculate the expression when bc = (2a) we would have to substitute the elements of the expression with the values provided above.
So, the expression would be replaced by the values of the elements as follows:
bc = (2a)
4*.-2=-(2*4)
-8=-8
The expression is valid as -8 is equal to -8.
Convert 63°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. C=--(F-32) 9 9 F= 0+32 c+33 63 F ic X Х $
Answers
Answer:
C = 17.2
Step-by-step explanation:
Suppose we have a temperature measured in degrees Fahrenheit(F). It can be measured in degrees Celsius according to the following formula:
[tex]C=\frac{5(F-32)}{9}[/tex]In this question, we want to find C when F = 63. So
[tex]C=\frac{5(F-32)}{9}=\frac{5(63-32)}{9}=\frac{5\ast31}{9}=\frac{155}{9}=17.2[/tex]So the answer is C = 17.2.
A store buys a pair of shoes for $40 and sells the shoes for $70.What was the percent markup?
Answers
EXPLANATION
Let's see the facts:
Buy price = $40
Sell price = $70
The markup percentage formula is:
[tex]\text{Markup\%}=\frac{Sell\text{ price - cost}}{\cos t}\cdot100[/tex]Substituting terms:
[tex]\text{Markup\% = }\frac{70-40}{40}\cdot100\text{ = 75\%}[/tex]The markup is 75%.
Estimate the values for x that will give you a solution of f(x)=2
Answers
We have the function f(x) =2.
Any pair of values with the form (x,2) is a solution to f(x)=2, as it is an horizontal line with value y=2 for any value of x.
Write as an algebraic expression of x that does not involve trigonometric functions.
Answers
Given:
[tex]\cos (\arcsin 3x+\arccos x)[/tex][tex]\text{Let A= arcsin3x ; B= arccosx}[/tex][tex]\sin A=3x\text{ ; }cosB=x[/tex][tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex][tex]\cos (A+B)=\cos A(x)-\sin B(3x)[/tex][tex]\cos (A+B)=\sqrt[]{1-\sin^2A}(x)-\sqrt[]{1-\cos^2B}(3x)[/tex][tex]\cos (A+B)=\sqrt[]{1-9x^2}(x)-\sqrt[]{1-x^2}(3x)[/tex][tex]\cos (A+B)=x\sqrt[]{1-9x^2}-3x\sqrt[]{1-x^2}[/tex]Therefore, 1st option is the correct answer.
Candace and Omar are debating on what happens to the circumference of a circle if the diameter is doubled. Who is correct and why? Justify your reasoning. The circumference is about three times as large! The circumference becomes twice as large! who is correct and why justify your reasoning
Answers
The answer is twice as large, by the proportion in comparison it is double in each measurement taken of the circumference
A painter charges $15.09 per hour, plus an additional amount for the supplies. If he made $170.95 on a job where he worked6 hours, how much did the supplies cost?
Answers
Give Data:
The cost per hour is, $15.09.
The toat amount made is, T = 170.95.
The time he worked is, 6 hours.
Ley x be the cost of the supplies.
The cost he made by working for 6 hours is,
[tex]C=6\text{hrs}\times15.09\text{ /hr=}90.54[/tex]Therefore, we have,
[tex]undefined[/tex]The vine grew 14 feet, & then Santa cut it back 9 feet. How long is it now?
Answers
Find out the difference between 14 and 9
that means
14-9=5 ft
therefore
the answer is 5 feetFind the length of the leg a of a right triangle with leg length b = 21.5 inches and the hypotenuse c = 31.9 inches. Use a calculator to estimate the square root to one decimal place.The length of the leg is approximately _____inches.
Answers
The length of the leg a of the right triangle is obtained by applying the Pythagorean theorem which is given as:
[tex]\text{opposite}^2+adjacent^2=hypothenus^2[/tex]Thus, we have that:
[tex]a^2+b^2=c^2[/tex]Given that b = 21.5 inches and c = 31.9 inches, we now have:
[tex]a^2+(21.5)^2=(31.9^2)[/tex][tex]a^2+462.25=1017.61[/tex][tex]a^2=1017.61-462.25[/tex][tex]a^2=555.36[/tex][tex]\begin{gathered} a=\sqrt[]{555.36}=23.57 \\ \Rightarrow a=23.6\text{ inches (to one decimal place)} \end{gathered}[/tex]Therefore, the length of the leg a of the right triangle is 23.6 inches
A new tire had a tread depth of 5 over 8 in, After driving one year the tire had 17 over 32 in. of tread remaining. What percent of the tread was worn?
Answers
Given:
a.) A new tire had a tread depth of 5 over 8 in. (5/8)
b.) After driving one year the tire had 17 over 32 in. of tread remaining. (17/32)
First, let's make the two fractions 5/8 and 17/32 into similar terms. (With the same denominator)
The LCM of 8 and 32 is 32. Therefore, let's transform 5/8 into its equivalent fraction with a denominator of 32.
We get,
[tex]\text{ }\frac{5}{8}\text{ = }\frac{5\text{ x 4}}{32}\text{ = }\frac{20}{32}[/tex]Therefore, the original tire depth is 5/8 or 20/32 in.
Next, let's determine the difference between the original and new depth after one year.
[tex]\text{ }\frac{5}{8}\text{ - }\frac{17}{32}\text{ = }\frac{20}{32}\text{ - }\frac{17}{32}\text{ = }\frac{20\text{ - 17}}{32}\text{ = }\frac{3}{32}[/tex]3/32 in. of the thread was worn out. Let's now determine its equivalent percentage.
[tex]\text{ Percentage worn = }\frac{\text{ Depth worn out}}{\text{ Original depth}}\text{ = }\frac{\frac{3}{32}}{\frac{20}{32}}\text{ x 100}[/tex][tex]\frac{3}{32}\text{ }\div\text{ }\frac{20}{32}\text{ = }\frac{3}{32}\text{ x }\frac{32}{20}\text{ = }\frac{3}{20}[/tex][tex]\text{ }\frac{3}{20}\text{ x 100 = 0.15 x 100}[/tex][tex]\text{ = 15\%}[/tex]Therefore,
The answer is 15%.15% of the thread was worn after a year.
The answer is 15%.
Recommendations 4. Math Language arts Science Eighth grade ) Y.2 Find the slope from two points ZAC Find the slope of the line that passes through (1, 10) and (10,5). Simplify your answer and write it as a proper fraction, improper fraction, or intege Submit Work it out
Answers
Point 1= (x1,y2) = (1,10)
Point 2 = (x2,y2)= (10,5)
Apply slope formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{5-10}{10-1}=\frac{-5}{9}=-\frac{5}{9}[/tex]A relation formed from a set of inputs to a set of possible outputs, where each input is related to exactly one output is called __________.functionequationinverse of functionreflection line
Answers
.
The Solution:
Given:
A FUNCTION is a relation formed from a set of inputs to a set of possible outputs, where each input is related to exactly one output.
Answer:
Function [option 1]
Find so the values of x satisfying the given conditions
Answers
It is given that y1 exceeds y2 by 28, it implies that:
[tex]y_1=y_2+28[/tex]Substitute the expressions for y1 and y2 into the equation:
[tex]\begin{gathered} (x^2-2)^2=12(x^2-2) \\ \end{gathered}[/tex]Expand the expressions on both sides and solve the equation for x:
[tex]\begin{gathered} x^4-4x^2+4=12x^2-24 \\ \Rightarrow x^4-4x^2-12x^2_{}+4+24=0 \\ \Rightarrow x^4-16x^2+28=0 \\ \text{let }x^2=y\text{ in the equation:} \\ \Rightarrow y^2-16y+28=0 \\ \Rightarrow y^2-14y-2y+28=0 \\ \Rightarrow y(y-14)-2(y-14)=0 \\ \Rightarrow(y-14)(y-2)=0 \\ \Rightarrow y=14,2 \end{gathered}[/tex]Substitute the values of y back into the equation x²=y:
[tex]\begin{gathered} x^2=14\text{ and }x^2=2 \\ \Rightarrow x=\pm\sqrt[]{14},\pm\sqrt[]{2} \\ \text{The solution set is }\times\mleft\lbrace-\sqrt[]{14},-\sqrt[]{2,}\sqrt[]{2},\sqrt[]{14}\mright\rbrace \end{gathered}[/tex]