Let:
Mp = Marked price = $310
r = Rate of discount = 20% = 0.2
D = Discount
Sp = Sale price
The discount will be given by:
[tex]\begin{gathered} D=r\cdot Mp \\ D=0.2\cdot310 \\ D=62 \end{gathered}[/tex]And the sale price will be:
[tex]\begin{gathered} Sp=Mp-D \\ Sp=310-62 \\ Sp=248 \end{gathered}[/tex]What is the y-intercept of the line x+2y=-14? (0,7) (-7,0) (0,-7) (2,14)
write each of the following numbers as a power of the number 2
Answer
The power on 2 is either -3.5 in decimal form or (-7/2) in fraction form.
Explanation
To do this, we have to first note that
[tex]\begin{gathered} \sqrt[]{2}=2^{\frac{1}{2}} \\ \text{And} \\ 16=2^4 \end{gathered}[/tex]So, we can then simplify the given expression
[tex]\begin{gathered} \frac{\sqrt[]{2}}{16}=\frac{2^{\frac{1}{2}}}{2^4}=2^{\frac{1}{2}-4} \\ =2^{0.5-4} \\ =2^{-3.5} \\ OR \\ =2^{\frac{-7}{2}} \end{gathered}[/tex]Hope this Helps!!!
Factor Problem Completely 16n^3 - 56n^2 + 8n - 28
Given
The equation is given as
[tex]16n^3-56n^2+8n-28[/tex]Explanation
Factorisation the equation,
[tex]4(4n^3-14n^2+2n-7)[/tex]Factorise the polynomial.
[tex]4(2n-7)(2n^2+1)[/tex]AnswerHence the answer is
[tex]4(2n-7)(2n^2+1)[/tex]1. P(video games and kid is 10 to 12 years old)2. P(basketball/kid is 13 to 15 years old)3. P(kid is 13 to 15 years old/basketball)4. P(darts/kid is 10 to 15 years old)5. P(basketball and darts)6. P(basketball and kid is 13 to 18 years old)Answer the following problems about two way frequency tables make sure to reduce your fraction.
1. P(video games and kid is 10 to 12 years old)
[tex]\begin{gathered} P(video\text{ games and kid i 10 to 12 years old)} \\ =\text{ }\frac{number\text{ of kids 10 - 12 years old playing video games}}{total\text{ number of students}} \\ =\text{ }\frac{17}{143} \end{gathered}[/tex]Therefore,
The P(video games and kid is 10 to 12 years old) = 17/143
2. P(basketball/kid is 13 to 15 years old)
[tex]\begin{gathered} P\mleft(basketball/kid\text{ is 13 to 15 years old}\mright)\text{ } \\ =\text{ }\frac{number\text{ of kids 13 - 15 years old playing basketball}}{number\text{ of kids of age 13 to 15 years old}} \\ =\text{ }\frac{14}{45} \end{gathered}[/tex]P(basketball/kid is 13 to 15 years old) = 14/45
3. P(kid is 13 to 15 years old/basketball)
[tex]\begin{gathered} P(\text{kid is 13 to 15 years old / basket ball)} \\ =\text{ }\frac{number\text{ of kids aged 13 to 15 years old }}{number\text{ of kids playing basketball}} \\ =\text{ }\frac{14}{54} \\ =\text{ }\frac{7}{27} \end{gathered}[/tex]P(kid is 13 to 15 years old/basketball) = 7/27
4. P(darts/kid is 10 to 15 years old)
[tex]\begin{gathered} P(\text{darts / kid is 10 to 15 years old)} \\ =\text{ }\frac{number\text{ of kids age 10 to 15 playing darts}}{\text{number of kids age 10 to 15}} \\ =\text{ }\frac{kids\text{ age 10 to 12 + age 13 to 15 playing darts}}{\text{kids age 10 to 12 + age 13 to 15}} \\ =\text{ }\frac{12\text{ + 15}}{34\text{ + 45}} \\ =\text{ }\frac{27}{79} \end{gathered}[/tex]P(darts/kid is 10 to 15 years old) = 27/79
5. P(basketball and darts)
[tex]\begin{gathered} P(basketball\text{ and darts)} \\ \sin ce\text{ there are no kids playing basketball and darts at the } \\ \text{same time} \\ \text{then,} \\ P(basketball\text{ and darts) = 0} \end{gathered}[/tex]P(basketball and darts) = 0
6. P(basketball and kid is 13 to 18 years old)
[tex]\begin{gathered} P(\text{basketball and kid is 13 to 18 years old)} \\ =\text{ }\frac{number\text{ of kids 13 to 18 years playing basket}}{nu\text{mber of kid 13 to 18 years }} \\ =\text{ }\frac{\text{kids 13 to 15 years + 16 - 18 years playing basketball}}{\text{kids 13 to 15years + 16 to 18 years}} \\ =\text{ }\frac{14\text{ + 18}}{45\text{ + 35}} \\ =\text{ }\frac{32}{80} \\ =\frac{2}{5} \end{gathered}[/tex]P(basketball and kid is 13 to 18 years old) = 2/5
Please assist me. I have no idea how to start this equation
Part a
Remember that the linear equation in slope-intercept form is
y=mx+b
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem
the equation is of the form
C=m(n)+b
where
m=8.50
b=350
therefore
C=8.50n+350Part b
A reasonable domain for n (number of cups)
Remember that the number of cups cannot be a negative number
so
the domain is the interval [0, infinite)
but a reasonable domain could be [0, 500]
Find out the range
For n=0 -----> C=350
For n=500 ----> C=8.50(500)+350=2,100 ZAR
the range is the interval [350,2,100]
Part c
calculate the cost
For n=100 cups ----> C=8.50(100)+350=1,200 ZAR
For n=200 cups ----> C=8.50(200)+350=2,050 ZAR
For n=400 cups ---> C=8.50(400)+350=3,750 ZAR
Part d
Average cost
Divide the total cost by the number of cups
For 100 cups ------> 1,200/100=12 ZAR per cup
For 200 cups ----> 2,050/200=10.25 ZAR per cup
For 400 cups ----> 3,750/400=9.38 ZAR per cup
Part e
it is better to order more cups, to reduce the initial ZAR 350 cost.
Part f
In this problem we have the ordered pairs
(200, 2150) and (400, 3750)
Find out the slope m
m=(3750-2150)/(400-200)
m=8 ZAR per cup
Find out the linear equation
C=mn+b
we have
m=8
point (200,2150)
substitute and solve for b
2150=8(200)+b
b=2150-1600
b=550
therefore
The linear equation is
C=8n+550Part g
A reasonable domain could be [0, 600]
Find out the range
For n=0 ------> C=550
For n=600 ----> C=8(600)+550=5,350
The range is the interval [550,5350]
Part h
The gradient is the same as the slope
so
slope=8
that means ----> the cost of each cup is 8 ZAR
Part i
For n=600
C=8(600)+550=5,350 ZAR
Part j
we have the inequality
8n+550 < 8.50n+350
Solve for x
550-350 < 8.50n-8n
200 < 0.50n
400 < n
Rewrite
n > 400
For orders more than 400 cups is more effective to order from Cupomatic
Verify
For n=401
C=8n+550=8(401)+550=3,758 ZAR
C=8.50n+350=8.5(401)+350=3,758.5 ZAR
the cost is less in CUPOMATIC, is ok
the answer is
For orders more than 400 cups is more effective to order from CupomaticCan you please help me find the area of the shaded triangle? Thank you :)
Area of shaded triangle = Area of triangle - area of circle
Area of triangle = 1/2 x base x height
Base= 16 yds
Height= 19 yds
Area of triangle = 1/2 x 16 x 19 = 8 x 19 =152 square yard
[tex]\begin{gathered} \text{Area of circle = }\pi\times r^2 \\ \pi=3.14 \\ r=5\text{yds} \\ \text{Area of circle = 3.14 }\times5^2=78.5yard^2 \end{gathered}[/tex]Area of shaded triangle = 152 - 78.5 =73.5 square yard
hello can you help me with this trigonometry question and this a homework assignment
You have:
sin 2A = -√7/4
In order to determine the value of sin A, first calculate the value of angle A by using sin⁻¹ over the previous equation, just as follow:
sin⁻¹(sin 2A) = sin⁻¹(-√7/4) In this way you cancel out the sin
2A = -41.41° divide by 2 both sides
A = -41.41°/2
A = -20.705°
however, take into account that angle A is in the third quadrant. Then, it is necessary to consider the result A=-20.705° is respect to the negative x-axis.
To obtain the angle respect the positive x-axis (the normal way), you simply sum 180° to 20.705°:
20.705 + 180° = 200.705°
Next, use calculator to calculate sinA:
sin(200.705°) = -0.3535
Hi, can you help me to solve thisexercise, please!!For cach polynomial, LIST all POSSIBLE RATIONAL ROOTS•Find all factors of the leading coefficient andconstant value of polynonnal.•ANY RATIONAL ROOTS =‡ (Constant Factor over Leading Coefficient Factor)6x^3+7x^2-3x-1
1) We can do this by listing all the factors of -1, and the leading coefficient 6. So, we can write them as a ratio this way:
[tex]\frac{p}{q}=\pm\frac{1}{1,\:2,\:3,\:6}[/tex]Note that p stands for the constant and q the factors of that leading coefficient
2) Now, let's test them by plugging them into the polynomial. If it is a rational root it must yield zero:
[tex]\begin{gathered} 6x^3+7x^2-3x+1=0 \\ 6(\pm1)^3+7(\pm1)^2-3(\pm1)+1=0 \\ 71\ne0,5\ne0 \\ \frac{1}{2},-\frac{1}{2} \\ 6(\pm\frac{1}{2})^3+7(\pm\frac{1}{2})^2-3(\pm\frac{1}{2})+1=0 \\ 2\ne0,\frac{7}{2}\ne0 \\ \\ 6(\pm\frac{1}{3})^3+7(\pm\frac{1}{3})^2-3(\pm\frac{1}{3})+1=0 \\ 1\ne0,\frac{23}{9}\ne0 \\ \frac{1}{6},-\frac{1}{6} \\ 6(\frac{1}{6})^3+7(\frac{1}{6})^2-3(\frac{1}{6})+1=0 \\ \frac{13}{18}\ne0,-\frac{5}{3}\ne0 \end{gathered}[/tex]3) So the possible roots are:
[tex]\pm1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6}[/tex]But there are no actual rational roots.
Jonathan is playing a game or a regular board that measures 60 centimeters long and 450 mm wide. which measurement is closest to the perimeter of the Jonathan's game board in meters?
According to the problem, the length is 60 cm and the width is 450 mm.
Let's transform 450mm to cm. We know that 1 cm is equivalent to 10 mm. So,
[tex]450\operatorname{mm}\times\frac{1\operatorname{cm}}{10\operatorname{mm}}=45\operatorname{cm}[/tex]Then, we use the perimeter formula for rectangles.
[tex]P=2(w+l)[/tex]Where w = 45 cm and l = 60 cm.
[tex]\begin{gathered} P=2(45\operatorname{cm}+60\operatorname{cm})=2(105cm) \\ P=210\operatorname{cm} \end{gathered}[/tex]The perimeter is 210 centimeters long.However, we know that 1 meter is equivalent to 100 centimeters.
[tex]P=210\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}}=2.1m[/tex]Hence, the perimeter, in meters, is 2.1 meters long.
Option A is the answer.What is the standard form of the equation of a line passing through points (2,3) and (2,-5)?
Answer:
[tex]x\text{ = 2}[/tex]Explanation:
Here, we want to find the standard form of the equation
We have the standard form as:
[tex]Ax\text{ + By = C}[/tex]We can arrive at this using the two-points form:
This is:
[tex]\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{y-y_1}{x-x_1}[/tex](x1,y1) = (2,3)
(x2,y2) = (2,-5)
Now, as we can see, the line is a vertical line since the x-value is the same
Thus, we have it that:
[tex]x\text{ = c}[/tex]where c will represent the x-intercept
Thus, we have the equation of the line as:
[tex]x\text{ = 2}[/tex]Describe it and decide if normal curve could be used as model
Answer:
The symmetric is symmetric
The distribution is unimodal
The mean, median, and mode are equal
A normal distribution is appropriate
Explanation:
The normal distribution is symmetric and unimodal, where the mode, the median, and the mean are equal. This distribution has the following shape
Therefore, the normal curve can be used as a model for the distribution.
So, the answers are:
The symmetric is symmetric
The distribution is unimodal
The mean, median, and mode are equal
A normal distribution is appropriate
Write a multiplication expression to represent each situation. Then find each product and explain its meaning. Ethan burns 650 calories when he runs for 1 hour. Suppose he runs 5 hours in one week.
We know that
• Ethan burns 650 calories per hour.
If he runs 5 hours we just have to multiply this time with the given rate.
[tex]650\cdot5=3,250[/tex]Therefore, Ethan burns 3,250 calories in 5 hours.exponent hw.simplify
Answer:
4
Explanation:
Given the below;
[tex]4m^0[/tex]To simplify the above, we have to note that any number or variable raised to the power of 0 is 1.
So, we'll have;
[tex]4m^0=4\times1=4[/tex]StatusRecovery8Help ResourcessAABC ~ AXYZFind the missing side length, s.B.3 65А&Х-ZCross multiplySE ][?] = [ ]153s
Since triangles ABC and XYZ are similar, the ratio between their corresponding sides is constant; thus,
[tex]\begin{gathered} \frac{AB}{XY}=\frac{BC}{YZ} \\ \Rightarrow\frac{3}{5}=\frac{6}{s} \end{gathered}[/tex]Solving for s,
[tex]\begin{gathered} \frac{3}{5}=\frac{6}{s} \\ \Rightarrow\frac{3}{5}\cdot s=\frac{6}{s}\cdot s \\ \Rightarrow\frac{3s}{5}=6 \\ \Rightarrow\frac{3s}{5}\cdot5=6\cdot5 \\ \Rightarrow3s=30 \\ \Rightarrow s=\frac{30}{3} \\ \Rightarrow s=10 \end{gathered}[/tex]Thus, the result of the cross multiplication is 3s=30 and the answer is s=10
The pentagonal prism below has a height of 13 units and a volume of 247 units ^3. Find the area of one of its bases.
• Volume of pentagonal prism = area of base x height
Volume = 247 unis^3
height = 13 units
Replacing:
V = A x h
A = V / h
A = 247/13 = 19 units^2
Consider the expression 6+(x+3)^2. Tabulate at least SIX different values of the expression.
Considering the expression 6+(x+3)^2. the table of at least SIX different values of the expression is
x y
0 15
1 22
2 31
3 42
4 55
5 70
How to determine the he table of at least SIX different values of the expressionThe table is completed by substituting the values of x in the given expression as follows
6 + ( x + 3 )^2
for x = 0, y = 6 + ( 0 + 3) ^2 = 15
for x = 1, y = 6 + ( 1 + 3) ^2 = 22
for x = 2, y = 6 + ( 2 + 3) ^2 = 31
for x = 3, y = 6 + ( 3 + 3) ^2 = 42
for x = 4, y = 6 + ( 4 + 3) ^2 = 55
for x = 5, y = 6 + ( 5 + 3) ^2 = 70
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Given that angle A lies in Quadrant III and sin(A)= −17/19, evaluate cos(A).
As we know;
[tex]sin^2(x)+cos^2(x)=1[/tex]We will use this equality. We take the square of the sine of the given angle and subtract it from [tex]1[/tex].
[tex]sin^2(A)=(-\frac{17}{19} )^2=\frac{289}{361}[/tex][tex]sin^2(A)+cos^2(A)=1[/tex][tex]sin^2(A)=1-cos^2(A)[/tex][tex]\frac{289}{361}=1-cos^2(A)[/tex][tex]cos^2(A)=1-\frac{289}{361} =\frac{72}{361}[/tex][tex]\sqrt{cos^2(A)} =cos(A)[/tex][tex]\sqrt{\frac{72}{361} }=\frac{6\sqrt{2} }{19}[/tex]In the third region the sign of cosines is negative. Therefore, our correct answer should be as follows;
[tex]cos(A)=-\frac{6\sqrt{2} }{19}[/tex]Shanice has 4 times as much many pairs of shoes as does her brother Ron. If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does. How many pairs of shoes will Shanice have left after she gives Ron the shoes?
Let's define:
x: pairs of shoes of Shanice
y: pairs of shoes of Ron
Shanice has 4 times as much many pairs of shoes as does her brother Ron, means:
x = 4y (eq. 1)
If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does, means:
x - 12 = 2y (eq. 2)
Replacing equation 1 into equation 2:
4y - 12 = 2y
4y - 2y = 12
2y = 12
y = 12/2
y = 6
and
x = 4*6 = 24
After she gives Ron the shoes, she will have left 24-12 = 12 pairs of shoes
solve 6 + 5 on the sqr root of 249 - 2x = 7
ANSWER
x = 124
EXPLANATION
First we have to clear the term that contains x in the equation. In this case, this term is the second term. So we have tu subtract 6 from both sides of the equation:
[tex]\begin{gathered} 6-6+\sqrt[5]{249-2x}=7-6 \\ \sqrt[5]{249-2x}=1 \end{gathered}[/tex]Then, we have to eliminate the root. Note that in the expression inside the root there are two terms. To do this, we have to apply the "opposite" operation on both sides of the equation, which in this case is exponent 5:
[tex]\begin{gathered} (\sqrt[5]{249-2x})^5=1^5 \\ 249-2x=1 \end{gathered}[/tex]Now we do something similar to the first step. We want to leave on one side of the equation only the term that contains x and the rest on the other side. To do this we can either add 2x on both sides, or subtract 249 from both sides. We'll apply the first option because then we'll have a positive coefficient for x:
[tex]\begin{gathered} 249-2x+2x=1+2x \\ 249=1+2x \end{gathered}[/tex]However, we now have to subtract 1 from both sides of the equation:
[tex]\begin{gathered} 249-1=1-1+2x \\ 248=2x \end{gathered}[/tex]Finally, to find x, we have to divide both sides by 2:
[tex]\begin{gathered} \frac{248}{2}=\frac{2x}{2} \\ 124=x \end{gathered}[/tex]Hence, the solution to the equation is x = 124.
Solve the quadratic equation x2 − 6x + 13 = 0 using the quadratic formula. What is the solution when expressed in the form a ± bi, where a and b are real numbers?
The given quadratic equation is:
[tex]x^2-6x+13=0[/tex]The quadratic formula is given by the equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac^{}}}{2a}[/tex]From the given quadratic equation;
[tex]a=1;b=-6\text{ and c=13}[/tex]Thus, we have:
[tex]x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(13)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{36-52}}{2} \\ x=\frac{6\pm\sqrt[]{-16}}{2} \\ In\text{ complex form, the }\sqrt[]{-16}=4i \\ \text{Thus, we have:} \\ x=\frac{6\pm4i}{2} \\ x=\frac{6}{2}\pm\frac{4i}{2} \\ x=3\pm2i \end{gathered}[/tex]Hence, the correct option is Option A
i inserted a picture of the question can you please state whether the answer is A,B, C or D check all that apply
Solution:
In the given figures, angles of the triangle ABC are corresponding equal to triangle DEF and the sides are proportional to each other.
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{1}{2}[/tex]Thus, the triangle ABC is similar to triangle DEF.
Therefore, the relationship between both triangles is the proportional side lengths.
Both triangles are not of the same size as their sides are not equal.
Both triangles are also not congruent as they do not satisfy any five conditions of congruence.
Hence, the correct option is A.
i inserted a picture of the questioncan you state whether the answer is A, B, C OR D
Looking at the triangles, they are both right triangles. They have congruent legs = 12. They have congruent acute angles of 45 degerees. Thus, they are congruent triangles. The answer is True
The table shows a linear relationship between x and y. Drag and drop the options provided into the correct boxes to complete the equation. х 1 0 6 -4 41 у 9 -39 The equation that represents the relationship Is y = -8 -41 ON 9 4 O?
To calculate the equation first we need to choose two points of the table
P1 (1,1)=(x1,y1)
P2(0,9)=(x2,y2)
then we calculated the slope m
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the points we have
[tex]m=\frac{9-1}{0-1}=\frac{8}{-1}=-8[/tex]then we can calculate the equation
[tex](y-y1)=m(x-x1)[/tex][tex](y-1)=-8(x-1)[/tex][tex]y-1=-8x+8[/tex][tex]y=-8x+8+1[/tex]the equation is
[tex]y=-8x+9[/tex]GRAPH each triangle and CLASSIFY the triangle according to its sides and angles.
Answer:
[tex]\Delta CAT\text{ is an ISOSCELES triangle}[/tex]Explanation:
To properly classify the traingle, we need to get the length of the sides
To get the length of the sides, we need to get the distance between each two points using the distance between two points formula
Mathematically,we have the formula as:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where (x1,y1) refers to the coordiantes of the first point while (x2,y2) refers to the coordinates of the second point
let us get the coordinates of the individual points as seen from the plot shown
C (1,8)
A (5,10)
T (7,6)
So, let us find the distance between each two points
For AC, we have:
[tex]D\text{ = }\sqrt[]{(5-1)^2+(10-8)^2}\text{ = }\sqrt[]{20}[/tex]For AT, we have:
[tex]D=\sqrt[]{(7-5)^2+(6-10)^2\text{ }}\text{ = }\sqrt[]{20}[/tex]Lastly, for CT, we have:
[tex]D\text{ = }\sqrt[]{(7-1)^2+(6-8)^2\text{ }}\text{ = }\sqrt[]{40}[/tex]From our calculations, we can see that AC = AT
If we have a triangle which has two of its sides equal in length (the angle facing these sides would be same too), we call this an isosceles triangle
So, the class of triangle CAT is isosceles triangle
3. The data in the table gives the number of barbeque sauce bottles (y) that are sold with orders of chicken wings (x) for each hour on a given day at Vonn's Grill. Use technology to write an equation for the line of best fit from the data in the table below. Round all values to two decimal places.
1) Let's visualize the points
2) To find the equation for the line of best fit we'll need to follow some steps.
2.1 Let's find the mean of the x values and the mean of the Y values
2.2 Now It's time to find the slope, with the summation of the difference between each value and the mean of x times each value minus the mean over the square of the difference of the mean of x and x.
To make it simpler, let's use this table:
The slope then is the summation of the 5th column over the 6th column, we're using the least square method
[tex]m=\frac{939.625}{1270.875}=0.7393\cong0.74[/tex]The Linear coefficient
[tex]\begin{gathered} b=Y\text{ -m}X \\ b=14.625-0.73(19.875) \\ b=0.11625\cong0.12 \end{gathered}[/tex]3) Finally the equation of the line that best fit is
[tex]y=0.73x+0.12[/tex]What is the value of 2(3x − 6) − 5y if x = −2 and y = 6?
−6 −18 −54 −78
Answer:
-54
Step-by-step explanation:
Finding a value means you will get a number answer. Since they said x
x = -2
fill in -2 in place of the x.
also they said
y = 6
so fill in 6 wherever you see a y.
2(3x - 6) - 5y
fill in -2 for x and 6 for y.
= 2(3•-2 - 6) - 5•6
Work on parentheses first. Multiply before adding or subtracting.
= 2(-6 - 6) - 5•6
= 2(-12) - 5•6
Again, multiply before adding or subtracting.
= -24 - 30
= -54
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
According to visual inspection, shape A has been rotated 180° counterclockwise about the origin and then translated 1 unit to the left.
What is meant by transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
The four basic transformations exist:
TranslationReflectionRotationDilationAccording to visual inspection, shape A has been rotated 180° counterclockwise about the origin and then translated 1 unit to the left.
Therefore, the correct answer is option C) translated 1 unit to the left and then rotated 180° counterclockwise about the origin
The complete question is:
Describe the transformation that maps the pre-image A to the image A.
A) translated 8 units up and then reflected across the y-axis
B) translated 8 units down and then reflected across the y-axis
C) translated 1 unit to left and then rotated 180° counterclockwise about the origin
D) translated 1 unit to right and then rotated 180° counterclockwise about the origin.
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One group (A) contains 155 people. One-fifth of the people in group A will be selected to win $20 fuel cards. There is another group (B) in a nearby town that will receivethe same number of fuel cards, but there are 686 people in that group. What will be the ratio of nonwinners in group A to nonwinners in group B after the selections aremade? Express your ratio as a fraction or with a colon.
According to the information given in the exercise:
- Group A contains a total of 155 people.
- One-fifth of that people will be selected to win $20 fuel cards.
- The total number of people in Group B is 686.
Then, you can determine that the number of people that will be selected to win $20 fuel cards is:
[tex]winners_A=\frac{1}{5}(155)=31[/tex]Therefore, the number of nonwinners in Group A is:
[tex]N.winners_A=155-31=124[/tex]You know that Group B will receive the same number of fuel cards. Therefore, its number of nonwinners is:
[tex]N.winners_B=686-31=655[/tex]Knowing all this information, you can set up the following ratio of nonwinners in Group A to nonwinners in Group B after the selections are made:
[tex]\frac{124}{655}[/tex]Hence, the answer is:
[tex]\frac{124}{655}[/tex]
3. Convert the angle 3π/4 to degrees.
Answer:
135°
Step-by-step explanation:
To convert an angle from radians to degrees, multiply by [tex]180/\pi[/tex].
[tex]\frac{3\pi}{4} \cdot \frac{180}{\pi}=135^{\circ}[/tex]
Find the value of x assume the triangles are the same
1) In this problem, we need to find the constant of proportionality assuming these triangles are similar. So let's divide each corresponding leg:
[tex]\frac{22}{18}=\frac{33}{27}\Rightarrow\:k=\frac{11}{9}[/tex]2) So, based on that constant of proportionality (k) we can find the missing leg.
[tex]\begin{gathered} x\div\frac{11}{9}=36 \\ \\ x\cdot\frac{9}{11}=36 \\ \\ 11\times\frac{9}{11}x=36\times11 \\ \\ 9x=396 \\ \\ \frac{9x}{9}=\frac{396}{9} \\ \\ x=44 \end{gathered}[/tex]Note that since the triangle on the top is larger than the one on the bottom, we can tell that x must be larger than 36.
