For this type of problem we first notice that the center of the first circle has coordinates (-4,-6) and the center of the second one has coordinates (4,2) then all point of circle 1 (x,y) are translated according to the rule (x+8,y+8).
For the scale factor, we notice that the radius of circle 1 is 9 cm and the radius of circle 2 is 6cm then the scale factor is (2/3).
find the values of x and y
From the given figure
Since every two opposite sides are parallel
AB // DC
AD // BC
Then the given quadrilateral is a parallelogram
ABCD is a parallelogram
From the properties of the parallelogram,
Every 2 opposite sides are equal in length, then
AB = DC
AB = x + 2, and DC = 13, then
x + 2 = 13
Subtract 2 from both sides to find x
x + 2 - 2 = 13 - 2
x = 11
Since the opposite angles in the parallelogram are equal in measures
Since
m
Since m
y = 70
The value of x is 11 and the value of y is 70
The following is a sample of 20 measurements.Answer b part
b)
Given:
[tex]\begin{gathered} \bar{x}=10.2 \\ s=2.12 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \bar{x}\pm s=10.2\pm2.12 \\ \bar{x}+s=12.32 \\ \bar{x}-s=8.08 \end{gathered}[/tex]So, the measurements in the data between 8.08 and 12.32 are 11, 9, 12, 10 12, 12 , 12, 9, 9, 9, 11, 11, 12 and 11.
Therefore, the number of measurements in interval x±s is 14.
The percentage of the measurements that fall between the interval x±s is,
[tex]\text{Percent}=\frac{14}{20}\times100=70[/tex]Therefore, the percentage of the measurements that fall between the interval x±s is 70%.
Now,
[tex]\begin{gathered} \bar{x}\pm2s=10.2\pm2\times2.12 \\ \bar{x}\pm2s=10.2\pm4.24 \\ \bar{x}+2s=14.44 \\ \bar{x}-2s=5.96 \end{gathered}[/tex]So, all the measurements in the data are between 5.96 and 14.44.Therefore, the number of measurements in interval x±2s is 20.
Therefore, the percentage of the measurements that fall between the interval x±2s is 100%.
Now,
[tex]\begin{gathered} \bar{x}\pm3s=10.2\pm3\times2.12 \\ \bar{x}\pm3s=10.2\pm6.36 \\ \bar{x}+3s=16.56 \\ \bar{x}-3s=3.84 \end{gathered}[/tex]So, all the measurements in the data are between 3.84 and 16.56.Therefore, the number of measurements in interval x±3s is 20.
Therefore, the percentage of the measurements that fall between the interval x±3s is 100%.
Last part: compare the percentage .
According to empirical rule, approximately 68% of the measurements in a sample will fall within the interval x±s.
From part b, the obtained percentage of measurements that fall within the interval x±s is 70%.
Therefore, percentage of measurements that fall within the interval x±s is greater than the predicted percentage for x±s using the empirical rule.
Option C is correct.
Can you please help me out with a question
Answer:
3 degrees
Explanation:
Using the theorem that states that the measure of the angle at the circumference is equal to the half of its intercepted arc. Hence;
31x+ 3 = 1/2(192)
31x + 3 = 96
Subtract 3 from both sides
31x + 3 - 3 = 96 - 3
31x = 93
Divide both sides by 31
31x/31 = 93/31
x = 3
Hence the value of x is 3 degrees
Solve the inequality, then select the graph that matches the solution.x +5 ≥ 5
Answer:
Explanation:
Given the inequality:
[tex]x+5\geqslant5[/tex]Subtract 5 from both sides of the inequality.
[tex]\begin{gathered} x+5-5\geq5-5 \\ x+0\geq0 \\ x\geq0 \end{gathered}[/tex](a)The solution to the inequality is x ≥ 0.
(b)Since the inequality sign is "greater than or equal to", the circle at 0must be shaded and the arrow pointing towards the right.
The correct graph is attached below:
The second and third options are correct.
Hello, I am having trouble with this problem. Thank you so much.
ANSWERS
• Graph:
• Interval notation: ,[-4, ∞)
EXPLANATION
The set is all x greater than or equal to -4. The value -4 is included in the interval, so we have to draw a dot and then a line from the dot to infinity.
When a value is included in the interval, we use the start or end bracket. For infinity or negative infinity, we always use parenthesis. To represent this set in interval notation we have to use a bracket, number -4, a comma, infinity, and a parenthesis: [-4, ∞)
The coordinates of the focus are (2,-7/4), the coordinates of the endpoints of the latus rectum are (3/2,-7/4) and (5/2,-7/4). The equation of the directions is y=-9/4, and the equation of the axis of symmetry is x=2.
General equation of a parabola:
[tex](x-h)^2=4p(y-k)[/tex]Equation of the axis of symmetry:
x = h
In this case, the axis of symmetry is x = 2, then h = 2.
Equation of the directrix:
y = k - p
In this case, the equation of the directrix is y = -9/4, then:
-9/4 = k - p (eq. 1)
Equation of the focus:
F(h, k+p)
In this case, the coordinates of the focus are (2,-7/4), then:
-7/4 = k + p (eq. 2)
Adding equation 1 to equation 2:
-9/4 = k - p
+
-7/4 = k + p
--------------------
-4 = 2k
(-4)/2 = k
-2 = k
Substituting this result into equation 2 and solving for p:
-7/4 = -2 + p
-7/4 + 2 = p
1/4 = p
Substituting with h = 2, k = -2, and p = 1/4 into the general equation, we get:
[tex]\begin{gathered} (x-2)^2=4\cdot\frac{1}{4}(y-(-2)) \\ (x-2)^2=y+2 \end{gathered}[/tex]
2.3= p + 0.6What does p equal?
The given equation is
[tex]2.3=p+0.6[/tex]First, we subtract 0.6 on each side
[tex]\begin{gathered} 2.3-0.6=p+0.6-0.6 \\ 1.7=p \end{gathered}[/tex]Therefore, p is equal to 1.7.Devonte creates a scatter plot of the relationship between his hourly pay in dollars, y, and the number of customers he serves at a coffee shop, X. He calculates the equation of the trend line to be y = 2.52 +7. Part A What does the y-intercept represent? Enter the correct answers in the boxes. per hour when he serves customers. The y-intercept represents that Devonte earns $
Given equation of line is,
what is the value of b -a if a=18, b=27,and c= 11
what is the value of b -a if a=18, b=27,and c= 11
we have
(b-a)
so
For a=18 and b=27
substitutte in the given expression
(27-18)=9
therefore
the answer is 9verify the following trigonometric identity (1+tanx)^2=sec^2x+2tanx
Verify the equation :
[tex](1+\tan x)^2=\sec ^2x+2\tan x[/tex]solve:
[tex]=(1+\tan x)^2[/tex]Use the formula :
[tex](a+b)^2=a^2+b^2+2ab[/tex][tex]\begin{gathered} =(1+\tan ^{}x)^2 \\ =1^2+(\tan x)^2+2(1)(\tan x) \\ =1+\tan ^2x+2\tan x \end{gathered}[/tex]Use the formua:
[tex]1+\tan ^2x=\sec ^2x[/tex][tex]\begin{gathered} =1+\tan ^2x+2\tan x \\ =\sec ^2x+2\tan x \end{gathered}[/tex]30 points helps What are the coordinates of each vertex if the figure is rotated 180° clockwise about the origin?[G.CO.2, G.CO.4, G.C0.5]
The coordinates of each of the vertices after the figure is rotated 180° clockwise about the origin: A' = (2, -2), B' = (-2, -5), C' = (-6, -3), D' = (-4, 3)
Explanation:
The first thing we do is to write the vertices of the original shape:
A = (-2, 2)
B = (2, 5)
C = (6, 3)
D = (4, -3)
A rotation of (x, y) 180° clockwise about the origin = (-x, -y)
We take the negative of the x and y coordinates of the original shape
180° clockwise about the origin becomes:
A' = (-(-2), -2) = (2, -2)
B' = (-2, -5)
C' = (-6, -3)
D' = (-4, -(-3)) = (-4, 3)
The coordinates of each of the vertices after the figure is rotated 180° clockwise about the origin: A' = (2, -2), B' = (-2, -5), C' = (-6, -3), D' = (-4, 3)
A tour bus is traveling at a constant speed. The relationship between it's time and distance is shown in the graph Which statement is correctA) The origin (0, 0) is the independent quantity and the time values are the dependent quantities.B) The time values are the independent quantities and the distance values are the dependent quantities.C) The distance values are the independent quantities and the time values are the dependent quantities.D) The rate of 50 miles per hour is the independent quantity and the distance values are the dependent quantities.
Jahna, this is the solution:
As you can see in the graph, the independent variable (Time) belongs on the x-axis and the dependent variable (Distance) belongs on the y-axis.
Therefore, the statement that is correct is:
B. The time values are the independent quantities and the distance values are the dependent quantities.
Will a truck that is 14 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one-way road that passes under the bridge shown in the figure on the right?
Given the equation of an elipse
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]from the question,
[tex]\begin{gathered} \text{major axis}\Rightarrow2a \\ \therefore2a=52 \\ a=\frac{52}{2}=26ft \\ b=13ft \end{gathered}[/tex]Given that
[tex]x=14ft[/tex]Substitute, for a,b, and x in the elipse formula to find y
[tex]\begin{gathered} \frac{14^2}{26^2}+\frac{y^2}{13^2}=1 \\ \frac{196}{676}+\frac{y^2}{169}=1 \end{gathered}[/tex]Multiply through by 169
[tex]\begin{gathered} 49+y^2=169 \\ y^2=169-49 \\ y^2=120 \\ y=\sqrt[]{120}=10.95ft \end{gathered}[/tex]Hence, it clear the arch because the height of the archway of the bridge 7 feet from the center is approximatelyfeet
I'm having trouble figuring out this problem. Problem: Using the formula below, solve when s = 2.50. A = 6s²
Given the formula:
[tex]A=6s^2[/tex]Let's solve for A when the value of s is = 2.50
To solve the equation, substitute 2.50 for s and evaluate.
Thus, we have:
[tex]\begin{gathered} A=6(2.50)^2 \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} A=6(2.50\ast2.50) \\ \\ A=6(6.25)^{} \\ \\ A=6\ast6.25 \\ \\ A=37.5 \end{gathered}[/tex]Therefore, when the value of s is 2.50, the value of A is 37.5
ANSWER:
37.5
find the sum of the first ten terms of an arithmetic series if the first term is 3 and the last term is 39a. 190b.210c.230d.275
Given the first term is 3 and the last term is 39.
Recall that the sum is given as:
[tex]S_n=\frac{n}{2}(a_1+a_n)[/tex]Substituting in the above equation gives:
[tex]\begin{gathered} S_n=\frac{10}{2}(3+39) \\ S_n=5(42) \\ S_n=210 \end{gathered}[/tex]Therefore, option (a) is correct.
Find anangle 0 coterminal to -560°, where 0° < 0 < 360°.
Given the angle -560
The coterminal angle will be:
[tex]\theta=-560+360=-200+360=160[/tex]So, the answer will be 160
consider the cube shown at the right. All the side lengths of the cube have been marked with the variable s. the firmula firvthe surface area of a cube is given by SA=6s2. explain where this equatiin comes from
The explanation goes as contained below.
The shape is a cube and for a cube all sides are equal,
from the question the Area of just one side is :
[tex]\begin{gathered} S\times S=S^2 \\ \text{Then for 6 sides we have 6 }\times S^2=6S^2 \end{gathered}[/tex]ginny is raising pumpkins to enter a contest to see who can grow the heaviest pumpkin. her best pumpkin weighs 22 pounds and is growing at the rate of 2.5 pounds per week. martha planted her pumpkins late. her best pumpkin weighs 10 pounds but she expects it grow 4 pounds per week. define the "let" statements for x and y. then write equations that represent the weight of ginny and martha's pumpkins.Let x=Let y=ginny's equations=Martha's equation:
Let x=
1) Gathering the data
Ginny
Best pumpkin: 22 pounds
The growing rate of 2.5 pounds per week
Martha
Best pumpkin: 10 pounds
The growing rate: 4 pounds per week
Let x for the growing rate and y for the weight
2) Setting equations
Ginny's equation
2.5x=22
Martha's equation:
4x=10
i don’t understand how to solve this promise and i need help.
We have been given a figure and we need to find its area.
To determine the area we will divide the figure into known shapes. From the division into shapes, we have a square and a trapezoid.
[tex]Area\text{ of the figure = Area of the square + Area of the trapezoid}[/tex][tex]\begin{gathered} Dimensions\text{ of the square:} \\ length\text{ = 12 ft} \\ Area\text{ of the square = length}^2 \\ \\ Area\text{ of the square = 12}^2 \\ \\ Area\text{ of the square = 144 ft}^2 \end{gathered}[/tex][tex]\begin{gathered} Dimensions\text{ of the trapezoid:} \\ base\text{ 1 = 10 ft, base 2 = 12 ft} \\ height\text{ = 6 ft} \\ \\ Area\text{ of trapezoid = }\frac{1}{2}(10\text{ + 12\rparen}\times\text{ 6} \\ \\ Area\text{ of trapezoid = }\frac{1}{2}\times22\text{ }\times6\text{ = 11}\times6 \\ \\ Area\text{ of trapezoid = 66 ft}^2 \end{gathered}[/tex][tex]\begin{gathered} Area\text{ of the figure = 144 + 66} \\ \\ Area\text{ of the figure = 210 ft}^2 \end{gathered}[/tex]Given Triangle XYZ, with Circumcenter O. If the distance from XO is 22mm. What is the distance of both YO and ZO?Required to answer. Single choice. 182022241313,
Solution
Circumcenter Theorem
The vertices of a triangle are equidistant from the circumcenter.
The perpendicular bisectors intersect in a point and that point is equidistant from the vertices.
Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.
Therefore, YO and ZO is 22mm( By the transitive property)
Write the equation of the line parallel to Y equals 2/3X +1 through the point (0,-4)  use slope intercept form
Writing the slope-intercept form of a linear equation, we have:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Since parallel lines have the same slope, we can see that the slope of the line y = 2/3x + 1 is equal m = 2/3, so for our equation we also have m = 2/3.
Now, using the point (0, -4), we have:
[tex]\begin{gathered} y=\frac{2}{3}x+b \\ (0,-4)\colon \\ -4=\frac{2}{3}\cdot0+b \\ b+0=-4 \\ b=-4 \end{gathered}[/tex]So our equation is:
[tex]y=\frac{2}{3}x-4[/tex]y = 2/3x - 4
48 ounces of juice are required to make 3 gallons of punch. How many ounces of juice are required to make 9 gallons of punch?
If we need 48 onces of juice for making 3 gallons of punch we can write our problem like:
[tex]\begin{gathered} 48\to3 \\ x\to9 \end{gathered}[/tex]where x is the juice needed to made 9 gallons of punch, so we can made a rulo of 3 to find x
[tex]x=\frac{48\cdot9}{3}=144[/tex]So we need 144 ounces of juice to made 9 gallons of punch
Error Analysis Denzel identified (3, 2) as a point on the line y - 2 = 2/3 (x + 3). What is the error that Denzel made?
Slope point formula:
y-y1= m (x-x1)
Where:
m= slope
(y1,x1) = point of the line
For:
y - 2 = 2/3 (x + 3)
m= 2/3
y1= 2
x1= -3
The error is that the point is not (3,2) is (-3,2)
y-2 = 2/3 (x-(-3))
y-2 = 2/3 (x+3)
How to fine the volume and surface are in a cone
PROJECT WORK:
Assumption:
For the given cone, assuming
[tex]\begin{gathered} r\text{ = 10 m} \\ h\text{ = 12 m} \end{gathered}[/tex]Slant height of cone is calculated as,
[tex]\begin{gathered} l^2\text{ = r}^2\text{ + h}^2 \\ l^2\text{ = 10}^2\text{ + 12}^2 \\ l^2\text{ = 100 + 144} \\ l^2\text{ = 244} \\ l\text{ = 15.62 m} \end{gathered}[/tex]Required:
Surface area and volume of cone.
Explanation:
The surface area of cone is given as,
[tex]\begin{gathered} Surface\text{ area = }\pi r(l+r) \\ Surface\text{ area = 3.14}\times\text{ 10\lparen15.62 + 10\rparen} \\ Surface\text{ area =3.14}\times\text{ 10\lparen25.62\rparen} \\ Surface\text{ area = 3.14}\times\text{ 256.2} \\ Surface\text{ area = 804.468 m}^2 \end{gathered}[/tex]Volume of cone is calculated as,
[tex]\begin{gathered} Volume\text{ = }\frac{1}{3}\pi r^2h \\ Volume\text{ = }\frac{1}{3}\times3.14\times10\times10\times12 \\ Volume\text{ = }\frac{3768}{3} \\ Volume\text{ = 1256 m}^3 \end{gathered}[/tex]Answer:
Thus the volume of the cone is 1256 cu.m.
The surface area of the cone is 804.468 sq.m.
What is the center and the radius of the circle: ( x + 7 ) 2 + ( y - 1 ) 2 = 9 ?
Given:
There is a equation of circle given in the question as below
[tex]\left(x+7\right)^2+(y-1)^2=9[/tex]Required:
We want to find the center and radius of given circle
Explanation:
The general equation of circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center of circle and r be the radius of circle
Now by comparing we get
[tex]\begin{gathered} (h,k)=(-7,1) \\ r^2=9\Rightarrow r=3 \end{gathered}[/tex]Final answer:
C
Bring the standard form of the equation of the line through the pair of points (5,2) and (5,-7)
The equation is
x = 5
Explanation:The equation of a line is given as:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Given the points (5, 2) and (5, -7)
The slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-2}{5-5}=-\frac{9}{0}=\infty[/tex]The slope is infinite, then the equation is:
[tex]x=5[/tex]the Firgure shows two triangles on a coordinate grid: Which set of transformations have been performed on triangle ABC to form triangle A'B'C'? A) Dilation by a scale factor of 1/3 followed by reflection about the x-axisB) Dilation by a scale factor of 3 followed by reflection about the x-axis C) Dilation by a scale factor of 1/3 followed by reflection about the y-axis D) Dilation by a scale factor of 3 followed by reflection about the y-axis
In transformations, the Pre-Image is the original figure and the Image is the figure transformated.
In this case you can identify that the Pre-Image is the triangle ABC and the Image is the triangle A'B'C'.
Notice that the vertices of ABC are:
[tex]A(-3,3);B(0,0);C(-6,-3)[/tex]By definition, when the scale factor used in the dilation is between 0 and 1, the Image obtained is a reduction and, therefore, it is smaller than the Pre-Image. Since A'B'C' is smaller than ABC, then you can determine that ABC was dilated by this scale factor:
[tex]sf=\frac{1}{3}[/tex]When a figure is reflected across the y-axis, the rule is:
[tex](x,y)\rightarrow\mleft(-x,y\mright)[/tex]If you dilate ABC by the scale factor shown above, and then you reflect it across the y-axis, the coordinates of the Image will be:
[tex]\begin{gathered} A\mleft(-3,3\mright)\rightarrow A^{\prime}(-(\frac{-3}{3}),\frac{3}{3})\rightarrow A^{\prime}(1,1) \\ \\ B\mleft(0,0\mright)\rightarrow B^{\prime}\mleft(0,0\mright) \\ \\ C\mleft(-6,-3\mright)\rightarrow C^{\prime}(-(\frac{-6}{3}),\frac{-3}{3})\rightarrow C^{\prime}(2,-1) \end{gathered}[/tex]Notice that the coordinates of A'B'C' shown in the picture match with the vertices found above.
Therefore, the answer is: Option C.
Hello I need help with this here please, I was studying but I can’t get this
ANSWER
B. False
EXPLANATION
The Pythagorean Theorem states that the sum of the squares of the two legs of a right triangle, a and b, is equal to the square of the hypotenuse, c:
[tex]c^2=a^2+b^2[/tex]And this theorem is true for all right triangles.
Hence, this statement is false.
Please help us in figuring out this math problem so that we can move onto the next one thank you very much
All numbers in scientific notation or standard form are written in the form
[tex]m\cdot10^n[/tex]where m is a number between 1 and 10 and the exponent n is a positive or negative integer.
To convert 64500 into scientific notation, follow these steps:
1. Move the decimal 4 times to left in the number so that the resulting number, m = 6.45, is greater than or equal to 1 but less than 10
2. Since we moved the decimal to the left the exponent n is positive
n = 4
3. Write in the scientific notation form, m × 10^n
= 6.45 × 10^4
Round 14.235 to the nearest tenth, hundredth, one and ten
The number 14.235 would round down to 14.2
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We need to round 14.235 to the nearest tenth, hundredth, one and ten
We can see that the 35 is below 50 so it goes down, and it rounds down to 14.2 instead of, 14.62 then that would round up to the decimal is higher than 50.
Since it is 235, then it rounds down to 14.2
Learn more about rounding numbers here:
https://brainly.com/question/1285054
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