Quadrilateral HGEF is a scaled copy of quadrilateral DCAB. What is themeasurement of lin EG?
Answers
Answer:
14 units
Explanation:
If quadrilaterals HGEF and DCAB are similar, then the ratio of some corresponding sides is:
[tex]\frac{FH}{BD}=\frac{EG}{AC}[/tex]Substitute the given side lengths:
[tex]\begin{gathered} \frac{6}{3}=\frac{EG}{7} \\ 2=\frac{EG}{7} \\ \implies EG=2\times7 \\ EG=14 \end{gathered}[/tex]The measurement of line EG is 14 units.
Related Questions
drag the location of each ordered pair after a reflection over the x axis stated. then, drag the correct algebraic representation of the reflection to the white box. answer choices: (y, x), (-2,-6),(x,-y),(-3,-2),(5,8),(-5,-8),(-x, y),(-6,-6),(-6,-1),(2,-6),(6,-1),(3,2),(-x, -y),(-7,-2),(6,-6),(7,2)
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Reflection over the x-axis transform the point (x, y) into (x, -y)
Applying this rule to the vertex of the triangle ABC, we get:
A(-6, 6) → A'(-6, -6)
B(-2, 6) → B'(-2, -6)
C(-6, 1) → C'(-6, -1)
Algebraic representation: (x, -y)
19. Write in algebraic terms: six times a number, minus five times the number, plus eight.
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Let the number be a
6a x 5a + 8
4. The temperature in Baguio is 18.6℃, while Manila the temperature is 31.5℃. How much warmer is it in Manila than Baguio?A. 12.6℃B. 12.7℃C. 12.9℃D. 13℃
Answers
Given:
The temperature in Baguio is 18.6℃.
The temperature in manila is 31.5℃.
To find:
The differene bin temperature etween imanila and aguio.
Explanation:
The difference between manila and Baguio's temperature s
[tex]31.5^{\circ}C-18.6^{\circ}C=12.9^{\circ}C[/tex]Thus, manila is 12.9 degrees Celcius warmer than Baguio.
Final answer:
anila is 12.9 degrees Celcius warmer than Baguio.
The figure below is a trapezoid:10011050mZ1 =m2 =mZ3=Blank 1:Blank 2:Blank 3:
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STEP 1: Identify and Set Up
We have a trapezoid divided by a straight line that divides it assymetrically. We know from the all too famous geometric rule that adjacent angles in a trapezoid are supplementary. Mathematically, we can express thus:
[tex]100^o+<2+<3^{}=180^o=50^o+110^o+<1[/tex]Hence, from this relation, we can find our unknown angles.
STEP 2: Execute
For <1
[tex]\begin{gathered} 180^o=50^o+110^o+<1 \\ 180^o=160^o+<1 \\ \text{Subtracting 160}^o\text{ from both sides gives} \\ <1=180-120=60^o \end{gathered}[/tex]<1 = 60 degrees
For <2 & <3
We know from basic geometry that a transversal across two parallel lines gives a pair of alternate angles and as such, <1 = <3 = 60 degrees
We employ our first equation to solve for <2 as seen below:
[tex]\begin{gathered} 100^o+<2+<3^{}=180^o \\ 100^o+<2+60^o=180^o \\ 160^o+<2=180^o \\ \text{Subtracting 160}^{o\text{ }}\text{ from both sides gives:} \\ <2=180-160=20^o \end{gathered}[/tex]Therefore, <1 = <3 = 60 degrees and <2 = 20
Write 5.8% as a fraction in lowest terms.
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Answer:
[tex]5.8\text{ \%}\rightarrow\frac{29}{500}[/tex]Explanation: We have to write 5.8% In fraction in lowest terms:
This percent number essentially is:
[tex]5.8\text{ \%=}\frac{5.8}{100}[/tex]Therefore we can write it as:
[tex]\frac{5.8}{100}=\frac{5.8\times10}{100\times10}=\frac{58}{1000}[/tex]In lowest terms, this would be:
[tex]\frac{58}{1000}=\frac{29}{500}[/tex]I need you to make a problem and solve it on the side and explain how explain it I’m making a practice test and I can show you examples of how I did the others This are the topics you can choose fromTopic 1: is the relation a function- domain and range Topic 2: zero is of a function
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For topic (1), we have the following question:
Which of the following is a function: y=x² or x=y²?
Identify domain and range of each equation.
We can identify a given relation if it is a function or not by identifying the number of possible values of y.
The equations below are both relations.
[tex]y=x^2\text{ and }x=y^2[/tex]However, only one of them is a function.
For the first equation, note that for each value of x, there is only one value of y. Some of the points on the equation are as follows.
[tex]\begin{gathered} x=-2 \\ y=x^2^{} \\ y=(-2)^2=4 \\ \\ x=0 \\ y=x^2 \\ y=0^2=0 \\ \\ x=2 \\ y=x^2 \\ y=2^2 \\ y=4 \end{gathered}[/tex]Thus, the equation passes through the following points.
[tex](-2,4),(0,0),(2,4)[/tex]Notice that no value of x is repeated. Therefore, the given relation is a function.
We can also determine it using graphs. The image below is the graph of the first equation.
If we test it using the vertical line test, no vertical line can pass through the graph twice. Therefore, it shows that the equation is a function.
On the otherhand, the other equation is not a function. This is because when we substitute -2 and 2 to the value of y, we will have the same value of x, which is equal to 4.
[tex]\begin{gathered} y=-2^{} \\ x=y^2 \\ x=(-2)^2=4 \\ \\ y=2 \\ x=y^2^{} \\ x=2^2=4 \end{gathered}[/tex]Since there are two values of y for only one value of x, the equation must not be a function.
To illustrate this using its graph, we can notice that the vertical line below passes through two points on the graph when x=4.
Therefore, the second equation is not a function.
As for the domain and range, we can obtain it from both graphs.
The domain the set of all possible values of x. Thus, for the first equation, since it extends indefinitely to the left and right, the domain must be from negative infinity to positive infinity.
[tex]D_1\colon(-\infty,\infty)[/tex]On the otherhand, since the second equation extends indefinitely to the right from 0, the domain must be from 0 to positive infinity, inclusive.
[tex]D_2\colon\lbrack0,\infty)[/tex]As for the range, it is the set of all possible values of y.
Thus, for the first equation, since the graph extends indefinitely upwards from 0, the range must be from 0 to positive infinity, inclusive.
[tex]R_1\colon\lbrack0,\infty)[/tex]On the otherhand, the graph of the second equation extends indefinitely upwards and downwards. Thus, its range must be from negative infinity to positive infinity.
[tex]R_2\colon(-\infty,\infty)[/tex]To summarize, here are the questions and the answers for each question.
Which of the following is a function: y=x² or x=y²?
Answer: y=x²
Identify domain and range of each equation.
Answer:
For y=x²:
[tex]\begin{gathered} D\colon\text{ (-}\infty,\infty\text{)} \\ R\colon\lbrack0,\infty) \end{gathered}[/tex]For x=y²:
[tex]\begin{gathered} D\colon\lbrack0,\infty) \\ R\colon(-\infty,\infty) \end{gathered}[/tex]A line passes through the point (-6,1) and has a slope of -5/2
Write an equation in slope - intercept form for this line .
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Answer: [tex]y=-\frac{5}{2}x+16[/tex]
Step-by-step explanation:
The equation in point-slope form is [tex]y-1=-\frac{5}{2}(x+6)[/tex]. To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]y-1=-\frac{5}{2}(x-6)\\\\y-1=-\frac{5}{2}x+15\\\\y=-\frac{5}{2}x+16[/tex]
In the picture below, measure 1 is 5x-14 degrees and measure 3 is 2x+10 degrees. Find measure 2.
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SOLUTION:
Step 1:
In this question, we have the following:
In the picture below, measure 1 is (5x-14) degrees and measure 3 is (2x+10) degrees.
Find the measure of 2.
Step 2:
From the diagram, we can see that angles 1 and 3 are vertically opposite and they are also equal.
Based on this fact, we can see that:
[tex]\begin{gathered} \angle\text{1 = }\angle3 \\ (\text{ 5 x- 14 ) = ( 2x + 10 )} \\ \text{collecting like terms, we have that:} \\ 5x\text{ - 2x = 10 + 14} \\ \text{3 x = 24} \end{gathered}[/tex]Divide both sides, we have that:
[tex]\begin{gathered} x\text{ =}\frac{24}{3} \\ \text{x = 8 } \end{gathered}[/tex]Then, we put x = 8 into the equation for Angle 1 , we have that:
[tex]\angle1=(5x-14)=5(8)-14=40-14=26^0[/tex][tex]\angle3=(2x+10)=2(8)+10=16+10=26^0[/tex]Hence, we can see that Angles 1 and 3 are equal.
Step 3:
From the diagram, we can see that:
we can see that angles 2 and 4 are vertically opposite and they are also equal.
Recall that angles 1 and 3 are also vertically opposite and they are also equal.
Therefore, we can see that:
[tex]\begin{gathered} \angle2\text{ = p} \\ \angle4\text{ = p} \\ \angle1\text{ = }26^0 \\ \angle3=26^0 \\ \text{Then, we have that:} \\ p+p+26^0+26^{\text{ 0 }}=360^0\text{ ( Sum of angles at a point)} \\ 2p+52^0=360^0 \\ 2p=360^0-52^0 \end{gathered}[/tex]Divide both sides by 2, we have that:
[tex]\begin{gathered} 2p=308^0 \\ p\text{ =}\frac{308^0}{2} \\ p=154^0 \end{gathered}[/tex]CONCLUSION:
[tex]\begin{gathered} \operatorname{Re}call\text{ that }\angle2\text{ = p} \\ \text{Then, we have that:} \\ \angle2=154^0 \end{gathered}[/tex]During a food drive, a local middle school collected 3,195…
Answers
Answer:
100 cans
Explanation:
• The total number of canned food items collected = 3,195
,• The number of classrooms that participated = 28
To estimate the number of items each classroom donated, divide 3195 by 28.
[tex]\frac{3195}{28}\approx\frac{3000}{30}=100[/tex]Note: Round to a whole number since the number of cans cannot be a decimal.
Each class donated about 100 cans.
5) Find the volume of the cylinder whose radius is 10in and height is 20in.V-π r 2 h
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Write the rate as a fraction in the simplest form $1680 for 8 weeks 236 miles on 12 gallons of gasoline
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The question asked to write the rate as a fraction in simplest form
[tex]\text{ \$1,680 for 8 w}eeks[/tex]To write the above relation in a fraction, we will have
[tex]\begin{gathered} =\frac{1680}{8} \\ \end{gathered}[/tex]Dividing to the lowest term, we will have
[tex]\begin{gathered} =\frac{210}{1} \\ whichis\text{ \$210 for 1 we}ek \end{gathered}[/tex]The question asked to write the rate as a fraction in simplest form
[tex]236\text{ miles on 12 gallons of gasoline}[/tex]To write the above relation in a fraction, we will have
[tex]=\frac{236}{12}[/tex]To express as a fraction in its lowest terms will be
[tex]\begin{gathered} =\frac{59}{3} \\ \text{which represents 59 miles for 3 gallons} \end{gathered}[/tex]3. In one linear function, when you subtracteach y-coordinate from the x-coordinate,the difference is 3. If the x-coordinate isnot greater than 10 and the y-coordinateis a positive whole number, how manyordered pairs are there?
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Problem
3. In one linear function, when you subtract each y-coordinate from the x-coordinate, the difference is 3. If the x-coordinate is not greater than 10 and the y-coordinate is a positive whole number, how many ordered pairs are there?
Solution
Here are the conditions
x- y= 3
x <10
y >0
And then we have these as possible answers:
4-1 =3
5-2= 3
6-3=3
7-4=3
8-5=3
9-6=3
Then the total possible pairs are: 6
can u find a b and c its parallelogramthank u
Answers
To answer this question, we need to remember two theorems of parallelograms:
1. If a quadrilateral is a parallelogram, the two sets of its opposite angles are congruent:
2. The consecutive angles of parallelograms are supplementary (they sum 180 degrees):
Then, with this information, we have that:
[tex]97\cong m\angle c\Rightarrow m\angle c=97[/tex]And also, we have that the diagonal forms two congruent triangles, and the sum of internal angles of a triangle is equal to 180, then, we have:
[tex]m\angle c+26+m\angle b=180\Rightarrow97+26+m\angle b=180\Rightarrow m\angle b=180-97-26[/tex]Then, we have:
[tex]m\angle b=180-123\Rightarrow m\angle b=57[/tex]Then, using that the consecutive angles of parallelograms are supplementary (they sum 180 degrees), we have:
[tex]97+m\angle a+m\angle b=180\Rightarrow97+m\angle a+57=180\Rightarrow m\angle a=180-97-57_{}[/tex]Thus, we have that the measure for angle a is:
[tex]m\angle a=180-154\Rightarrow m\angle a=26[/tex]In summary, we have that (all the measures in degrees):
m< a = 26
m< b = 57
m< c = 97
What is the answer to this equation?
Answers
Answer:
D 7.5
Step-by-step explanation:
n + n-3 + 2n-4 = perimeter ≥ 37
4n-7≥37
4n≥30
n≥7.5
Look at triangles A through F shown in the rectangles below.Which triangles are acute triangles?
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The acute triangles are those whose all 3 angles have a measure less than 90 degrees.
We need to follow the next image:
Let us check each triangle.
Triangle A:
It has a right angle, hence, it can not be an acute triangle.
Triangle B:
All three sides are less than 90 degrees. Hence, it is an acute triangle
Triangle C:
It has an angle with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle D
All three sides are less than 90 degrees. Hence, it is an acute triangle.
Triangle E
It has a side with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle F
It has a right angle, hence, it can not be an acute triangle.
Hence, the correct answer is H. B and D
What is the product of V3 and 7V30 in simplest radical form?
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Determine the product of two expressions.
[tex]\begin{gathered} \sqrt[]{3}\times7\sqrt[]{30}=7\sqrt[]{30\cdot3} \\ =7\sqrt[]{3\cdot3\cdot10} \\ =7\cdot3\sqrt[]{10} \\ =21\sqrt[]{10} \end{gathered}[/tex]So answer is,
[tex]21\sqrt[]{10}[/tex]The table below shows the probability distribution of students in a highschool with 1500 students. What is the expected value for the ageof arandomly chosen student?Age131415161718Probability.0.010.250.300.280.150.01A. 15.28B. 15.64C. 15.34D. 15.36
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Solution
We are required to determine the expected value of the given distribution
The formula for expected value is shown below
Thus,
[tex]\begin{gathered} Expected\text{ value =13\lparen0.01\rparen+14\lparen0.25\rparen+15\lparen0.30\rparen+16\lparen0.28\rparen+17\lparen0.15\rparen+18\lparen0.01\rparen} \\ = \end{gathered}[/tex][tex]=0.13+3.5+4.5+4.48+2.55+0.18[/tex][tex]=15.34[/tex]The correct option is C
O is the center of the regular hexagon below. Find its perimeter. Round to the nearest tenth if necessary.
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To solve this problem, we have to find the side length and multiply it by the number of sides of the figure.
To find the length side we will use the following formula:
[tex]ap=\sqrt[]{I^2-(\frac{I^{}}{2})^2}\text{.}[/tex]Where ap is the length of the apothem, and I is the side length.
Substituting the given values, we get:
[tex]10=\sqrt[]{I^2-(\frac{I}{2})^2}.[/tex]Solving the equation for I, we get:
[tex]\begin{gathered} \\ I=\frac{2\times10}{\sqrt[]{3}}. \end{gathered}[/tex]Therefore, the perimeter of the hexagon is:
[tex]6I=6\times\frac{2\times10}{\sqrt[]{3}}\approx69.3\text{ units.}[/tex]Answer:
[tex]69.3\text{ units.}[/tex]Be sure to include the correct unit in your answer
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The fence required is:
[tex]388.3125ft^2[/tex]Explanation:For the farmer to build an accurate fence, he needs to know the area of the rose garden. The area is the sum of the area of the rectangle and the area of the semicircle.
The area of the rectangle is:
[tex]\begin{gathered} A=wl \\ =15ft\times20ft \\ =300ft^2 \end{gathered}[/tex]The area of the semicircle is:
[tex]\begin{gathered} A=\frac{\pi}{2}r^2 \\ \\ \text{Where r is the radius }=\frac{15}{2}=7.5ft,\pi=3.14 \\ \\ A=\frac{3.14}{2}(7.5)^2=88.3125ft^2 \end{gathered}[/tex]The area of the rose garden is:
[tex]300ft^2+88.3125ft^2=388.3125ft^2[/tex]9.5.35 Assigned Media An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 300 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden What is the length of the garden? The length of the garden is
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Answer:
• The dimensions of the garden are 90 feet by 60 feet.
,• The length of the garden is 90 feet.
Explanation:
Let the length of the garden = l
The width is exactly two-thirds of the length, Width = (2/3)l
If 300 feet of antique picket fencing are to be used to enclose the garden, this means that the perimeter of the proposed garden is 300 feet.
[tex]\begin{gathered} \text{Perimeter}=2(\text{Length}+\text{Width)} \\ 300=2(l+\frac{2}{3}l) \end{gathered}[/tex]Next, solve the equation for the length, l:
[tex]\begin{gathered} \frac{300}{2}=l+\frac{2}{3}l \\ 150=\frac{5l}{3} \\ l=150\times\frac{3}{5} \\ l=90\text{ feet} \end{gathered}[/tex]The length of the garden is 90 feet.
Next, we determine the width.
[tex]\begin{gathered} \text{Width}=\frac{2}{3}l \\ =\frac{2}{3}\times90 \\ =2\times30 \\ =60\text{ feet} \end{gathered}[/tex]The dimensions of the garden are 90 feet by 60 feet.
what is equivalent to 2^4 x 4^2?
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Given an indices shown below
[tex]2^4\text{ }\times4^2^{}[/tex]Addition method of indices
The second power need to be split into the power of 2
[tex](2^4\text{ }\times2^2)2^2)[/tex]Hence the equivalent is Option B
If the trend shown in the graph above continued into the next year, approximately how many sport utility vehicles were sold in 1999?
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ANSWER :
EXPLANATION :
a. Rotate the letter W 180° around the origin. Then translate the image up 4 units. Draw the final image. What new letter did you form? b. Is the new letter congruent to the original letter? Explain.
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ANSWER and EXPLANATION
We have letter W on the graph.
The cordinates of its vertices are:
(0, 4), (1, 0), (2, 2), (3, 0), (4, 4)
Now, on a cartesian plane, (x - y plane), we have 4 quadrants. The letter is on the first quadrant.
Because it rotates 180 degrees around the origin, it means that it mmoves by 2 quadrants:
So, it moves from quadrant 1 to quadrant 4.
The new cordinates become:
(0, -4), (-1, 0), (-2, -2), (-3, 0), (-4, -4)
Then it is translated 4 units up, so we add 4 units to each of the y values (Remember that cordinates are written as (x, y)):
(0, 0), (-1, 4), (-2, 2), (-3, 4), (-4, 0)
Now, plot those:
a) It forms the letter M.
b) For one shape to be congruent to another, it means that they have the same size. So, yes, the M is congruent to the W.
Which calculation and answer show how to convert 13 to a decimal?
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when evalueatong the expression 13/15,
13 serves as the dividend and
15 is the divisor
Divisor is always placed outside the division sign and the dividend inside.
According to the option, you can see that 15 which is the divisor is placed outside and 13 is placed inside.
check the diagram below:
Option A is the correct answer in this case
I’m not sure how to graph the equation and not sure what it means by “interpret”
Answers
(a) Graphing the equation
(i) let x = 0 ; then
y = -0.05 (0) +16
∴ y = 16
Point 1 = ( 0;16 )
(ii) let y = 0 , then
0 = -0.05x +16
0.05x = 16
x = 16 /0.05
∴ x = (320 )
point 2 = ( 320; 0 )
The graph of the line ( y = -0.05x+16) will then be as follows :
(b) Interpret the x and y intercept :{To interpret means to explain in details or translate in writing the meaning of the values of x and y . }
• x represents the number of miles travelled
,• y represents gasoline used i gallons
Interpretation:
• when ,x is 0 miles, , the ,gasoline ,is sitting at, 16 gallons.,( this might be the initial stage of travelling)
,• however, when the, person has travelled 320 miles,, all gasoline is ,completly used up and sits at 0 gallons, .( this might be the end stage of travelling)
what is a youth group that
Answers
(3+ 1i) (2 - 2i)
open the parenthesis
3(2 - 2i) + 1i(2 - 2i) (note: i² = -1)
6 - 6i + 2i + 2
Rearrange
6 + 2 - 6i + 2i
8 - 4i
comparing with a + bi
The real number a equals 8
The real number b equals -4
The speedometer on Leona's car shows the speed in both miles per hour and kilometers per hour. Using 1.6 km as the equivalent for 1 mi, find the mile per hour rate that is equivalent to 40 kilometers per hour.
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To find the mile per hour rate equivalent to 40 km per hour, let's convert 40km to miles using the given equivalence in the question.
[tex]\begin{gathered} 1.6\operatorname{km}=1mi \\ 40\operatorname{km}\times\frac{1mi}{1.6\operatorname{km}}=\frac{40\operatorname{km}mi}{1.6\operatorname{km}}=25mi \end{gathered}[/tex]Therefore, 40 km = 25 miles.
The mile per hour rate equivalent to 40km per hour is 25 miles per hour.
James is putting a frame around a rectangular photograph. The photograph is 12 inches long
and 10 inches wide, and the frame is the same width all the way around. What will be the
area of the framed photograph? (Hint: use "x" as your variable.)
Polynomial:________
=_________
=_________
=_________final answer in standard form.
PLEASSEEEEEE i need know this asap
Answers
Answer:
The area is 4x² + 44x + 120Step-by-step explanation:
GivenDimensions of rectangle are 12 in and 10 in,Width of the frame is x.To find The area of the framed photographSolutionDimensions of the framed photograph are:
12 + 2x and 10 + 2xArea of the framed photograph is:
A = lwA = (12 + 2x)(10 + 2x) = 12*10 + 12*2x + 10*2x + 2x*2x = 120 + 24x + 20x + 4x²= 4x² + 44x + 120Which sample size will produce the widest 95% confidence interval, given asample proportion of 0.5?A. 40B. 70C. 60D. 50
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The confidence interval depends on the margin of error. When finding the margin of error, the z score corresponding to the 95% confidence level would be multiplied by the square root of the product of the estimated proportion of success and failure divided by the sample size. The greater the sample size, the smaller thie value that would be gotten from this operation. The smaller the sample size, the greater the value that would be gotten from this operation. A greater value would give a bigger margin of error. Thus, the confidence interval would be wider. Hence, the correct option for the sampe size is
A. 40
The employees in a firm earn $8.50 an
hour for the first 40 hours per week, and
1.5 times the hourly rate for any hours
worked over 40. How much does an
employee who works 52 hours in one
week eam?
Answers
Using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).So, the amount earned by a person who works 52 hours a week:
Salary if a person works for 40 hours: $8.50 per hourSalary if a person works for more than 40 hours: 1.5 times $8.50 per hour that is, 8.50 × 1.5 = $12.75 per hour.So, if a worker works for 52 hours, his salary will be:
52 - 40 = 12 Hours40 × 8.50 = $34012 × 12.75 = $153Sum: $493Therefore, using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.
Know more about mathematical operations here:
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