13. Use your fraction manipulatives to find other ways to form a whole circle. Write an equation for each way you find. 14. One fourth of a circle plus one tenth of a circle is what percent of a whole circle? 15. Two fourths of a circle plus two tenths of a circle is what percent of a whole circle?
3. Kyle and Mark started at the same location. Kyle traveled 5 miles due east, while Mark traveled 3 miles due West. How far apart are they?
(A) 2 miles
(B) 8 miles
(C) 15 miles
(D) 12 miles
7. RT has endpoints R(0,2) and T(3,2). Find the image after a dilation with scale factor 2 centered at
(1,3) followed by T(−2,−3).
R′=1+2(0−1),3+2(2−3)=(−1,1)T′=1+2(3−1),3+2(2−3)=(5,1)R′′=(−3,−2)T′′=(3,−2)
Part 1 of 3 The graph below shows a rectangular sum of n=8 rectangles to approximate the area under the line from x=0 to x=2. Is this a right-hand or left-hand sum?
right-hand sum ✓∨σ∞□
What is the equation of the line?
y=2x
Part 3 of 3 What is the value of the sum?
Joe has a barn in his back yard.
Figure A is a diagram representing the side view of the barn. Figure A Find the perimeter of the side of the barn. The perimeter of the side of the barn is □ft.
Find the area of the side of the barn. The area of the side of the barn is □ sq. ft.
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $10 per linear foot to install and the farmer is not willing to spend more than $7000, find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $8 per linear foot to install and the farmer is not willing to spend more than $4000, find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)
Площадь квадрата и прямоугольника Вариант 2
1.В прямоугольнике одна сторона равна 10 , другая сторона равна 14. Найдите площадь прямоугольника. 2. Найти сторону квадрата, если площадь равна: а) 289m2;
б) 54CM2
в) 12 дм 2
3.В прямоугольнике одна сторона равна 14 , периметр равен 54 . Найдите площадь прямоугольника. 4. Периметр квадрата равен 20 cm . Найдите его площадь.
5.Найдите площадь прямоугольника, если его периметр равен 58 и одна сторона на 5 больше другой. 6. Пол комнаты, имеюощей форму прямоугольника со сторонами 4 m и 7 m , требуется покрыть паркетом из прямоугольных дощечек со сторонами 7 cm и 20 cm . Сколько потребуется таких дощечек?
Exercice n∘3:(8pts)
Soit ABC un triangle tel que : AB=4;AC=6 et BC=8.
Soit M un point du segment [AB] tel que AM=1.
1) a/ Faites une figure.
b/ Construire le point N du segment [AC] tel que AN=41AC.
c/ Montrer que les droites (MN) et (BC) sont parallèles.
d/ Montrer que MN =2.
2) Les droites (MC) et ( BN ) se coupent en I et la parallèle à (BC) passant par I co (AB) en J.
a/ Montrer que MNIJ=BMIIBIII puis BCII=MBMI.
b/ En déduire que MNIJ+BCIJ=1.
c/ Calculer alors IJ puis MJ.
\begin{problem}
(c) Rajah di bawah menunjukkan pelan, dongakan depan dan dongakan sisi bagi sebuah pepejal. Diagram below shows the plan, front elevation and side elevation of a solid. \begin{enumerate}
\item Lakar bentuk tiga dimensi pepejal itu.
Sketch the three-dimensional shape of the solid.
\item Diberi isi padu sebuah kuboid adalah 12cm3. Bandingkan isi padu antara kuboid dan isi padu pepejal dalam jawapan (i), seterusnya bandingkan nilai isi padu pepejal tersebut dalam bentuk nisbah.
Given the volume of a cuboid is 12cm3. Compare the volume between the cuboid and the solid in answer (i). Hence, compare the volume of the solids in the form of ratio.
\end{enumerate} Jawapan / Answer:
(i)
\end{problem}
Find the circumference and area of the circle. Express answers in terms of π and then round to the nearest tenth. Find the circumferencetn terms of π.
C=□□ (Type an exact answer in terms of π.)
8) In the diagram, ABC is an arc of a circle with centre O and radius 5 cm . The lines AD and CD are tangents to the circle at A and C respectively. Angle AOC=32π radians. Calculate the area of the region enclosed by AD,DC and the arc ABC , giving you answer correct to 2 significant figures.
13. A landscape architect designed a flower garden in the shape of a trapezoid. The area of the garden is 13.92 square meters. A fence is planned around the perimeter of the garden. How many meters of fencing are needed? 14. (11) Justify Conclusions Suppose for some value of x the solution to the equation 2.5(y−x)=0 is y=6. What must be true about x ? Justify your conclusion. 15. (11) Persevere with Problems Keith is 5 years older than Trina. Two times the sum of their ages is 62 . Write and solve an equation to find Keith's age.
B) Solve.
11) In \triangle A B C, m \Varangle A=-7 x+1, m \Varangle B=-x+13, and m \Varangle C=-2 x-4. Draw and label of the triangle.
a) Solve for x and the measures of the angles.
\begin{array}{l}
x= \\
m \Varangle A= \\
m \Varangle B= \\
m \Varangle C=
\end{array}
b) Order the sides from least to greatest. ANSWER:
<
Part A
Continue the rotation and draw the fan blade in the third and second quadrants after two more rotations of 90∘ each. Use the Polygon Tool to graph the rotations. Show Hints
Polygon
Undo → Redo × Reset
Shalu and Monu have a garden which is in the shape of a rectangle, having dimensions 4m×3m. It has tulip and rose flowered plants. Half of the garden is filled with tulip and half is covered with rose plants. What is the area of the garden? *
1 point
(a) 12 sq.m
(b) 12 m
(c) 12sq.cm
(d) none of these How much area is covered with tulip flowers? *
1 point
(a) 12 sq.m
(b) 12sq.cm
(c) 6sq⋅m
(d) 6 sq. cm Now they decided to fence the garden. They tries to buy the wire which
* 1 point
can cover the border 4 times. When they went to buy it, it was found that there are three types of wires Type1: rs 2/m
Type2: rs 4/m
Type3: rs 6/m
As they had only 300 rupees with them, which type of wire can they buy?
(a) Type 1 or 2
(b) Type 2 or 3
(c) Type 3
(d) all the three
Übung 22
Gegeben ist ein Dreieck ABC mit A(1∣2),B(9∣0) und C(5∣6).
a) Stellen Sie Parametergleichungen der Mittelsenkrechten gAB und gAC auf.
b) Berechnen Sie den Schnittpunkt der Mittelsenkrechten gAB und gAC.
c) Stellen Sie das Dreieck ABC sowie die Mittelsenkrechten gAB und gAC zeichnerisch dar.
```latex
f(x) \text{ est une fonction périodique telle que } f(x) = 2x - 1 \text{ pour } x \in \left(0, \frac{3}{2}\right). \text{Nous devons dessiner la courbe périodique sur l'intervalle } [-1, 2] \text{ avec une période } T = \frac{3}{2}.
```
Find the intercepts and then use them to graph the equation.
5x+4y=20 Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line. Click to enlarge graph
Watch Video Question
Find the vertices of the ellipse defined by the equation shown below. If necessary, round to the nearest tenth
4x2+25y2+24x−200y+336=0 Answer Attempt 2 out of 2 Vertices: □ , □ and □ , □
Submit Answer
Two ants crawl around a circle of radius r=6 with both x and y measured in inches. Both start at the point ( 6,0 ) at the same time. One bug is moving at a rate of 3in/sec. The other is moving twice as fast.
When will one ant be directly above the other ant as shown below? (Give the first time this happens assuming they start at t=0.)
Number
Units
Complete the congruence statement in two different ways.
△RPQ≅ ? Select all that apply.
A. △RPQ≅△ZYX
B. △RPQ≅△YXZ
C. △RPQ≃△XZY
D. △RPQ≅△XYZ
E. △RPQ≅△ZXY
F. △RPQ≃△YZX
Name:
Use this diagram to answer the following questions.
6. In the above diagram, what is the length of side XZ ?
a. 4.8 cm
b. 8.3 cm
c. 16.4 cm
d. 23.0 cm
7. In the above diagram, what is the measure of ∠X ?
a. 37.6∘
b. 39.7∘
c. 50.2∘
d. 52.4∘ 8. In the above diagram, what is the measure of ∠Z ?
a. 37.6∘
b. 39.7∘
c. 50.2∘
d. 52.4∘
Question
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Show Ex Find the center of the ellipse defined by the equation 25(x−4)2+16(y+5)2=1. If necessary, round to the nearest tenth Answer Attempt 1 out of 2 Center: □□
Submit Answer
Considera le due funzioni:
f(x)=∣x−2∣−1 e g(x)=−21x+2
a. Traccia i loro grafici e determina l'area del triangolo che essi individuano.
b. Risolvi graficamente la disequazione f(x)≥g(x).
Which of the following equations represents a line that passes through the points (−1,−2) and (−2,−5) ?
I. y+5=3(x+2)
II. 3x+y=−1 Answer
Neither I only
Submit Answer
II only
I and II
Triangle XYZ has side lengths 4, 10, and 12. Click and drag each transformation into one of the two boxes to classify them as producing a triangle similar to triangle XYZ or not similar to triangle XYZ. Similar to Triangle XYZ
Not Similar to Triangle XYZ Add 10 to each side length.
Subtract 1 from each side length.
Multiply each side length by 4.
Divide each side length by 3.
The angle measurements in the diagram are represented by the following expressions.
∠A=7x+24∘∠B=3x+92∘ Solve for x and then find the measure of ∠A :
∠A=□∘
Select the correct answer from each drop-down menu.
Given: ∠BON≅∠NOC
Prove: ∠AOM≅△MOD
\begin{tabular}{|l|l|}
\hline Statements & Reasons \\
\hline 1. AC,MN, and DB intersect at O & 1. given \\
\hline 2. ∠AOM≅∠NOC & 2. vertical angles theorem \\
\hline 3. △MOD≅∠BON & 3. vertical angles theorem \\
\hline 4. ∠BON≅∠NOC & 4. given \\
\hline 5. ∠AOM≅∠MOD & 5. transitive property of congruence \\
\hline
\end{tabular} Convert the proof to the paragraph format.
Since AC,MN, and DB intersect at O,∠AOM≅∠NOC and ∠MOD≅∠BON by the □ It is given that ∠BON≅∠NOC, so by the □ , ∠AOM≅∠MO.
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linear pair postulate
congruent supplements theorem
vertical angles theorem
transitive property of congruence
Suppose that △QRS is isosceles with base SQ.
Suppose also that m∠S=(3x+19)∘ and m∠Q=(5x−9)∘.
Find the degree measure of each angle in the triangle.
m∠Q=□∘m∠R=□∘m∠S=□∘
The longer leg of a right triangle is 7 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle. Length of the shorter leg: □ cm Length of the longer leg: □ cm Length of the hypotenuse: □ cm
1
2
4 A ladder leans against the side of a house. The top of the ladder is 20 ft from the ground. The bottom of the ladder is 15 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth.
□ ft
1 Identifier les mesures données
Diamètre de la cheminée :
d=3,4m Volume de la cheminée :
V=385m3 2 Déterminer la formule à utiliser
Puisqu'on fait référence au volume d'un cylindre, on utilise :
V=Ab×h=πr2×h 3 Remplacer les variables par les mesures données
385=π(23,4)2×h 4 Isoler la variable recherchée
2,89π38542,40m=2,89π2,89π×h≈h
The length of a rectangle is 1 m more than double the width, and the area of the rectangle is 28m2. Find the dimensions of the rectangle. Length : □ m Width : □ m □
A kite flying in the air has a 12-ft line attached to it. Its line is pulled taut and casts an 11−ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.
□
ft
JIT
Page Department of Hydraulic \& Water Resource Engineering 41. A stream has the following cross -sectional data
\begin{tabular}{|c|c|c|c|c|}
\hline \multirow[t]{2}{*}{Station} & \multirow[t]{2}{*}{Distance up the stream (km)} & \multirow[t]{2}{*}{Elevation of the stream bed (m)} & \multicolumn{2}{|l|}{Cross-section Trapezoid} \\
\hline & & & Bed width B(m) & side slope (m) \\
\hline 1 & 50 & 100.0 & 15 & 1.5 \\
\hline 2 & 52 & 101.0 & 14 & 1.5 \\
\hline 3 & 54 & 102 & 13 & 1.25 \\
\hline
\end{tabular} For a discharge of 150m3/s, the depth of flow of the downstream -most section one (1) is 5.10m Assume n=0.025 and gradual transition .using the standard - step method computes the wate surface elevation at section 2&3.
△PQR is rotated 180∘ around the origin to form △P′Q′R′. Which coordinate is the same as the x-coordinate of point P′ ?
x-coordinate of point Py-coordinate of point P Opposite of x-coordinate of point P Opposite of y-coordinate of point P
i-Ready
Rotations - Instruction - Level H
△GHI will be rotated 180 around the origin to form △G′H′I′.
180∘ rotation:
(x,y)→(−x,−y) What are the coordinates of point H′ after the rotation?
(7,−5)(5,−7)(−7,−5)(5,7)
Math 2
Mid - Unit 4 Test
Name: Iineen PART 1: For each question choose the best answer from the choices provided. 1. Fill in the Blank: Supplementary angles are two angles whose measure of a sum of -
Complementary angles are two angles whose measures have a sum of -
. Vertical angles are .
OPTIONS
Supplementary
Linear
Congruent
Adjacent
- ∠1 and ∠2 are supplementary. The m∠1=3x−15 and m∠2=5x+27. Find the value of x.
x= Find the value of x in the triangle. (Picture not drawn to scale)
x= MATCH each triangle with its correct classification by its sides. (Drag-and-Drop in Canvas)
Classification by sides
BANK of CLASSIFICATIONS Scalene
Isosceles
Equilateral
The length of a shadow of a building is 29 m . The distance from the top of the building to the tip of the shadow is 36 m . Find the height of the building. If necessary, round your answer to the nearest tenth.
□ m
LEVEL: 1/1
7 more questions to go
AFTER LEVEL: 1 Given that point G is the incenter of △HJK, which of the following is true?
GF=EGGJ=EGHE=EK
Two of these
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Desk 1
Graph the following equation and if possible, determine the slope.
x=−3 Use the graphing tool on the right to graph the equation. Click to enlarge graph What is the slope of the line?
A. m=□
(Type an integer or a fraction.)
B. The slope is not defined.
Question
Q) Walk-Through Example TSIA Style Two hikers start at a ranger station and leave at the same time. One hiker heads due west at 3 mph . The other hiker heads due north at 4 mph . How far apart are the hikers after 2 hours of hithen?
A) 3 miles
(8) 7 miks
C) 10 miks
b) 14 mils
Swing an arc that intersects the angle's rays. Question 2(Multiple Choice Worth 1 points)
(01.02 LC) Angle ABC has point E on ray BA and point D on ray BC. Points E and D are equidistant from point B. To copy angle ABC, which of the following needs to be identified for construction?
The distance between points E and D
The point in the angle that is equidistant from points E and D
The endpoint of rays BA and BC
The point outside of the angle that is equidistant from points E and D Question 3(Multiple Choice Worth 1 points)
(01.02 LC)
Question 3(Multiple Choice Worth 1 points)
(01.02 LC) Sasha is bisecting a segment. First, she places the compass on one endpoint, opens it to a width larger than half of the segment, and swings an arc on either side of the segm Then, she keeps the compass the same with and places it on the other endpoint. What is her next step?
Swing arcs on both sides to intersect the first two arcs created.
Swing an arc that intersects the segment.
Swing arcs that intersect a point that is not on the segment.
Swing an arc that intersects the opposite endpoint.
Question 4(Multiple Choice Worth 1 points)
uestion
Question 1 (Answered)
10. In the diagram below, circle center O has diameter AC,AO is 4 units long, and the measure of arcAB is 120∘. What is the area of the shaded region?
F. 316π−83
G. 38π−23
H. 38π−43
J. 38π−83
K. 34π−43
The figure below represents part of a regular polygon with n sides inscribed in a circle with center O. In terms of n, what is the degree measure of ∠OBC ?
A. 90−n180
B. 180−n
C. 180n−360
D. 180−n360
E. n360
A rectangular box with length 22 inches, width 5 inches, and height 5 inches is to be packed with steel balls of radius 2 inches in such a way that the centers of the balls are collinear. What is the maximum number of balls that can fit into a box, given that balls should not protrude out of the box?
A. 0
B. 5
C. 6
D. 10
E. 11
A quadrilateral PQRS is inscribed in a circle. The length of PQ is 16 inches, and the length of PS is 12 inches. Given that the measure of arcPQ equals the measure of arc SR and the measure of arc PS equals the measure of arcQR, what is the area of the circle in square inches?
F. 20π
G. 50π
H. 100π
J. 200π
K. 400π
USING THE SHAPE TOOL, CREATE A LINE TO CONNECT EACH PROBLEM TO ITS SOLUTION AT THE RIGHT. NOT ALL CHOICES WILL BE USED.
a
Kevin needs to replace four rectangular windows. Each window measures 2.75 ft by 4 ft . Find the square feet of glass that Kevin will need for the windows. B Julie is making a banner shaped like a parallelogram with a base of 841 feet and a height of 6 feet. How many square feet of material will Julie need for the banner?
```
C Rhett's rectangular room measures
12.5 feet by 13 feet. His rectangular
closet measures 3.5 feet by 5 feet.
How much greater is the area of his room
than his closet?
```
11ft249.5ft2145ft244ft2162.5ft2
- Manouvering the Middle LLC, 2019
The volume of a sphere with radius r is given by V=34πr3. The volume of a cylinder with height h and base area A is given by V=Ah.
\text{What is the volume of the silo to the nearest cubic foot?}
A. 5,864B. 7,959C. 20,944D. 23,038E. 245,044
\text{Radius of the base of the cylinder is 10 feet and the height of the cylindrical part is 60 feet.}
In the diagram below, a chord of length 18 centimeters is bisected by a line segment that starts at the center and is 6 centimeters from the center. What is the radius of the circle in centimeters?
A. 313
B. 35
C. 10
D. 12
E. 15
Watch Videc Given: BD and AC bisect each other.
Prove: AB∥CD. Step 1 2 3 BD and AO bisect each other
AE≅ECDE≅EB Reason Given A segment bisector divides a segment into two congruent segments Select a Reason. A B
Reorder the steps of the proof to make sure that steps that are logically dependent on Given: ∠B≃∠E,OH≃FD and BO∼DE, Prove: ∠CGI≅∠DIG.
\begin{tabular}{cc}
step & statement \\ 1. & ∠B≅∠E \\
\hline 2 & CH≅HD \\
3 & BC≅DE \\
4 & △BCG≅DI \\
5 & GH≅IH \\
6 & ∠HDC≅∠EDI \\
7 & ∠CGI≅∠DIG \\
8 & ∠BCD≅∠HDC \\
9 & ∠BCG≅∠HCD \\
\hline & ∠EDI
\end{tabular} Heaton Given Corresponding Parts of Congrient Triangles are Congruent (CRCTC)
ABA
Congruent segments added to congruent sezments form congrelt se
Vertical angle are congment
In a triangle, angles opposite of congnent sides are congruent
In a triangle, angles opposite of congrient sitis are congrient
Vertical angles are congruent
Transitive Property
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5.18 Quiz: Quadrilaterals and Their Properties What is the length of the midsegment of this trapezoid?
Enter your answer in the box.
□ units
1
2
3
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As part of his sinister plan, Dr. Evil decides to mail Mini-Me to Austin Powers, in order to conduct his dirty work. The box to be used for shipment must be a rectangular storage container with a volume of 10ft3. The top and bottom of the box will be square, but the sides will be somewhat longer. In addition, a different material will be used for the top and bottom. Dr. Evil has invented a breathable cardboard that costs $5 per square foot (the regular cardboard sides cost only $2 per square foot). Design a container for Mini-Me that will meet the volume requirements while minimizing the cost.
Unfortunately, Dr. Evil's henchmen (who will eventually build the box) can only measure within half a foot. Rounding your dimensions to the nearest half-foot, what is the volume of the new box and how much will it cost to build?
6 Vier gleichseitige Dreiecke bilden den Mantel einer quadratischen Pyramide mit der Kantenlänge 10 cm .
a) Berechne die Länge des eingezeichneten Streckenzuges. A, B, C sind Kantenmitten.
b) Zeichne das Schrägbild der Pyramide und trage den Streckenzug ein.
Find the standard form of the equation of a circle with center (2,3) and touching the x -axis. Graph the equation. The standard form of the equation of a circle is (x−2)2+(y−3)2=9.
(Type an equation. Simplify your answer.)
Use the graphing tool to graph the circle.
Question
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Show Examples What is the volume of a sphere with a diameter of 3.6 ft , rounded to the nearest tenth of a cubic foot? Answer Attempt 1 out of 2
□ft3
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Question
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Show Examples What is the volume of a sphere with a radius of 6.6 cm , rounded to the nearest tenth of a cubic centimeter? Answer Attempt 1 out of 2