Area Questions and Answers

The shaded triangle has an area of 18 in Find the area of the entire rectangle Be sure to Include the correct unit in your answer

Find the area of the right triangle 1 unit C Area 0

a In the diagram below what value of x would make AB CD b mABHF m4CFG c Classify the following angles ABHF and ACFH A C 7x 20 Et F B H 3x 60

x A government in which one person holds supreme power within the state is called x A an autocracy B an oligarchy C a confederation D a democracy

Which of the following functions have an average rate of change that is negative on the interval from x 1 to x 2 Select all that apply f x x 3x 5 f x 3x Submit 5x f x x 3x 5 f x 3x 5x

What type of angles are shown in the diagram Same Side Interior Angles O Corresponding Angles Alternate Interior Angles Alternate Exterior Angles

Given the following characteristics select the function family that is described Shape single curve End Behavior one rising one falling Domain dependent on asymptote Range all real numbers Asymptote vertical O quadratic O logarithmic Onone of these Olinear exponential

State the domain and range and determine if it s a function X 3 0 4 3 Domain Range Function Y 1 5 0 Yes

X W 40 10 Y Write your answer as an integer or as a decimal rounded to the nearest tent WX

Find XZ Y 24 XZ 9 N X Write your answer as an integer or as a decimal rounded to the nearest ter

13 What additional information is enough to prove that parallelogram ABCD is also a rhombus C A BD bisects AC B AB is parallel to DC C AC is congruent to DB D AC is perpendicular to DB B E D

12 In the trapezoid below AB DC and BC AD If AB x 5 BC 2x 14 CD 4x and BA 5x 4 what is the value of DA DC B a 20 b 44 c 49 d 93

In the triangle ABC side b 9 side c 9 and side a 8 what is the value of the sin A Round your answer to the nearest hundredth B picture of triangle is purely for labeling use angles and side lengths specified in the problem Type your answer

Classify each angle as right obtuse or acute

Enter any fractions as decimals rounded to the tenths place A EFG is a dilation image of A ABD E C A B F

A window has the shape of a parabola above and a circular arc below Find the area of the window 15 ft 14 5 ft Use the dotted line as your y axis and the solid gray line as the x axis 4 67 ft Find the distance from the x axis to the top of the circle feet Write the equation of the circle Write the equation of the parabola

Sketch the region enclosed by y 5 y e6x and x 1 Find the area of the region

The shaded region between the graphs of y and y 3x 15 is displayed below in orange X I I 40 The shaded region lies between x 2x 20 X and x A typical rectangle is shown in the diagram located at position x What is the height of this rectangle in terms of Now find the total area of the orange shaded region

The triangles in the diagram A A 40 OB 60 OC 80 OD 100 OE 120 B 00 E G A

1 point Which diagram shows a pair of angles measures that show a b a 120 60 d H H b 120 60 120 120 a 120 H 120 b C

Is this statement always sometimes or never true If ZX is an acute angle in a right triangle then sin X cos X always sometimes never

Find the sine cosine and tangent of ZU T 17 sin U cos U tan U U 31 S Write your answer in simplified rationalized form Do not round

Is this statement always sometimes or never true If mZF and mZG sum to 90 then sin F sin G always sometimes never

Find the cosine of ZP 48 P 55 73 R Simplify your answer and write it as a proper fraction improper fraction or whole nur cos P

Find the cosine of ZW V 11 U 33 00 22 W Write your answer in simplified rationalized form Do not rou cos W

15 If KL 5x 10 and LM 3x 2 then find the length of KM a 6 b 20 c 24 d 40 K

Write the rule to describe the transformation O Dilation of 2 5 Dilation of T Dilation of 3 2 5 4 F S Dilation of 0 25 U

x A B 2 4 9 D 10 k and k 3 what is the value of x

Find the rule to describe the transformation E 1 3 F 0 1 G 3 2 E 1 5 4 5 F 0 1 5 G 4 5 3 Dilation of 1 5 Dilation of 3 O Dilation of 0 25 O Dilation of 1 25

Using the given scale factor identify the dilation as an enlargement or reduction k 1 1 1 4 O Enlargement O Reduction No answer text provided No answer text provided

12 In rhombus ABCD BA x 4 units and the perimeter is 2x 4 units What is the area of the rhombus a 10 units b 100 units 6 units d 36 units C C

1 Use the graphs of y f x the parabola and y g x the line to sketch the graph of y f x g x then identify its domain and range Estimate the range where necessary 10 yo 10 10 15

nd the flux of the vector field F across the surface S in the indicated direction 2 2 x y z 10xi 10yj 2k S is the surface cut from the bottom of the paraboloid z x y by the plane z 3 direction is outward OA 828x OB 84T OC 1 584 OD 792

MYSTERY FUNCTION 1 What function could be shown here Why Describe its key features and discuss how you could represent this function with a formula

5 point 0 2 and satisfying the differential equation through the dy dx 7 y cos x cos x is such that 1 It is a differentiable function VXER 2 It is continuous VXE R 3 It is periodic 4 It is passing through 1 2 Orthogonal 2 dy dx trajectories of the system of curves a are X 1 9a y c 2 4x 3 y c x3 2 3 a 4 9a y c 4x 6 A curve has the property that area of triangle formed by the x axis the tangent to the curve and radius vector of the point of tangency is k The equation of all such curves passing through 0 1 is X a k 2y by then 2 X312 9 a 2 y c 0 8 odE 2 b 1 Juice 4 b 2 1 a 1 3 a 2 The tangent at any point P of a curve C meets the x axis at Q whose abscissa is positive and OP OQ O being the origin the equation of curve C satisfying these conditions may be 1 y 1 4x 2 y 9 12x 3 16 16x 4 y 25 20x Consider a curved mirror y f x passing through 8 6 having the property that all light rays emerging from origin after getting reflected from the mirror becomes parallel to x axis The equation of the mirror is ya blc 9 The equation of all possibl orthogonal to the family of c x y 2 2cx 0 where c is 2 1 x y ky 0 3 x y kx 0 4 10 If a mothball loses volume b proportional to its instantane of the ball decreases from 2 so the time before which the is less than or equal to 1 4 months 3 2 months 11 Let x 1 x dy dx x y 1 General solution of g xy 1 x In 1 x 2 General solution of c xy 1 x In 1 x Instner to eqois or arti 3 It y f x is a sol equation then lim X 4 If y f x is solution then lim f x 1 X 1 12 Let a curve passes th differential equation 1 It represents equ 2 It represents equ 3 Area enclosed b 4 Line y 1 is a ta 13 A curve satisfie dy x 1 xy dx x y y 1 The equation c x y 2x 2 an

correct b 1 is 2 x 3 0 and of the axis 6 7 y x and y x in sq units is 1 The area defined by lyse 1 in the cartesian 2 plane is y 1 4 2 In2 sq units 2 4 In2 sq units 3 2 In2 sq units 4 2 1 In2 sq units The area bounded by the curves y 3 13 x and 1 2 3 4 1 3 5 x is 12 5log 5 2 4log 5 3 4log 5 2 2 4log 5 2 2 3n 2 8 2 2 8 2 sq units sq units sq units 8 The area enclosed by the curves y 4 x and y2 2 sin and x axis in sq units is sq units TCX 2 2 2 3 2 4 54 6 3n 2 8 2 2 2 8 3

CO 10 X 11 12 13 14 15 16 A binomial experiment with probability of success p 0 2 and 1 4 trials is conducted What is the probability that the experiment results in exactly 2 successes Do not round your intermediate computations and round your answer to three decimal places If necessary consult a list of formulas 0 17 18

7 3 points Let A be a 2 x 2 with eigenvalues 3 and 1 3 and corresponding eigenvectors V 1 V Let x be a solution of the difference equation Xk 1 Axk Xo 9 Compute x Axo 2 points Referring to question 7 find a formula for XK involving k and the

ABCD is a square inscribed in a circle and circumscribed to another concentric circle with the first one A B 3 D C Show Transcribed Text Knowing that the area of the larger circle is 100 and that the area of the square ABCD is 200 determine the exact value of the area of the colored region Displays the requested value in square meters Solution 150pi 200 m 2

In the diagram AABC is isosceles BC is extended to D ABAC and m ZA 80 B C D

Find the volume of the region in the first octant bounded by the coordinate planes the plane y 2 2 and the cylinder x 4 y

In Exercises 35 and 36 use the cylindrical shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis 35 a the x axis c the line y 8 5 y b the line y 1 d the line y 2 5 x 12 y y

Consider the function g x x 2 3x 2 a Use the limit definition of the derivative to compute a formula for y g x b Determine the slope of the tangent line to y g x at the value x 2 c Compute g 2 d Find an equation for the tangent line to y g x at the point 2 g 2 Write your result in point slope form e Sketch an accurate labeled graph of y g x along with its tangent line at the point 2 g 2

What is the value of x 2x 33 OA 24 OB 33 0 C 72 2x 15 OD 75 2x

1 Penalty First try was incorrect AGHI ASTU Complete each of the following congruence statements comparing the corresponding parts in the congruent triangles GI DOC HI TS HG SU

1 In kite KITE above mzQTE 4x 10 m TEQ 3x 10 a Solve for x b Determine mzKET c mzQIT 45 determine m QKI E K d If KQ 2y 1 feet KT y 10 feet Determine the length of KT T

The graph of a 4th degree polynomial f x is shown below 5 f x 5 5 50 Find the rule of this function Enter your answer in either factored

Chap 6 from standard form find features and sketch Dec 2022 Find the y intercept as taught Show all your work in a neat and well organized manner Graph a Quadratic Relation by its x intercepts y intercept vertex and AOS Make a sketch It is not necessary to put a scale on each axis You must indicate the co ordinates of each feature as taught Not necessary to reflect any point y x 8x 20 Answer the rest of the question on this side of the sheet 4 marks

17 30 students return to the playing Over the course each person produces The room How many BTUS A 15 3 BTU ft C 16 BTU per Ff is classroom after of the next hour 800 BTUS of heat 20 feet by 20 feet by 12 feet per cubic foot B 51 BTU per D 5 0 per ft3 were produced ft

bounded by the xy plane yz plane XZ plane and the plane x 3 y 3 2 9 1 if the density of the solid is given by 8 x y z x 4y text mass