Prove

Problem 301

28. Use the figure to answer questions aa and bb. a. Are the triangles above similar? Explain. b. If possible, find the missing side length, xx.

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Problem 302

Check if triangles ABC\triangle ABC and XYZ\triangle XYZ are congruent using transformations: reflect and translate.

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Problem 303

Find angle OQPO Q P given points P,Q,RP, Q, R on a circle with mQPR=35m\angle Q P R=35^{\circ} and mORP=30m\angle O R P=30^{\circ}.

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Problem 304

Prove that 24x+1+3245(x+1)2^{4x+1} + 32^{\frac{4}{5}(x+1)} is divisible by 9.

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Problem 305

Prove that 5+232+3=43\frac{5+2 \sqrt{3}}{2+\sqrt{3}} = 4-\sqrt{3}.

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Problem 306

Given (2h3k):(h+2k)=3:5(2 h-3 k):(h+2 k)=3: 5, show h=3kh=3 k and find h:kh: k.

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Problem 307

Prove that 2n+1+32n12^{n+1}+3^{2n-1} is divisible by 7 for all positive integers nn.

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Problem 308

Soit II et JJ deux intervalles ouverts, avec (IQ)(JQ)=(I \cap \mathbb{Q}) \cap (J \cap \mathbb{Q}) = \varnothing. Prouvez que IJ=I \cap J = \varnothing.

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Problem 309

Démontrez que les nombres suivants sont irrationnels : 1. x+y\sqrt{x}+\sqrt{y} avec x,yx,y rationnels positifs irrationnels. 2. 2+3+5\sqrt{2}+\sqrt{3}+\sqrt{5}.

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Problem 310

Prove that sin60tan45tan30sin240tan315tan210=0\sin 60^{\circ} \cdot \tan 45^{\circ} \cdot \tan 30^{\circ} - \sin 240^{\circ} \cdot \tan 315^{\circ} \cdot \tan 210^{\circ} = 0.

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Problem 311

Prove the identity: sinx1+cosx+1+cosxsinx=2sinx\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=\frac{2}{\sin x}.

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Problem 312

Soient AA et BB deux parties non-vides de R\mathbb{R} avec aba \leq b pour tout aAa \in A et bBb \in B. Montrez que AA est majoré, BB est minoré et sup(A)inf(B)\sup (A) \leq \inf (B).

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Problem 313

A. Verify (3,125+3,168)+4,375=3,125+(3,168+4,375)(3,125+3,168)+4,375=3,125+(3,168+4,375) using the associative property. B. Show 3,125+3,168+4,365=11,078(550+692)3,125+3,168+4,365=11,078-(550+692). C. Prove 3,168+4,375+3,125=(3,168+3,125)3,168+4,375+3,125=(3,168+3,125). D. Confirm (4,168+3,125)+4,375=3,125+(1,168+3,168)(4,168+3,125)+4,375=3,125+(1,168+3,168).

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Problem 314

Beweisen Sie durch Induktion, dass 2n+1n22n2n + 1 \leq n^2 \leq 2^n für alle n4n \geq 4 gilt.

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Problem 315

Jika r=25r=25, maka r2=625r^{2}=625. Jika r2=625r^{2}=625, maka r=25r=25.

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Problem 316

From Unit 3, Lesson 8.) Suppose Quadrilaterals AA and BB are both squares. Are AA and BB necessarily scaled copies of one another? Explain. (From Unit 1, Lesson 2.)

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Problem 317

Prove: BDECDE\triangle B D E \cong \triangle C D E. \begin{tabular}{cc} Step & Statement \\ 1 & ADBADC\triangle A D B \cong \triangle A D C \\ BEDCED\angle B E D \cong \angle C E D \\ 2 & ADBADC\angle A D B \cong \angle A D C \\ 3 & ADB\angle A D B and BDE\angle B D E are supplementary \end{tabular}
Reason
Given
Corresponding Parts of Congruent Triangles are Congruent (CPCTC) If two angles form a linear pair, then they are supplementary 4ADC4 \quad \angle A D C and CDE\angle C D E are supplementary If two angles form a linear pair, then they are supplementary 5 DEDE\overline{D E} \cong \overline{D E} Reflexive Property 6 BDECDE\triangle B D E \cong \triangle C D E ASA
Note: the segment AEA E is a straight segment.
Answer Altempt iout of 2
The proof is incorrect \sim and step number \square is the first unjustified step due to a missing prior step Submit Answer

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Problem 318

4. Determine the exact value of each trigonometric expression. a) sin30×tan60cos30\sin 30^{\circ} \times \tan 60^{\circ}-\cos 30^{\circ} c) tan230cos245\tan ^{2} 30^{\circ}-\cos ^{2} 45^{\circ} b) 2cos45×sin452 \cos 45^{\circ} \times \sin 45^{\circ} d) 1sin45cos451-\frac{\sin 45^{\circ}}{\cos 45^{\circ}}
5. Using exact values, show that sin2θ+cos2θ=1\sin ^{2} \theta+\cos ^{2} \theta=1 for each angle. a) θ=30\theta=30^{\circ} b) θ=45\theta=45^{\circ} c) θ=60\theta=60^{\circ}
6. Using exact values, show that sinθcosθ=tanθ\frac{\sin \theta}{\cos \theta}=\tan \theta for each angle. a) θ=30\theta=30^{\circ} b) θ=45\theta=45^{\circ} c) θ=60\theta=60^{\circ}

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Problem 319

Create a truth table to show that [(pq)r](pr)(qr)\quad[(p \vee q) \rightarrow r] \equiv(p \rightarrow r) \wedge(q \rightarrow r).
Explain how the truth table shows these are logically equivalent.

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Problem 320

שאקות 3
יהיו F ו- G קבוצות של קבוצות. הוכיחו או הפריכו: . FG=F \cap G=\varnothing אז, ( (F)(G)=(\bigcup F) \cap(\bigcup G)=\varnothing (ב) בסעיפים הבאים נניח ש- F ו- G אינן ריקות. (F)(G)={XYXF,YG} (ה) \begin{array}{l} \cdot(\bigcap F) \cup(\bigcap G)=\bigcap\{X \cup Y \mid X \in F, Y \in G\} \text { (ה) } \end{array}

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Problem 321

יהיו F ו- G קבוצות של קבוצות. הוכיחו או הפריכו: UFG זא ,FG א (א) FG= אז, ( (F)(G)= (ב)  בסעיפים הבאים נניח ש- F ו- G אינן ריקות. \begin{array}{l} \text {. } U F \subseteq \bigcup G \text { זא }, F \subseteq G \text { א (א) } \\ \text {. } F \cap G=\varnothing \text { אז, ( }(\bigcup F) \cap(\bigcup G)=\varnothing \text { (ב) } \\ \text { בסעיפים הבאים נניח ש- F ו- G אינן ריקות. } \end{array}

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Problem 322

Soit (C) un cercle de centre 0 , de diamètre [AB] et de rayon 3 cm . Soit EE un point variable de ( CC ) et soit MM le symétrique de AA par rapport à EE. La droite (BM) coupe à nouveau le cercle en un point PP. On désigne par J le point d'intersection de (BE) et (AP) et par TT le point d'intersection de (AB) et (JM). a. Montrer que le triangle ABEA B E est rectangle. b. Montrer que le triangle ABMA B M est isocèle. c. Montrer que (AT) est perpendiculaire à (JM). d. Montrer que les points E,B,TE, B, T et MM appartiennent à un même cercle.

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Problem 323

o. A diagram is shown, where k/fk / f and mm Is a transversal.
Move statements and reasons to the table to prove that <1<5<1 \equiv<5. \begin{tabular}{|l|l|} \hline Statements & \multicolumn{1}{|c|}{ Reasons } \\ \hline 1.kI1 . k \| I & 1. Given \\ \hline 2. & \begin{tabular}{l}
2. Corresponding angles \\ are congruent. \end{tabular} \\ \hline 3. & 3. \\ \hline 4.154 . \angle 1 \geqq \angle 5 & 4. \\ \hline \end{tabular} 12<1<31<4<2<3\angle 1 \cong \angle 2<1 \cong<3 \quad \angle 1 \cong<4 \quad<2 \leftleftarrows<3 24252634\angle 2 \cong \angle 4 \quad \angle 2 \equiv \angle 5 \quad \angle 2 \cong \angle 6 \quad \angle 3 \equiv \angle 4 354546\angle 3 \cong \angle 5 \quad \angle 4 \cong \angle 5 \quad \angle 4 \cong \angle 6 Transitive property Symmetric property Vertical angles are congruent. Straight angles form a linear pair. Corresponding angles are congruent. Alternate exterlor angles are congruent.

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Problem 324

5. Prove the following identities a) cos(β)+tan(β)sin(β)=sec(β)\cos (\beta)+\tan (\beta) \sin (\beta)=\sec (\beta)

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Problem 325

\begin{tabular}{|l|l|l|} \hline Pulley Setup & Weight of Load & Tension in Rope \\ \hline Pulley A & 10 N & 10 N \\ \hline Pulley B & 10 N & 5 N \\ \hline \end{tabular}
Based on the data and the diagram, why is the tension in the rope lower in pulley B? Prove your explanation using force-acceleration equaticns for the loads in both pulley systems. \square B I \underline{\cup} x2x2Ωx^{2} \quad x_{2} \Omega 2

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Problem 326

csc2(x)csc(x)cot(x)=11+cos(x)\csc ^{2}(x)-\csc (x) \cot (x)=\frac{1}{1+\cos (x)}

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Problem 327

Prove this Idenity is true 1+cos2xsin2x=cotx\frac{1+\cos 2 x}{\sin 2 x}=\cot x

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Problem 328

2. Про функції f,g:[1,)Rf, g:[1, \infty) \rightarrow \mathbb{R} відомо, що f(x)g(x)f(x) \leq g(x) для всіх x1x \geq 1 і інтеграл 1f(x)dx\int_{1}^{\infty} f(x) d x \in розбіжним. Чи можна щось сказати про збіжність інтеграла 1g(x)dx\int_{1}^{\infty} g(x) d x ?

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Problem 329

4. Відомо, що an0a_{n} \geq 0 для всіх nNn \in \mathbb{N}, і що ряд n=1an2\sum_{n=1}^{\infty} a_{n}^{2} збігається. Чи обов'язково ряд n=1an\sum_{n=1}^{\infty} a_{n} також збігається?

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Problem 330

A twill weave is characterized by strong diagonal ribs/lines visible on the fabric surface. True False

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Problem 331

Warp knit fabrics are often used in high-performance applications \qquad True False

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Problem 332

The proof that EFGJHG\triangle E F G \cong \triangle J H G is shown. Given: GG is the midpoint of HF,EF//HJ\overline{\mathrm{HF},} \overline{\mathrm{EF}} / / \overline{\mathrm{HJ}}, and EFHJ\overline{\mathrm{EF}} \cong \overline{\mathrm{HJ}}. Prove: EFGJHG\triangle \mathrm{EFG} \cong \triangle \mathrm{JHG}
What is the missing statement in the proot? FEGHJG\angle F E G \cong \angle H J G GFEGHJ\angle \mathrm{GFE} \cong \angle \mathrm{GHJ} EGFJGH\angle E G F \cong \angle J G H GEFJHG\angle G E F \cong \angle J H G

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Problem 333

Is [0.82.50.32.5]\left[\begin{array}{l}\frac{0.8}{2.5} \\ \frac{0.3}{2.5}\end{array}\right] the steady state vector for the transition matrix P=[0.70.20.30.8]P=\left[\begin{array}{ll}0.7 & 0.2 \\ 0.3 & 0.8\end{array}\right] ? (Hint: You don't need to solve, there's an easier way.) [This question is based on your assigned pre-reading/prep for the upcoming Assignment] True False

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Problem 334

Prove the polynomial identity. x4y4=(xy)(x+y)(x2+y2)x^{4}-y^{4}=(x-y)(x+y)\left(x^{2}+y^{2}\right)
To prove the polynomial identity, start on the right side of the equation and use the Difference of Squares Identity to multiply the left two factors. (xy)(x+y)(x2+y2)=(x4y4)(x2+y2)(x-y)(x+y)\left(x^{2}+y^{2}\right)=\left(x^{4}-y^{4}\right)\left(x^{2}+y^{2}\right)
Difference of Squares Identity
Square of a Sum Identity
Sum of Cubes Identity
Difference of Cubes Identity

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Problem 335

Direction : After each lesson, do the designated HW question. Once done with ALL 3 Lessons HW, take a photo of all your work and upload it. Place to upload on G.C will be open sometime on 11/20. \square Lesson 12 HW
Given: Parallelogram ABCD,BFAFDA B C D, \overline{B F} \perp \overline{A F D}, and DEBEC\overline{D E} \perp \overline{B E C} Prove: AFBCED\triangle A F B \cong \triangle C E D \square this!

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Problem 336

40. Let F(x,y,z)=3x2yi+(x3+y3)j\mathbf{F}(x, y, z)=3 x^{2} y \mathbf{i}+\left(x^{3}+y^{3}\right) \mathbf{j}. (a) Verify that curl F=0\mathbf{F}=\mathbf{0}. (b) Find a function ff such that F=f\mathbf{F}=\nabla f. (Techniques for constructing ff in general are given in Chapter The one in this problem should be sought by trial and error. 1

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Problem 337

A,BA, B and CC are points on a circle. - BCB C bisects angle ABQA B Q. - PBQP B Q is a tangent to the circle.
Angle CBQ=xC B Q=x Prove that AC=BCA C=B C

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Problem 338

Dans une formule physique, on peut multiplier des grandeurs qui n'ont pas les mêmes dimensions (In a physical formula, we can multiply quantities that do not have the same dimensions)
Select one: Vrai (True) Faux. (False)

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Problem 339

Decide whether the following statement is true or false. If the discriminant b24ac=0b^{2}-4 a c=0, the graph of f(x)=ax2+bx+c,a0f(x)=a x^{2}+b x+c, a \neq 0, will touch the xx-axis at its vertex.
Choose the correct answer below. True False

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Problem 340

Est-ce que p2p^{2} est un nombre premier si pp est un nombre premier?

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Problem 341

Is the statement "A number can only be divisible by exactly one number" true or false? Explain your choice.

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Problem 342

Is it true that in an isosceles right triangle, the hypotenuse is 2\sqrt{2} times one leg's length? A. Yes B. No C. Maybe D. Sometimes E. Not applicable

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Problem 343

Explain why, when multiplying powers like amana^m \cdot a^n, we add the exponents to get am+na^{m+n}.

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Problem 344

Is it true that if two chords in the same circle are congruent, their minor areas are also congruent? A. Yes B. No C. Maybe D. Sometimes E. Not applicable

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Problem 345

Identify the two true statements: 1) A line is one-dimensional. 2) A plane has an endpoint. 3) The intersection of two planes can be a line. 4) Parallel lines intersect at 45 degrees.

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Problem 346

If BB is the midpoint of AC\overline{AC}, DD is the midpoint of CE\overline{CE}, and ABDE\overline{AB} \cong \overline{DE}, prove that AE=4ABAE=4AB.

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Problem 347

Calculate the products of matrices SS and TT: STS T and TST S to show multiplication is not commutative. Fill in the boxes.

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Problem 348

Billy needs help matching customers to cars based on arrival times and licenses. Use clues to find out who rented the Mustang.

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Problem 349

Show that matrix multiplication is not commutative by calculating STS T and TST S for the matrices S=[4132]S=\begin{bmatrix} 4 & 1 \\ -3 & -2 \end{bmatrix} and T=[0443]T=\begin{bmatrix} 0 & 4 \\ -4 & 3 \end{bmatrix}.

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Problem 350

Prove that 2x46x3+3x2+3x22 x^{4}-6 x^{3}+3 x^{2}+3 x-2 is divisible by x23x+2x^{2}-3 x+2 without division.

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Problem 351

Is the equation 4x1+8x=74x - 1 + 8x = 7 true? Yes or No.

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Problem 352

Show that (4916)1=64343\left(\frac{49}{16}\right)^{-1}=\frac{64}{343} without a calculator, detailing all steps.

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Problem 353

Prove that (4916)32=64343\left(\frac{49}{16}\right)^{-\frac{3}{2}}=\frac{64}{343} without a calculator, showing all steps.

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Problem 354

Use rigid motions to prove that figure ABCA B C is congruent to figure EFGE F G.
Type your response in the space below. B I U Σ\Sigma : 2{ }_{2}{ }^{\equiv}
Type here

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Problem 355

34sin(x+5.793)=34(cos)34 \sin (x+5.793) = 34 \left( \cos \square \right)
Hello there! It seems we have a math problem involving the verification of a trigonometric identity using the sum formula for sine. However, it looks like there is some missing information. Could you provide the result from part (a) or any specific details you have for this problem? This will help me guide you through the solution effectively.
34 \sin(x + 0.493)

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Problem 356

Here is parallelogram ABCDA B C D :
Prove segment AMA M is congruent to segment CMC M. Type your response in the space below.
B II
U Type here

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Problem 357

(k) Prove that bisectors of any two adjacent angles of a parallelogram are at right (ii) Prove that bisectors of any two opposite angles of a parallelogram are parallel. (iii) If the diagonals of a quadrilateral are equal and bisect each other at right angles, then prove that it is a square. (i) If ABCD is a rectangle in which the diagonal BD bisects B\angle \mathrm{B}, then show that ABCDA B C D is a square. (ii) Show that if the diagonals of a quadrilateral are equal and bisect each other a

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Problem 358

a) Show that the prime factor decomposition of 324 , when written in index form, is 22×342^{2} \times 3^{4}. b) Use your answer to part a) to work out the square root of 324 . Give your answer as an integer.

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Problem 359

The straight line 2x+y=142 x+y=14 intersects the curve 2x2y2=2xy62 x^{2}-y^{2}=2 x y-6 at the points AA and BB. Show that the length of ABA B is 24524 \sqrt{5} units.

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Problem 360

Statement Rule (csc2x1)sec2x\left(\csc ^{2} x-1\right) \sec ^{2} x =cot2xsec2x=\cot ^{2} x \sec ^{2} x
Rule? =(cos2xsin2x)sec2x=\left(\frac{\cos ^{2} x}{\sin ^{2} x}\right) \sec ^{2} x Rule? =(cos2xsin2x)(1cos2x)=\left(\frac{\cos ^{2} x}{\sin ^{2} x}\right)\left(\frac{1}{\cos ^{2} x}\right) Rule? =1sin2x=\frac{1}{\sin ^{2} x} Rule? =csc2x=\csc ^{2} x Rule?

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Problem 361

p)
4. Fie xx şi yy două numere reale, astfel încât x(3;7)x \in(-3 ; 7) şi y(4;5)y \in(-4 ; 5). Arătaţi că numărul a=(2xy+11)2+(x2y15)2x+y+7a=\sqrt{(2 x-y+11)^{2}}+\sqrt{(x-2 y-15)^{2}}-|x+y+7| este natural.

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Problem 362

Drag the blocks to complete the proofs.
Statements 1) 2) 18\angle 1 \cong \angle 8 3) 4) 816\angle 8 \cong \angle 16 5)
Reasons 1) given 2) 3) given 4) 5) Transitive prop. \cong
Linked slide Corresponding Angles <1<16<1 \triangleq<16 a|lb clld
Alt Ext Angles

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Problem 363

Given EBCECB,AEDE\angle E B C \cong \angle E C B, \overline{A E} \cong \overline{D E} Prove ABDC\overline{A B} \cong \overline{D C}
Statements
1. EBC=ECB\angle E B C=\angle E C B
2. AE=DEA E=D E
3. EB=ECE B=E C
4. AEB=DEC\angle A E B=\angle D E C
5. ABE : DCE\triangle D C E
6. AB=DCA B=D C

Reasons
1. \square Click to add text
2. \square Click to add text Click to add text \square 3. \square 4. 5.

Click to add text \square
6. \square

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Problem 364

Time left 0:06:46 Hide
By using proof by induction specify the firbe arrec sieps iv prove that P(n)P(n) is true such that P(n)P(n) is: 8+16+24++8n=8n(n+1)28+16+24+\cdots+8 n=\frac{8 n(n+1)}{2} is true for all positive integers (n1)(n \geq 1)

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Problem 365

C=323;B=1+23;A=8+27827C=3-2 \sqrt{3} ; B=\sqrt{1+2 \sqrt{3}} ; A=\sqrt{8+2 \sqrt{7}}-\sqrt{8-2 \sqrt{7}} 5 A B C 2 B,AB, A A AA

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Problem 366

(1.24) Show that A,B\boldsymbol{A}, \boldsymbol{B}, and C\boldsymbol{C} are linearly dependent if AB×C=0\boldsymbol{A} \cdot \boldsymbol{B} \times \boldsymbol{C}=0.

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Problem 367

Given the function ff and point a below, complete parts (a)-(c). f(x)=76x,a=16f(x)=7-6 x, a=\frac{1}{6}
1 (x) - 6 b. Graph f(x)f(x) and f1(x)f^{-1}(x) together. Choose the correct graph below. A. B. C. D. c. Evaluate dfdx\frac{d f}{d x} at x=ax=a and df1dx\frac{d f^{-1}}{d x} at x=f(a)x=f(a) to show that df1dxx=f(a)=1(df/dx)x=a\left.\frac{d f^{-1}}{d x}\right|_{x=f(a)}=\frac{1}{\left.(d f / d x)\right|_{x=a}} dfdxx=16=\left.\frac{d f}{d x}\right|_{x=\frac{1}{6}}= \square df1dxx=f(16)=\left.\frac{d f^{-1}}{d x}\right|_{x=f\left(\frac{1}{6}\right)}= \square (Simplify your answers. Use integers or fractions for any numbers in the expressions.)

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Problem 368

4. Given f(x)=exf(x)=e^{x} and g(x)=x3g(x)=|x-3|. (a) Show that (fg)(x)={ex3,x3e(x3),x<3(f \circ g)(x)=\left\{\begin{array}{ll}e^{x-3}, & x \geq 3 \\ e^{-(x-3)}, & x<3\end{array}\right.. (b) Determine (fg)1(x)(f \circ g)^{-1}(x), for x3x \geq 3. [3 marks] [4 marks] (c) Find the function h(x)h(x) for x>13x>\frac{1}{3}, given that (hf)(x)=2ex13ex(h \circ f)(x)=\frac{2 e^{x}}{1-3 e^{x}}. Hence, show that h(x)h(x) is a one to one function.

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Problem 369

Verifica se le funzioni y=1+x24x2y=\frac{1+x^{2}}{4-x^{2}} e y=x223x4y=\frac{x^{2}-2}{3 x^{4}} sono pari.

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Problem 370

Suppose f(x)=x3+4,x[0,1]f(x)=x^{3}+4, x \in[0,1]. (a) Find the slope of the secant line connecting the points (x,y)=(0,4)(x, y)=(0,4) and (1,5)(1,5). (b) Find a number c(0,1)c \in(0,1) such that f(c)f^{\prime}(c) is equal to the slope of the secant line you computed in (a), and explain why such a number must exist in ( 0,1 ).

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Problem 371

(1.72) Show that (AB×r)=A×B\nabla(A \cdot B \times r)=A \times B where rr is the position vector, AA and BB are constant vectors.

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Problem 372

(a) Verify that for all n1n \geq 1, 261014(4n2)=(2n)!n!2 \cdot 6 \cdot 10 \cdot 14 \cdots \cdots(4 n-2)=\frac{(2 n)!}{n!} (b) Use part (a) to obtain the inequality 2n(n!)2(2n)2^{n}(n!)^{2} \leq(2 n) ! for all n1n \geq 1.

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Problem 373

If AA is a 3×33 \times 3 matrix such that det(A)=3\operatorname{det}(A)=3 then det(A2)=6\operatorname{det}\left(A^{2}\right)=6.
Select one: True False

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Problem 374

Focus 1 Explain why vertically opposite angles are equal.

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Problem 375

{1x+2y=24x5y=47\left\{\begin{array}{l} -1 x+2 y=-2 \\ -4 x-5 y=-47 \end{array}\right.
True or False: The point (8,3)(8,3) is a solution of the system. True False

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Problem 376

8-2: MathXL for School: Practice and Problem-soiving ( Part 3 of 4
How can you derive the Law of Cosines for obtuse angle Q? x2+h2=p2x^{2}+h^{2}=p^{2}
Use the Pythagorean Theorem to write an equation for q2q^{2} in terms of r,xr, x, and hh. q2=\mathrm{q}^{2}=\square Video Textbook Get more help - Question 14 of 26 Back Next

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Problem 377

2. In this problem we outline a proof of Theorem 7.4 .3 in the case n=2n=2. Let x(1)\mathbf{x}^{(1)} and x(2)\mathbf{x}^{(2)} be solutions of Eq. (3) for α<t<β\alpha<t<\beta, and let WW be the WW ronskian of x(1)x^{(1)} and x(2)x^{(2)}. (a) Show that dWdt=dx1(1)dtdx1(2)dtx2(1)x2(2)+x1(1)x1(2)dx2(1)dtdx2(2)dt\frac{d W}{d t}=\left|\begin{array}{cc} \frac{d x_{1}^{(1)}}{d t} & \frac{d x_{1}^{(2)}}{d t} \\ x_{2}^{(1)} & x_{2}^{(2)} \end{array}\right|+\left|\begin{array}{cc} x_{1}^{(1)} & x_{1}^{(2)} \\ \frac{d x_{2}^{(1)}}{d t} & \frac{d x_{2}^{(2)}}{d t} \end{array}\right| (b) Using Eq. (3), show that dWdt=(p11+p22)W\frac{d W}{d t}=\left(p_{11}+p_{22}\right) W (c) Find W(t)W(t) by solving the differential equation obtained in part (b). Use this expression to obtain the conclusion stated in Theorem 7.4.3.

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Problem 378

12) 11+sinθ+11sinθ=2sec2θ\frac{1}{1+\sin \theta}+\frac{1}{1-\sin \theta}=2 \sec ^{2} \theta

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Problem 379

If the distance between two points is zero, then the points are the same. True False

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Problem 380

Points P,Q,RP, Q, R and SS have position vectors p=(63),q=(35),r=(13)\mathbf{p}=\binom{6}{3}, \mathbf{q}=\binom{-3}{-5}, \mathbf{r}=\binom{1}{-3} and s=(105)\mathbf{s}=\binom{10}{5} Prove that the quadrilateral PQRSP Q R S is a parallelogram.

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Problem 381

Show that the ratio 5:6 is equivalent to the ratio 35:42.

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Problem 382

Prove that 350\frac{3}{50} equals 0.06 using long division.

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Problem 383

Show that 725\frac{7}{25} equals 0.28 using long division.

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Problem 384

Prove that if 16r5=38-\frac{1}{6} r - 5 = 38, then r=258r = -258 using a two-column format.

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Problem 385

A True f(x)y(x)+f(x)g(x)dx=F(x)y(x)+C B, Falst \begin{array}{l}\int_{\text {A True }} f(x) y^{\prime}(x)+f^{\prime}(x) g(x) d x=F^{\prime}(x) y^{\prime}(x)+C \\ \text { B, Falst }\end{array}

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Problem 386

ln(e7)=7\ln \left(e^{-7}\right)=-7 A1A_{1} True B. False

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Problem 387

Exercice6: 1) justifier sans calculer que 804 et 204 ne sont pas premierentre cus. 3) Calculer PCCD (804,204)(804,204) 4) Simplifier la fraction 204804\frac{204}{804} pour la rendre irréductible.

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Problem 388

athematics/P2 13 FET - Grade 11 MDE Novembe In the diagram, PQ is a tangent at Q. PRS is a secant od circle RSTWQ. RW cuts S QT at L. PS || QT and RS = TW. R 3 2 ove that: .2.1 KQ is a tangent to circle LQW. 2.2 PRQ=RIQ 2.3 2.4 2.5 RÎQ=KOP PRKQ is a cyclic quadrilateral. RSLQ is not a cyclic quadrilateral. 4 S 2 1 K 2 W GRAND TOTA

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Problem 389

На ребрах SM,SNS M, S N и SPS P тетраэдра SMNPS M N P отмечены точки K,LK, L и RR так, что SK:KM=SL:LN=SR:RPS K: K M=S L: L N=S R: R P. а) Докажите, что плоскости KLRK L R и MNPM N P параллельны. 6) Найдите площадь треугольника KLRK L R, если площадь треугольника MNPM N P равна 27 cm227 \mathrm{~cm}^{2} и SR:RP=2:1S R: R P=2: 1.

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Problem 390

3. Given m(x)=ln(4x+12)m(x)=\ln (4 x+12) and n(x)=ex43n(x)=\frac{e^{x}}{4}-3
Without finding the inverse, show that m(x)m(x) and n(x)n(x) are inverse of each other. [7 Marks]

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Problem 391

(b) Given the parametric equation x=t2tx=t-\frac{2}{t} and y=t+2ty=t+\frac{2}{t} where t0t \neq 0. (i) show that dydx=14t2+2\frac{d y}{d x}=1-\frac{4}{t^{2}+2} (ii) Find d2ydx2\frac{d^{2} y}{d x^{2}} when t=1t=1

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Problem 392

\log x + \log y = \log(xy)

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Problem 393

DELBAC\triangle D E L \cong \triangle B A C by the ASA congruence theorem None of these DLEBAC\triangle D L E \cong \triangle B A C by the ASA congruence theorem DELBAC\triangle D E L \cong \triangle B A C by the HL congruence theorem Submit Collect Go Just play cool Gold You will h Parents Feedback Questions? About Careers Terms of Service PRIVACY POUCY Contact Us playing th

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Problem 394

Complete the sentence.
The lines 2x+4y=322 x+4 y=32 and y=12x+16y=-\frac{1}{2} x+16 are perpendicular

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Problem 395

NAME \qquad DATE \qquad PERIOD \qquad
Determine whether each equation is an identity.
5. (x+3)2(x3+3x2+3x+1)=(x2+6x+9)(x+1)3(x+3)^{2}\left(x^{3}+3 x^{2}+3 x+1\right)=\left(x^{2}+6 x+9\right)(x+1)^{3} (x+3)(x+3)\left.(x+3)^{(x+3}\right) (x2+3x+3x+9)\left(x^{2}+3 x+3 x+9\right)

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Problem 396

Exercice n5\mathrm{n}^{\circ} 5 ( 5 pts ). (Relations binaires). Les questions suivantes sont indépendantes 1) On définit sur R2\mathbb{R}^{2} la relation \ll par: (x,y)(x,y)xxyy(x, y) \ll\left(x^{\prime}, y^{\prime}\right) \Leftrightarrow\left|x^{\prime}-x\right| \leq y^{\prime}-y. Vérifier qu'il s'agit d'ume relation d'ordre. Cet ordre est-il total ? 2) On définit sur R2\mathbb{R}^{2} la relation S\mathcal{S} par: (x,y)S(x,y)x5y=x5y(x, y) \mathcal{S}\left(x^{\prime}, y\right) \Leftrightarrow x-5 y^{\prime}=x^{\prime}-5 y a) Montrer que S\mathcal{S} est une relation d'équivalence. b) Vérifier que la classe d'équivalence du couple (0,0)(0,0) est une droite D\mathcal{D} à préciser.

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Problem 397

2. Δ\Delta ivovta ol σuvαρtησεıς\sigma u v \alpha \rho t \eta ่ \sigma \varepsilon ı \varsigma φ(x)=2x2,f(x)=2x2+8x+11καg(x)=2x28x11\varphi(x)=2 x^{2}, f(x)=2 x^{2}+8 x+11 \kappa \alpha \prime g(x)=-2 x^{2}-8 x-11 II. NaN a סıкаюдоү III. NαδεiξτεN \alpha \delta \varepsilon i \xi \tau \varepsilon ó τf(x)=2(x+2)2+3,xR\tau \mathrm{f}(\mathrm{x})=2(\mathrm{x}+2)^{2}+3, \mathrm{x} \in \mathbb{R}. (Mová δ\delta ec 1+2+2+2+2+1)

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Problem 398

Pro = A(1,4) C Statements 1 AB BC 18-1-4 Reasons applicazion of the stopa Semula
3. draw the vortical line segment. AC 4/ABCzangrange
5. AABCs aright bange datinizon of perpendicula datiniton of a night age 6.BA = V1+ TİQJJ he deance simua 7 (v1+d²) + (√²²+1)-(de) Pagam

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Problem 399

Exercice 5 Démontrer que les énégalités suivantes, valables pour tout x0,sinh(x)x0,cosh(x)1+x22x \geq 0, \sin h(x)-x \geq 0, \cos h(x) \geq 1+\frac{x^{2}}{2}
1

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Problem 400

Listen
Decide whether there is enough information to prove that WXZYZX\triangle W X Z \simeq \triangle Y Z X using the SAS Congruence Theorem. Explain your reasoning, yes; Because ZWXY,WY\overline{Z W} \simeq \overline{X Y}, \angle W \simeq \angle Y, and WXYZ\overline{W X} \simeq \overline{Y Z}, the two triangles are congruent by the SAS Congruence Theorem. yes; Because ZWXY,WY\overline{Z W} \simeq \overline{X Y}, \angle W \simeq \angle Y, and ZXXZ\overline{Z X} \simeq \overline{X Z}, the two triangles are congruent by the SAS Congruence Theorem. no; There is one pair of congruent sides and one pair of congruent angles, but there is no other pair of congruent sides. no; There are two pairs of congruent sides and one pair of congruent angles, but the angles are not the included angles.

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