Rational

Problem 101

Question Watch Video
Express as a fraction in simplest form with a rational denominator: 97+14\frac{-9}{7+\sqrt{14}}
Answer Attempt 1 out of 2 \square Submit Answer

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Problem 102

Question Watch Video
Express as a fraction in simplest form with a rational denominator: 7715\frac{-7}{-7-\sqrt{15}}
Answer Attempt 1 out of 2 \square Submit Answer

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Problem 103

Question Watch Vided
Express the product (35)(3+5)(\sqrt{3}-5)(\sqrt{3}+5) in simplest form.
Answer Attempt 1 out of 2 \square Submit Answer \sqrt{ }

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Problem 104

Question Watcl
Express as a fraction in simplest form with a rational denominator: 15+6\frac{1}{5+\sqrt{6}}
Answer Attempt 1 out of 2 \square Submit A

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Problem 105

Question Wexth Vides Srow Elample
Express as a fraction in simplest form with a rational denominator: 71017\frac{7}{-10-\sqrt{17}}
Answer Amametrant ofiz \square Siltritalus

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Problem 106

Find the domain of the rational function. f(x)=x216x27x+10f(x)=\frac{x^{2}-16}{x^{2}-7 x+10}
The domain of the function is all real numbers except x=x= \square (separate answers with commas, if necessary)

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Problem 107

Question Watch Video
Express as a fraction in simplest form with a rational denominator: 176\frac{1}{-7-\sqrt{6}}
Answer Attempt 1 out of 2 \square Submit Answer

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Problem 108

62v22+32v\frac{6}{2 v^{2}-2}+\frac{3}{2 v}

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Problem 109

Find the xx - and yy-intercepts for the function. f(x)=923x24x264f(x)=\frac{92-3 x^{2}}{4 x^{2}-64}
The xx-intercept(s) is (are) \square The yy-intercept is \square (Enter ordered pairs for each, separated by commas if necessary If no such intercept exists, enter DNE.)

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Problem 110

385\frac{3}{-8-\sqrt{5}}

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Problem 111

Find the slant asymptote of the function. f(x)=12x3+4x29x84x23f(x)=\frac{12 x^{3}+4 x^{2}-9 x-8}{4 x^{2}-3}
The slant asymptote is at y=y= \square

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Problem 112

Find the xx-intercepts, the yy-intercept, the vertical asymptotes, and the horizontal or slant asymptot of the function. Use that information to sketch a graph. Separate answers by commas, if necessary a(x)=x23x+2x21a(x)=\frac{x^{2}-3 x+2}{x^{2}-1}
The function has xx-intercept(s) at \square and yy-intercept at \square (Enter an ordered pair or a list of ordered pairs for each answer.)
The function has vertical asymptote(s) at x=x= \square The function has a Select an answer ^\hat{\approx} asymptote at y=y= \square

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Problem 113

Make yy the subject of the formula c=w4ay3c=w-4 a y^{3}

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Problem 114

Find the xx - and yy-intercepts of the rational function. (If an answer does not exist, enter DNE.) r(x)=x5x+6x-intercept (x,y)=()y-intercept (x,y)=()\begin{array}{c} r(x)=\frac{x-5}{x+6} \\ x \text {-intercept } \quad(x, y)=(\square) \\ y \text {-intercept } \quad(x, y)=(\square) \end{array} Need Help? Read It Watch It Master It Submit Answer
5. [-/3 Points]

DETAILS MY NOTES
SPRECALC7 3.6.023.MI.
Find the xx - and yy-intercepts of the rational function. (If an answer does not exist, enter DNE.) t(x)=x22x24x9x-intercept (x,y)=() (smaller x-value) x-intercept (x,y)=()y-intercept (x,y)=()\begin{array}{ll} \qquad t(x)= & \frac{x^{2}-2 x-24}{x-9} \\ x \text {-intercept } & (x, y)=(\square) \quad \text { (smaller } x \text {-value) } \\ x \text {-intercept } & (x, y)=(\square) \\ y \text {-intercept } & (x, y)=(\square) \end{array}

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Problem 115

Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE.) s(x)=4x2+12x2+9x5s(x)=\frac{4 x^{2}+1}{2 x^{2}+9 x-5} vertical asymptote x=x= \square (smaller value) vertical asymptote x=x= \square (larger value) horizontal asymptote \square

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Problem 116

5) /9(4v9)+2v/ 9(4 v-9)+2 v

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Problem 117

Simplify. Express your answer as a single fraction in simplest form. 4t4+85+5\frac{4}{t^{4}}+85+5

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Problem 118

Question 12
Simplify 11xx210x+25+9x5\frac{11 x}{x^{2}-10 x+25}+\frac{9}{x-5} State the sum in simplest form. \square Calculator

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Problem 119

3. 7{3+12÷3518}2+107-\{3+12 \div 3 \cdot 5-18\}^{2}+10

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Problem 120

Solve the proportion. 3x4=65\frac{3 x}{4}=\frac{6}{5} x=x= \square (Type an integer or a simplified fraction.)

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Problem 121

1 Peaches cost $6\$ 6 for a 3 pound bag. If peaches cost less per pound than apples but more per pound than oranges, which of the following could be the price per pound of apples and oranges?
4 apples are $2.21\$ 2.21 per pound and oranges are $1.71\$ 1.71 per pound 4 apples are $2.00\$ 2.00 per pound and oranges are $1.71\$ 1.71 per pound 4 apples are $1.71\$ 1.71 per pound and oranges are $2.21\$ 2.21 per pound 4 apples are $2.21\$ 2.21 per pound and oranges are $2.43\$ 2.43 per pound

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Problem 122

Graph all vertical and horizontal asymptotes of the rational function. f(x)=3x+2x2+4f(x)=\frac{3 x+2}{x^{2}+4} Explanation Check

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Problem 123

Graph all vertical and horkzum f(x)=x23x4x22x+1f(x)=\frac{x^{2}-3 x-4}{x^{2}-2 x+1} Explanation Check

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Problem 124

Rationalize the denominator. 627627=\begin{array}{c} \frac{6}{2-\sqrt{7}} \\ \frac{6}{2-\sqrt{7}}= \end{array} \square (Simplify your answer. Type an exact answer, using radicals as needed.)

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Problem 125

6x27x53x2+x10\frac{6x^{2} - 7x - 5}{3x^{2} + x - 10}

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Problem 126

y=2x+1x+2 y = \frac{2x + 1}{x + 2}
What are the restrictions?

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Problem 127

Find all excluded values for the expression. That is, find all values of ww for which the expression is undefined. w2+7w+10w2+4w+4\frac{w^{2}+7 w+10}{w^{2}+4 w+4}
If there is more than one value, separate them with commas.

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Problem 128

Write the partial fraction decomposition of the rational expression. x(x+5)(x+3)x(x+5)(x+3)=\begin{array}{l} \frac{x}{(x+5)(x+3)} \\ \frac{x}{(x+5)(x+3)}= \end{array} \square (Use integers or fractions for any numbers in the expression.)

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Problem 129

For which values of x is the expression undefined? x2166x6\frac{x^{2}-16}{6 x-6}
Answer (†) Additional Solution No Solution x=x= \square Submit Answer

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Problem 130

c0.2+0.9=3.9\frac{c}{0.2}+0.9=3.9

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Problem 131

38d+34\frac{3}{8}d + \frac{3}{4}

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Problem 132

Find all vertical asymptotes of the following function. f(x)=25x26415x+24f(x)=\frac{25 x^{2}-64}{15 x+24}

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Problem 133

f(x)=3x+3x2+9f(x)=\frac{-3 x+3}{x^{2}+9}

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Problem 134

1. Determine the xx-intercepts of each function. a) f(x)=3x2x+5f(x)=\frac{-3 x}{2 x+5}

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Problem 135

For the real-valued functions f(x)=x6x+5f(x)=\frac{x-6}{x+5} and g(x)=2x11g(x)=2 x-11, (fg)(x)=(f \circ g)(x)=
Domain of fgf \circ g :

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Problem 136

2. Solve algebraically. Check each solution. a) x310=4x\frac{x-3}{10}=4 x b) 3x2=5x\frac{3}{x}-2=\frac{5}{x} c) 3x+21x=15x\frac{3}{x+2}-\frac{1}{x}=\frac{1}{5 x}

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Problem 137

3-2:Multiply Rational Numbers
Part 1 of 2
Suppose there is a 1.2F1.2^{\circ} \mathrm{F} drop in temperature for every thousand feet that an airplane climbs into the sky. The temperature on the a. Write a multiplication equation to represent the change in temperature after the plane ascends 10,000ft10,000 \mathrm{ft}. b. What will be the temperature when the plane reaches an altitude of 10,000ft10,000 \mathrm{ft} ? a. The change in temperature would be| (Type an integer or a decimal.) \square == \square F{ }^{\circ} \mathrm{F}.

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Problem 138

Solve the following equation for vv. F=aMv2rF=\frac{a M v^{2}}{r}

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Problem 139

Question 23 (1 point) Solve 8x24=4x+2\frac{8}{x^{2}-4}=\frac{4}{x+2} for xx

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Problem 140

Question 7 (1 point) Find the solution set for x2x+3<9x+3\frac{x^{2}}{x+3}<\frac{9}{x+3}.

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Problem 141

f(x)=x2+9x+20x+4f(x)=\frac{x^{2}+9 x+20}{x+4}
Answer Attempt 1 out of 2
Horizontal Asymptote: y=y= \square
No horizontal asymptote Vertical Asymptote: x=x= \square
No vertical asymptote x-Intercept: (,0)x \text {-Intercept: }(\square, 0)
No xx-intercept yy-Intercept: 0\quad 0, \square ) No yy-intercept

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Problem 142

All work must be clearly shown to get full credit. No clear work, no credit
1. For the following rational equation, a) Are there any holes? If so, what are they b) Find the Vertical, Horizontal and Oblique; Infinite Asymptotes if any. c) Find the roots; x-intercept(s) d) Find the yy-intercept(s) e) Find the Domain and Range f) Find the end behavior g) Sketch a graph i) f(x)=x3+7x2+10xx2+5x6f(x)=\frac{-x^{3}+7 x^{2}+10 x}{x^{2}+5 x-6} a) \qquad b) \qquad

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Problem 143

1) f(x)=x2+9x+18x2+2x24f(x)=\frac{x^{2}+9 x+18}{x^{2}+2 x-24} (x+6)(x+3)(x+6)(x4)\frac{(x+6)(x+3)}{(x+6)(x-4)} x+6=0(6+3)x=6(64)x10\begin{array}{cc} x+6=0 & (-6+3) \\ x=-6 & (-6-4) \\ x & -10 \end{array} vertical Horizontal x4=0x=1x=4x\begin{array}{ll} x-4=0 & x^{\prime}=1 \\ x=4 & x^{\prime} \end{array}

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Problem 144

olve for all values of x. x2x8=7x-\frac{2}{x-8}=7
Answer Attempt 1 out of 3

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Problem 145

№5. Сократить дробь: 1) 3362;\frac{3-\sqrt{3}}{\sqrt{6}-\sqrt{2}} ; \quad 2) a255+a\frac{a-25}{5+\sqrt{a}}. №6. Найти значение выражения: 423+14231\frac{4}{2 \sqrt{3}+1}-\frac{4}{2 \sqrt{3}-1}.

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Problem 146

№5. Сократить дробь: 1) 3362;\frac{3-\sqrt{3}}{\sqrt{6}-\sqrt{2}} ; \quad 2) a255+a\frac{a-25}{5+\sqrt{a}}.

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Problem 147

Ex : Donner ie domaine de dstration de fonctions suivantes: 1) f(x)=x2+51+y5f(x)=\frac{x^{2}+5}{1+y^{5}} S) (x)=31+8(x)=\frac{3}{1+8} 5) r(x)=log(x2+2x+2)x2+3x6)r(x)=\log \left(\frac{\left.x^{2}+2 x+2\right)}{x^{2}+3 x-6}\right)

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Problem 148

2yxx22y=\frac{2 \sqrt{y} x}{\frac{x^{2}}{2 \sqrt{y}}}=

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Problem 149

- 9 مبا c+iwrrwww1c+i w \frac{r}{r}-w \frac{w}{w}-1

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Problem 150

4c7c+2c2\frac{\frac{4}{c}}{\frac{7}{c}+\frac{2}{c^{2}}}

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Problem 151

7x314x\frac{7 x^{3}}{14 x}

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Problem 152

Subtract 3x14x+3\frac{3}{x-1}-\frac{4}{x+3}. A. x+13(x1)(x+3);x3\frac{-x+13}{(x-1)(x+3)} \quad ; x \neq-3 or 1

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Problem 153

Rewrite the expression in terms of the given function. 11cosxcosx1+cosx;cotx\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x} ; \cot x

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Problem 154

x2+5x+4x26x7\frac{x^{2}+5 x+4}{x^{2}-6 x-7}

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Problem 155

x2+19x+90x2+12x+20\frac{x^{2}+19 x+90}{x^{2}+12 x+20}

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Problem 156

Step 1 need to divide. However, we note that the denominator can be factored as follows. Q(x)=6x2+7x+1=(6x+1)()\begin{aligned} Q(x) & =6 x^{2}+7 x+1 \\ & =(6 x+1)(\square) \end{aligned} Submit Skip (you cannot come back)

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Problem 157

Find L1{1s2+12s+36}L^{-1}\left\{\frac{1}{s^{2}+12 s+36}\right\}

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Problem 158

2. The following exercise has the incorrect answer. Circle the mistake(s). There may be more than one error in calculations. ×\times Clear Undo \rightarrow Redo x/(1/5)=3/4x /(1 / 5)=3 / 4 x=3451x=\frac{3}{4} \cdot \frac{5}{1} x=154x=\frac{15}{4}
Explain the mistake(s) and give the correct solution with calculations.
B I U 宣 x\sqrt{x} \square\square

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Problem 159

3. Which of the following functions has a horizontal asymptote of y=0y=0.
1. f(x)=4x+52x21f(x)=\frac{4 x+5}{2 x^{2}-1} J. g(x)=2x2+5x22g(x)=\frac{2 x^{2}+5}{x^{2}-2} K. h(x)=2x3+5x22h(x)=\frac{2 x^{3}+5}{x^{2}-2} L. m(x)=3x2+8x34m(x)=\frac{3 x^{2}+8}{x^{3}-4}

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Problem 160

2. Rewrite g(x)=5x318x3+4g(x)=\frac{-5 x^{3}-18}{x^{3}+4} in the form g(x)=q(x)+rb(x)g(x)=q(x)+\frac{r}{b(x)}.

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Problem 161

1. Simplify the complex rational expression: 1x11x1x2x\frac{\frac{1}{x-1}-\frac{1}{x}}{\frac{1}{x^{2}-x}} A. 1 B. 2x1\frac{2}{x-1} C. xx1\frac{x}{x-1} D. xx2x-x^{2} E. None of the above

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Problem 162

Solve the inequality. Answer should be in interval notation: x+8x+21\frac{x+8}{x+2} \geq-1 Interval notation solution: \square No solution Question Help: Video 1 Video 2 Written Example 1 Submit Question

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Problem 163

3. A bike store sells scooters at a 54%54 \% markup. If the store sells each scooter for \69.30,thenwhatistheirnonmarkupprice?(A)69.30, then what is their non-markup price? (A) \25.00 25.00 (C) $45.00\$ 45.00 (B) $35.00\$ 35.00 (D) $55.00\$ 55.00

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Problem 164

14. 928+3x+2=34\frac{9}{28}+\frac{3}{x+2}=\frac{3}{4}

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Problem 165

4. 11c5811 \frac{c}{-5}-8

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Problem 166

Answer the questions about the following function. f(x)=x+12x8f(x)=\frac{x+12}{x-8} (a) Is the point (3,9)(3,-9) on the graph of ff ? (b) If x=4x=4, what is f(x)f(x) ? What point is on the graph of ff ? (c) If f(x)=2f(x)=2, what is xx ? What point(s) is (are) on the graph of ff ? (d) What is the domain of ff ? (e) List the x -intercepts, if any, of the graph of f . (f) List the yy-intercept, if there is one, of the graph of f . (a) Choose the correct answer below. A. Yes, because substituting x=3x=3 into the given equation results in -9 . B. No, because substituting x=9x=-9 into the givenequation does not result in 3 . C. No, because substituting x=3x=3 into the given equation does not result in -9 . D. Yes, because substituting x=9x=-9 into the given equation results in 3 .

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Problem 167

2. a. x3+x8x2+37x+4=x212x+49159x+4\frac{x^{3}+x-8 x^{2}+37}{x+4}=x^{2}-12 x+49-\frac{159}{x+4} b. 10x39x28x+115x2=2x2x2+75x2\frac{10 x^{3}-9 x^{2}-8 x+11}{5 x-2}=2 x^{2}-x-2+\frac{7}{5 x-2} c. 3x+2x3x2=x22x1\frac{3 x+2-x^{3}}{x-2}=-x^{2}-2 x-1 d. x42x2+12x4=x3+4x2+14x+56+236x4\frac{x^{4}-2 x^{2}+12}{x-4}=x^{3}+4 x^{2}+14 x+56+\frac{236}{x-4} e. x52x47x3+13x2+2x18x22x3=x34x+53x22x3\frac{x^{5}-2 x^{4}-7 x^{3}+13 x^{2}+2 x-18}{x^{2}-2 x-3}=x^{3}-4 x+5-\frac{3}{x^{2}-2 x-3}

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Problem 168

Simplify completely: 2+10m125m2\frac{2+\frac{10}{m}}{1-\frac{25}{m^{2}}}
Enter the numerator and denominator separately in the boxes below. If the denominator is 1 , enter the number 1. Do not leave either box blank. Make sure that the coefficient on the variable is positive. Answer: \square \square Numerator preview:

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Problem 169

1. Rewrite as the first rational expression [A] by the reciprocal of the second.
2. [B][B] the numerators and denominators.
3. Multiply the numerators.
4. Multiply the denominators.
5. Simplify.

Choose the words for [A][A] and [B][B] that correctly complete the steps. [A] : multiplied [B][B] : Factor [A] : multiply [B] : Look at [A] : divided [B] : Factor [A] : divided [B] : Look at

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Problem 170

Follow the steps for graphing a rational function to graph the function R(x)=x+3x(x+7)R(x)=\frac{x+3}{x(x+7)}
If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of R(x)\mathrm{R}(\mathrm{x}). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. R(x)=R(x)= \square (Type your answer in factored form. Do not simplify.) B. R(x) cannot be factored further
What is the domain of R(x)R(x) ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. {xx0,7}\{x \mid x \neq 0,-7\} \square (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. {xx<\{x \mid x< \square \} (Type an integer or a simplified fraction.) C. {xx\{x \mid x \geq \square \} (Type an integer or a simplified fraction.) D. The domain is the set of all real numbers.
Write R(x)\mathrm{R}(\mathrm{x}) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. R(x)=R(x)= \square (Simplify your answer.) B. R(x)R(x) is already in lowest terms.

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Problem 171

A turtle travels 512\frac{5}{12} mile in 13\frac{1}{3} hour and a snail travels 18\frac{1}{8} mile in 34\frac{3}{4} hour. Which animal is faster? The turtle's rate is greater than 1 mile per hour.
The snail's rate is less than 1 mile per hour.
Find the turtle's speed in miles per hour.
The turtle's speed is mile(s) per hour.

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Problem 172

b+3e=f2\frac{b+3}{e} = \frac{f}{2} solve for ee

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Problem 173

yc=53y+23\frac{y}{c}=\frac{-5}{3 y+23}

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Problem 174

20. 2x+13x+1x13x+1\frac{2 x+1}{3 x+1} \leq \frac{x-1}{3 x+1}

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Problem 175

11 \leftarrow Suppose a is to b as c is to d ; that is, ab=cd\frac{a}{b}=\frac{c}{d}. Complete parts a through dd below. (a) Beginning with ab=cd\frac{a}{b}=\frac{c}{d}, show that bb is to aa as dd is to cc. What is the first step? A. Cross multiply. B. Add ba\frac{b}{a} to the left side and dc\frac{d}{c} to the right side. C. Subtract bb from the left side and dd from the right side. D. Subtract ba\frac{b}{a} from the left side and dc\frac{d}{c} from the right side.

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Problem 176

Analyzing Work for Errors
Jason used the commutative property to write an expression that is equivalent to 34+5.6b+9\frac{3}{4}+5.6 b+9. 34+5.6b+9\frac{3}{4}+5.6 b+9 is equivalent to 9.0+56b+3.49.0+56 b+3.4.
Is Jason's work correct? No, Jason changed the terms. Yes, Jason's work is correct. No, Jason forgot the parentheses. No, Jason should not have changed the order of the terms.

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Problem 177

Problem 1. (1 point) Which of the following is the correct form of the partial frachon decomposition of 2x(x+3)(3x+1)?\frac{2 x}{(x+3)(3 x+1)} ? A. Ax+Bx+3+Cx+D3x+1\frac{A x+B}{x+3}+\frac{C x+D}{3 x+1} B. Ax+3+B3x+1\frac{A}{x+3}+\frac{B}{3 x+1} c. Ax+Bx+3+C3x+1\frac{A x+B}{x+3}+\frac{C}{3 x+1} D. Ax+3+Bx+C3x+1\frac{A}{x+3}+\frac{B x+C}{3 x+1}

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Problem 178

9z6÷272z12\frac{9}{z-6} \div \frac{27}{2 z-12}

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Problem 179

Write an equation for a rational function with:
Vertical asymptotes at x=2x=-2 and x=2x=2 xx intercepts at x=3x=3 and x=6x=6 yy intercept at 5 y=y=

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Problem 180

solve proportions." ronfer with an elbow partner \checkmark Review "Math Notes: Proportions (1" Onty)" (Spiral notebook \downarrow Google Classroom) VWatch "Proportions (\#S Oniy)" YouTube videos (Google Classroom) \checkmark Refer to enVisionmath 2.0 Textbook volume 2 (Pages 263-274)
Unit 3 Math Worksheet \#2 Solve for xx. Round answers to the hundredths place, if applicable.
1. 1216=x20\frac{12}{16}=\frac{x}{20}
2. x12=128\frac{x}{12}=\frac{12}{8}

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Problem 181

Question 20
Let f(x)=2x2+7x+33x216x+16f(x)=\frac{2 x^{2}+7 x+3}{3 x^{2}-16 x+16} This function has: 1) A yy intercept at the point \square 2) xx intercepts at the point(s) \square 3) Vertical asymptotes at x=x= \square 4) Horizontal asymptote at y=y= \square Question Help: \square Video 11 \square Video 2 Check Answer

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Problem 182

3) Write an equation for a rational function with vertical asymptotes at x=3x=-3 and x=6,xx=6, x-intercepts at (2,0)(-2,0) and (1,0)(1,0), and a horizontal asymptote at y=2y=-2. Check that your answer is reasonable using Desmos.

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Problem 183

Solve the following rational inequality x7x2640\frac{x-7}{x^{2}-64} \geq 0. State your answer using interval notation. Use U for union and oo for \infty.

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Problem 184

3x+5y27y6x4\frac{\frac{3}{x}+\frac{5}{y^{2}}}{\frac{7}{y}-\frac{6}{x^{4}}}

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Problem 185

Solve the inequality x+8x+1<4\frac{x+8}{x+1}<-4 Give your answer in interval notation.

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Problem 186

Solve the inequality 1x+5>1\frac{1}{x+5}>-1 Give your answer in interval notation.

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Problem 187

5. A lemonade recipe calls for 74\frac{7}{4} tablespoons of powdered lemonade mix for every 12 ounces of water. How many batches can you make with 7 tablespoons of lemonade mix and 48 ounces of water? Explain your reasoning.

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Problem 188

Perform the indicated operation. x+72x2+5x+3+x2x2+3x+1x+72x2+5x+3+x2x2+3x+1=\begin{array}{l} \frac{x+7}{2 x^{2}+5 x+3}+\frac{x}{2 x^{2}+3 x+1} \\ \frac{x+7}{2 x^{2}+5 x+3}+\frac{x}{2 x^{2}+3 x+1}= \end{array} \square (Simplify your answer. Type your answer in factored form.)

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Problem 189

39/45 3=8+2x12-3=\frac{8+2 x}{-12}
Write your answer as a number only! Do not write " x=x= "

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Problem 190

Graph the function. Plot at least 4 points. t(x)=x2+4x5x+2t(x)=\frac{x^{2}+4 x-5}{x+2}

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Problem 191

[-/2 Points] DETAILS MY NOTES MCKTRIG7 5.1.
Multiply the numerator and denominator of the fraction by the conjugat (a) 121+2\frac{1-\sqrt{2}}{1+\sqrt{2}} \square (b) 1sinx1+sinx\frac{1-\sin x}{1+\sin x} \square

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Problem 192

Learning Intention: "I can write and solve proportions."
Need assistancent \checkmark Confer with an elbow parener \checkmark Review "Math Notes: Proportions ("Is On(y)" (Spiral notebook \& Google Classroom) WWatch "Proportions ("Is Oniy)" YouTube videos (Google Classroom) \checkmark Refer to envisionmath 2.0 Textbook volume 2 (Pages 263-274)
Unit 3 Math Worksheet \#2 Solve for xx. Round answers to the hundredths place, if applicable.
1. 1216=x20\frac{12}{16}=\frac{x}{20}
2. x12=128\frac{x}{12}=\frac{12}{8}
3. 1420=21x\frac{14}{20}=\frac{21}{x}
4. 4x=156\frac{4}{x}=\frac{15}{6}
5. 207=3x\frac{20}{7}=\frac{3}{x}
6. x20=1845\frac{x}{20}=\frac{18}{45}
7. 220450=x225\frac{220}{450}=\frac{x}{225}
8. 9x=4036\frac{9}{x}=\frac{40}{36}
9. 355=x2\frac{35}{5}=\frac{x}{2}
10. 50x=12530\frac{50}{x}=\frac{125}{30}

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Problem 193

Learning Intention: "I can write and solve proportions."
Need assistancent \checkmark Confer with an elbow parener \checkmark Review "Math Notes: Proportions ("Is On(y)" (Spiral notebook \& Google Classroom) WWatch "Proportions ("Is Oniy)" YouTube videos (Google Classroom) \checkmark Refer to envisionmath 2.0 Textbook volume 2 (Pages 263-274)
Unit 3 Math Worksheet \#2 Solve for xx. Round answers to the hundredths place, if applicable.
1. 1216=x20\frac{12}{16}=\frac{x}{20}
2. x12=128\frac{x}{12}=\frac{12}{8}
3. 1420=21x\frac{14}{20}=\frac{21}{x}
4. 4x=156\frac{4}{x}=\frac{15}{6}
5. 207=3x\frac{20}{7}=\frac{3}{x}
6. x20=1845\frac{x}{20}=\frac{18}{45}
7. 220450=x225\frac{220}{450}=\frac{x}{225}
8. 9x=4036\frac{9}{x}=\frac{40}{36}
9. 355=x2\frac{35}{5}=\frac{x}{2}
10. 50x=12530\frac{50}{x}=\frac{125}{30}

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Problem 194

2. Graph the function: f(x)=4x2+1x2+x+3f(x)=\frac{-4 x^{2}+1}{x^{2}+x+3}

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Problem 195

Clever | Portal Big Ideas Math:Assessment bigideasmath.com/BIM/student/assignment?studentAssignmentId=cda1057e-bdb8-45d7-80f1-8 몸ㅁㅁㅁㅣ 煰品 Play Kahootl-Enter. 0 Classroom Learn to Type I Type. BIG IDEAS MATH Course 3: CA > Chapter 3: Angles of Polygons > Section Exercises 3.3 > Exercise 36
Solve the proportion. 9x=62\frac{9}{x}=\frac{6}{2} x=18xx=18 x x \qquad \qquad 36

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Problem 196

If f(x)=3x1x2f(x)=\frac{3 x-1}{x-2} then f1(x)=f^{-1}(x)= A) x2x3\frac{x-2}{x-3} B) 2x1x3\frac{2 x-1}{x-3} C) 2x+1x3\frac{2 x+1}{x-3} D) x32x1\frac{x-3}{2 x-1}

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Problem 197

=(112z2[12z2)=\left(1 \frac{1}{2} z^{2}-\left[\frac{1}{2} z^{2}\right)\right.

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Problem 198

The sketch below represents the graphs of f(x)=2x31f(x)=\frac{2}{x-3}-1 and g(x)=dx+eg(x)=d x+e. Point B(3;6)\mathrm{B}(3 ; 6) lies on the graph of gg and the two graphs intersect at A and C . 7.1 Write down the equations of the asymptotes of ff. 7.2 Write down the domain of ff. 7.3 Determine the values of dd and ee, correct to the nearest integer, if the graph of gg makes an angle of 7676^{\circ} with the xx axis. 7.4 Determine the coordinates of A and C . 7.5 For which value(s) of xx is: 7.5.1 f(x)g(x)f(x) \leq g(x) ? 7.5.2 x. f(x)0f(x) \geq 0 ? [20]

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Problem 199

ewrite f(x)=(ax+b)/(x+c)f(x)=(a x+b) /(x+c) in f(x)=a+d/(x+c)f(x)=a+d /(x+c) form. 5) f(x)=x3x4f(x)=\frac{x-3}{x-4}

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Problem 200

Solve the rational inequality. 7) 4x+75x2+6>0\frac{-4 x+7}{5 x^{2}+6}>0

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