Algebra

Problem 23101

Find $c$ using the formula $d=(r-c) t$ for $d=26$ , $r=15$ , and $t=2$ . $c=$

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Problem 23102

Solve the following equations: a. $5x - 6 = 0$ b. $25x^2 - 36 = 0$ c. $25x^2 - 36 = 589$ d. $25x^2 - 36 = 60x - 72$

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Problem 23103

Simplify the polynomial expression: $3(x+5)^{2}-3(x+5)+6$ .

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Problem 23104

A tennis ball hits a wall at $10.0 \mathrm{~m/s}$ and returns at $8.0 \mathrm{~m/s}$ . Find the average acceleration over $0.045 \mathrm{s}$ .

See Solution

Problem 23105

Simplify the polynomial expression: $2(x-4)^{2}+3(x-4)+1$ .

See Solution

Problem 23106

Find $y$ in the equation $6.4(3) + 2.8y = 44.4$ .

See Solution

Problem 23107

Expand $\left(\frac{5}{3} x+4\right)^{2}$ into a trinomial in simplest form.

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Problem 23108

Expand the expression to standard polynomial form: $(x-1)(-x^{2}+x+9)$ .

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Problem 23109

Expand $\left(\frac{5}{3} x-2\right)^{2}$ into a trinomial in simplest form.

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Problem 23110

Solve for $x$ in the equation $x^{4}-13x^{2}+36=0$ and factor it if possible.

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Problem 23111

Factor the expression $x^{4}-12 x^{2}+32$ .

See Solution

Problem 23112

Find the equation of a line parallel to $y=\frac{4}{5} x+2$ that goes through the point $(1,2)$ .

See Solution

Problem 23113

Expand the expression: (2x + 1)(x² - 5x - 7) to standard polynomial form.

See Solution

Problem 23114

Find a two-digit number where the sum of its digits is 13 and adding 27 reverses its digits. Options: (a) 48 (b) 53 (c) 58 (d) 57 (e) None.

See Solution

Problem 23115

Convert the repeating decimal $0.\overline{51}$ into a fraction.

See Solution

Problem 23116

Solve for $x$ using the quadratic formula: $8 x^{2}-8 x-1=0$ . Provide solutions separated by commas. $x=$

See Solution

Problem 23117

Find $w$ in the equation $4 w^{2}+20 w=-25$ . List all solutions or state "No solution."

See Solution

Problem 23118

Find the discriminant and the real solutions for the equation: $-9 x^{2}-6 x-1=0$ .

See Solution

Problem 23119

Find a number to complete the expression as a perfect square: $x^{2}+6x+10$ .

See Solution

Problem 23120

Solve for $w$ : $w^{2}-9w+20=0$ . If multiple solutions, list them; if none, say "No solution."

See Solution

Problem 23121

Find the quadratic equation with roots 5 and -2, and leading coefficient 4. Use Yetter $x$ for the variable.

See Solution

Problem 23122

Plot five points on the parabola $y=-\frac{3}{4} x^{2}$ : the vertex and two points on each side of it.

See Solution

Problem 23123

Graph the solution to the inequality $(x+4)(x-6) \leq 0$ on a number line.

See Solution

Problem 23124

Select the factored form of the expression: $16 x^{2}-8 x+1=$

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Problem 23125

Choose the factored form for each expression: $16 x^{2}-8 x+1$ , $x^{2}-x-30$ , $9 x^{2}-49$ , $3 x^{2}+17 x-6$ .

See Solution

Problem 23126

Determine if the function $f(x)=-2 x^{2}+12 x-20$ has a minimum or maximum, and find its value and location.

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Problem 23127

Evaluate the following functions at $x=3$ : $f(x)=x-3$ , $g(x)=x^{2}-3x+5$ , $h(x)=\sqrt[3]{x^{3}+x+3}$ , $p(x)=\frac{x^{2}+1}{x+4}$ , $f(x)=|x-5|$ . Also, for $f(x)=x+8$ , find $f(4)$ , $f(-2)$ , $f(-x)$ , $f(x+3)$ , and $f\left(x^{2}+x+1\right)$ .

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Problem 23128

Express $v^{\frac{1}{2}}$ as a radical expression.

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Problem 23129

Simplify $9^{\frac{3}{2}}$ .

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Problem 23130

Simplify the expression: $\frac{z^{\frac{1}{3}}}{z^{\frac{1}{4}} z^{-\frac{3}{4}}}$ using only positive exponents.

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Problem 23131

Rewrite $\sqrt[4]{t^{3}}$ as an exponential expression.

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Problem 23132

Simplify the expression: $\frac{z^{-\frac{1}{4}}}{z^{\frac{1}{3}} z^{\frac{1}{2}}}$ using only positive exponents.

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Problem 23133

Simplify and write without exponents:
$\left(\frac{1}{81}\right)^{\frac{3}{4}}=\square$ and $32^{-\frac{3}{5}}=\square$

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Problem 23134

Simplify the expression $y^{-\frac{1}{2}} y^{-\frac{1}{7}} y^{\frac{3}{2}}$ using only positive exponents.

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Problem 23135

Simplify the expression: $\frac{b^{-\frac{1}{2}} b^{\frac{1}{3}}}{b^{\frac{1}{4}}}$ using only positive exponents.

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Problem 23136

Simplify the expression $\left(c^{2} \cdot a^{-\frac{4}{5}}\right)^{\frac{1}{5}}$ without negative exponents.

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Problem 23137

Simplify the expression $\left(z^{-3} \cdot y^{\frac{5}{4}}\right)^{\frac{1}{5}}$ without negative exponents.

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Problem 23138

Simplify: $-5 \sqrt{80} + \sqrt{20}$ .

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Problem 23139

Simplify the expression $\frac{x^{-\frac{1}{3}}}{x^{-\frac{4}{7}}}$ using only positive exponents.

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Problem 23140

Simplify: $4 \sqrt{48} \times \sqrt{98}$ .

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Problem 23141

Simplify: $\sqrt{50}+2 \sqrt{98}$

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Problem 23142

Simplify $\sqrt{18} \times 2 \sqrt{98}$ .

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Problem 23143

Simplify: $\sqrt{54} \times 4 \sqrt{48}$

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Problem 23144

Simplify the expression: $\sqrt{32} \times 2 \sqrt{50}$ .

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Problem 23145

Find the common difference and the 20th term of the sequence: 1, 2, 5, 8, 11, ...; use $a_{20}$ .

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Problem 23146

Esther paints 7 faces in 21 minutes. Find the equation relating $f$ , the number of faces, and $m$ , the time in minutes.

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Problem 23147

Find the equation relating $p$ (hours parked) and $c$ (cost in dollars) if Alexandra paid \$7 for 3 hours.

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Problem 23148

Carlos harvests cassavas at a constant rate. If he takes 35 mins for 15 cassavas, find the equation for $t$ and $c$ .

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Problem 23149

Flannery made 6 identical arrangements with 30 lilies and 78 roses. Find the equation relating $l$ and $r$ .

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Problem 23150

Find the common difference and the 20th term of the sequence: $2, 5, 8, 11, \ldots$

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Problem 23151

Create an equation for $y$ (yellow paint) and $b$ (blue paint) where $y + b = 8$ liters for the Green Goober's paint.

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Problem 23152

Find the GCF of 48 and 30, then express $48 + 30$ as $GCF \cdot (a + b)$ .

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Problem 23153

Решите уравнения: 1) $4-6(x+2)=3-5x$ ; 2) $(3x-20)(4x+28)(0,2-0,06x)=0$ ; 3) $\frac{x+2}{5}-\frac{x+6}{30}=\frac{x+4}{10}+\frac{x-5}{15}$ .

See Solution

Problem 23154

Based on the equation $C=\frac{5}{9}(F-32)$ , which statements about temperature changes are true? A) I only B) II only C) III only D) I and II only

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Problem 23155

If $3x - y = 12$ , find the value of $\frac{8^x}{2^y}$ . A) $2^{12}$ B) $4^{4}$ C) $8^{2}$ D) Cannot determine.

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Problem 23156

Combine the terms in the expression: $-3x + y - y + 7x$ . What is the simplified result?

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Problem 23157

Simplify the expression $x + 5y + 3x$ .

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Problem 23158

Simplify the expression $-2x - 3y + 4x + 5yi$ .

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Problem 23159

Belinda has 400 R5 coins and wants at least 120 left after taking out 56 each week. What inequality models this?
Options: a. $400-56k \leq 120$ b. $400-56k > 120$ c. $400-56k < 120$ d. $400-56k \geq 120$

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Problem 23160

Simplify the expression: $-2 x + (-3 y) - (-4 x) + 5 y$ .

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Problem 23161

Simplify the expression: $-3 x(-2 y - 5 z + 3 z)$ .

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Problem 23162

Emily's semester grade is from 4 quizzes (15% each) and 1 final (40%). Scores: 70, 80, 85, 85. What final score for at least 82?

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Problem 23163

Choose the incorrect statement given $i>0, j>0, k>0$ : a. If $i>j$ then $i+k>j+k$ b. If $i<j$ then $j>i$ c. If $i>j$ then $i \times k>j \times k$ d. If $j<i$ and $i<k$ then $k<j$

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Problem 23164

Solve for $x$ in the equation $2 - \frac{x}{2} + 20 = 0$ .

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Problem 23165

Find $k$ if $k\%$ of 127 equals 32. A) 0.25 B) 0.55 C) 25 D) 55

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Problem 23166

Solve the equation $\frac{x}{2}+20=0$ for $x$ .

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Problem 23167

Solve the equation: $2 x^{2}-10 x=0$ for the variable $x$ .

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Problem 23168

Solve the equation $x^{2}+2x=5x$ .

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Problem 23169

Find $a_{23}$ given $a_{1}=-5$ and $d=4$ .

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Problem 23170

Choose the false statement about binomials: A binomial has two terms. Is $q^{5}+8 q-2$ a binomial? Is $q^{5}+8 q$ a binomial?

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Problem 23171

Find the linear function $f$ such that $f\left(\frac{3}{5}\right)=\frac{1}{2}$ and $f(2)=4$ .

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Problem 23172

What function represents the world's population P (in billions) $t$ years after 1975, given a 1.9% growth rate? A) $P(t)=4(1.019)^{t}$ B) $P(t)=4(1.9)^{t}$ C) $P(t)=1.19 t+4$

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Problem 23173

Choose the false statement about monomials:
1. A monomial is a number, variable, or product of a number and variables with whole number exponents.
2. $-3 x^{4} y$ is a monomial.
3. $-3 x^{4} y + 2 x y$ is a monomial.

See Solution

Problem 23174

Find $a_{71}$ using $a_{1}=0.1$ and common difference $d=-2$ .

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Problem 23175

Choose the false statement about degrees of polynomials:
1. For $4 x^{3}+2 x^{2}$ , the degree is 3.
2. For $2 x^{2}-5 x^{4}$ , the degree is 4.
3. For $-5 x^{2}+10 x$ , the degree is 3.

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Problem 23176

Choose the false statement about coefficients: 1) It's the number in front of a monomial. 2) It's always a number. 3) It's the number at the end of a polynomial in standard form.

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Problem 23177

Choose the false statement about polynomials:
1. Number of terms = monomials.
2. Trinomial has three terms.
3. Number of terms = highest exponent.

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Problem 23178

Choose the false statement about polynomials:
1. A polynomial can include whole number exponents.
2. A polynomial can include only addition or subtraction.
3. A polynomial cannot include an equal sign.

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Problem 23179

Model kakapo population growth with a recurrence relation. Assume 50% female, 1 egg/4 years, and 29% hatchling survival.

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Problem 23180

Find $a_{18}$ in an arithmetic sequence with $a_{1}=\frac{1}{3}$ and common difference $c=3$ .

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Problem 23181

Find $a_{18}$ given $a_{1}=\frac{1}{3}$ and common difference $d=3$ .

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Problem 23182

Find the roots of the equation $2x^3 + x^2 - 4 = 0$ .

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Problem 23183

Find the equivalent polynomial for $(-3 n+1)^{2}$ . Options: -9 n^{2}-6 n+1, -9 n^{2}+1, 9 n^{2}-6 n+1, 9 n^{2}+1.

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Problem 23184

A charged ball (20.0 nC) is at the center of a hollow shell (8 cm inner, 10 cm outer). Find:
(a) Inner surface charge density.
(b) Outer surface charge density.
(c) Electric flux through spheres of radii 5 cm, 9 cm, and 11 cm.

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Problem 23185

A Grade 2 teacher plans a picnic for 30 people. Find seating rules and table counts for two patterns: $8; 10; 12; \ldots$ and $8; 12; 16; \ldots$ .

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Problem 23186

Simplify the expression: $3x + 3x$ .

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Problem 23187

1. Find the identity element for $a * b = a + b - 3$ . A. 3 B. 2 C. 0 D. -3
2. Find the sum of the sequence $4, -2, 1, -\frac{1}{2}, \ldots$ . A. $-\frac{3}{4}$ B. $\frac{3}{4}$ C. $\frac{8}{3}$ D. 8
3. Solve $256^{(x+1)} = 8^{(1 - x^{2})}$ . A. $-1, -\frac{5}{3}$ B. $-\frac{3}{8}, -\frac{5}{3}$ C. $\frac{8}{3}, \frac{3}{5}$ D. $\frac{8}{3}, \frac{5}{3}$
4. If $\alpha$ and $\beta$ are roots of $x^{2} + 3x - 4 = 0$ , find $\alpha^{2} + \beta^{2} - 3\alpha\beta$ . A. -11 B. 20 C. 21 D. 29
5. Rationalize $\frac{1}{\sqrt{3} - \sqrt{2}}$ . A. $\sqrt{3} - \sqrt{2}$ B. $\frac{\sqrt{3} + \sqrt{2}}{3}$ C. $\frac{\sqrt{3} + \sqrt{2}}{2}$ D. $\sqrt{3} + \sqrt{2}$

See Solution

Problem 23188

A football is kicked from 6 ft with a speed of 75 ft/s. Use $h=6+75t-16t^{2}$ to find height at $t=4$ seconds.

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Problem 23189

1. Find the identity element for the operation $a * b = a + b - 3$ . A. 3 B. 2 C. 0 D. -3
2. Calculate the sum of the sequence $4, -2, 1, -\frac{1}{2}, \ldots$ . A. $-\frac{3}{4}$ B. $\frac{3}{4}$ C. $\frac{8}{3}$ D. 8
3. Solve $256^{(x+1)} = 8^{(1-x^{2})}$ . A. $-1, -\frac{5}{3}$ B. $-\frac{3}{8}, -\frac{5}{3}$ C. $\frac{8}{3}, \frac{3}{5}$ D. $\frac{8}{3}, \frac{5}{3}$
4. For roots $\alpha$ and $\beta$ of $x^{2} + 3x - 4 = 0$ , find $\alpha^{2} + \beta^{2} - 3\alpha\beta$ . A. -11 B. 20 C. 21 D. 29
5. Rationalize $\frac{1}{\sqrt{3} - \sqrt{2}}$ . A. $\sqrt{3} - \sqrt{2}$ B. $\frac{\sqrt{3} + \sqrt{2}}{3}$ C. $\frac{\sqrt{3} + \sqrt{2}}{2}$ D. $\sqrt{3} + \sqrt{2}$
6. Solve $\log_{5}(6x + 7) - \log_{5} 6 = 2$ for $x$ .

See Solution

Problem 23190

Simplify the expression: $3(9x - 8) + 15x$ .

See Solution

Problem 23191

Solve for $x$ : $3(9x - 8) + 15x = 0$ .

See Solution

Problem 23192

Simplify the expression: $4(-3 x^{2}+5 x) - (3 x - 3 x^{2})$

See Solution

Problem 23193

Simplify the expression: $3(9x - 8) + 15x$ .

See Solution

Problem 23194

Find the upper limit of the heart range for a 27-year-old, given lower limit $H=\frac{7}{10}(220-a)$ .

See Solution

Problem 23195

Find the expression for individual stamps from $F$ books of "Forever" stamps, where each book has 20 stamps. $20F$

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Problem 23196

Calculate daily calories for females aged 4-8 using $F=-81 x^{2}+655 x+616$ . Does it overestimate or underestimate the graph? By how much?

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Problem 23197

Find the lower limit of heart rate $H=\frac{7}{10}(220-a)$ for a 27-year-old.

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Problem 23198

Find calories needed per day for females aged 4 to 8 using $F=-81 x^{2}+655 x+616$ . Does it overestimate or underestimate?

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Problem 23199

Is the statement $2 + 7x = 9x$ true or false? If false, correct it to make it true.

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Problem 23200

Is the statement $3 + 9x = 12x$ true or false? If false, correct it to make it true.

See Solution

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Algebra

Problem 23101

Find ccc using the formula d=(r−c)td=(r-c) td=(r−c)t for d=26d=26d=26, r=15r=15r=15, and t=2t=2t=2. c=c=c=

Problem 23102

Solve the following equations: a. 5x−6=05x - 6 = 05x−6=0 b. 25x2−36=025x^2 - 36 = 025x2−36=0 c. 25x2−36=58925x^2 - 36 = 58925x2−36=589 d. 25x2−36=60x−7225x^2 - 36 = 60x - 7225x2−36=60x−72

Problem 23103

Simplify the polynomial expression: 3(x+5)2−3(x+5)+63(x+5)^{2}-3(x+5)+63(x+5)2−3(x+5)+6.

Problem 23104

A tennis ball hits a wall at 10.0 m/s10.0 \mathrm{~m/s}10.0 m/s and returns at 8.0 m/s8.0 \mathrm{~m/s}8.0 m/s. Find the average acceleration over 0.045s0.045 \mathrm{s}0.045s.

Problem 23105

Simplify the polynomial expression: 2(x−4)2+3(x−4)+12(x-4)^{2}+3(x-4)+12(x−4)2+3(x−4)+1.

Problem 23106

Find yyy in the equation 6.4(3)+2.8y=44.46.4(3) + 2.8y = 44.46.4(3)+2.8y=44.4.

Problem 23107

Expand (53x+4)2\left(\frac{5}{3} x+4\right)^{2}(35​x+4)2 into a trinomial in simplest form.

Problem 23108

Expand the expression to standard polynomial form: (x−1)(−x2+x+9)(x-1)(-x^{2}+x+9)(x−1)(−x2+x+9).

Problem 23109

Expand (53x−2)2\left(\frac{5}{3} x-2\right)^{2}(35​x−2)2 into a trinomial in simplest form.

Problem 23110

Solve for xxx in the equation x4−13x2+36=0x^{4}-13x^{2}+36=0x4−13x2+36=0 and factor it if possible.

Problem 23111

Factor the expression x4−12x2+32x^{4}-12 x^{2}+32x4−12x2+32.

Problem 23112

Find the equation of a line parallel to y=45x+2y=\frac{4}{5} x+2y=54​x+2 that goes through the point (1,2)(1,2)(1,2).

Problem 23113

Expand the expression: (2x + 1)(x² - 5x - 7) to standard polynomial form.

Problem 23114

Find a two-digit number where the sum of its digits is 13 and adding 27 reverses its digits. Options: (a) 48 (b) 53 (c) 58 (d) 57 (e) None.

Problem 23115

Convert the repeating decimal 0.51‾0.\overline{51}0.51 into a fraction.

Problem 23116

Solve for xxx using the quadratic formula: 8x2−8x−1=08 x^{2}-8 x-1=08x2−8x−1=0. Provide solutions separated by commas. x=x= x=

Problem 23117

Find www in the equation 4w2+20w=−254 w^{2}+20 w=-254w2+20w=−25. List all solutions or state "No solution."

Problem 23118

Find the discriminant and the real solutions for the equation: −9x2−6x−1=0-9 x^{2}-6 x-1=0−9x2−6x−1=0.

Problem 23119

Find a number to complete the expression as a perfect square: x2+6x+10x^{2}+6x+10x2+6x+10.

Problem 23120

Solve for www: w2−9w+20=0w^{2}-9w+20=0w2−9w+20=0. If multiple solutions, list them; if none, say "No solution."

Problem 23121

Find the quadratic equation with roots 5 and -2, and leading coefficient 4. Use Yetter xxx for the variable.

Problem 23122

Plot five points on the parabola y=−34x2y=-\frac{3}{4} x^{2}y=−43​x2: the vertex and two points on each side of it.

Problem 23123

Graph the solution to the inequality (x+4)(x−6)≤0(x+4)(x-6) \leq 0(x+4)(x−6)≤0 on a number line.

Problem 23124

Select the factored form of the expression: 16x2−8x+1=16 x^{2}-8 x+1=16x2−8x+1=

Problem 23125

Choose the factored form for each expression: 16x2−8x+116 x^{2}-8 x+116x2−8x+1, x2−x−30x^{2}-x-30x2−x−30, 9x2−499 x^{2}-499x2−49, 3x2+17x−63 x^{2}+17 x-63x2+17x−6.

Problem 23126

Determine if the function f(x)=−2x2+12x−20f(x)=-2 x^{2}+12 x-20f(x)=−2x2+12x−20 has a minimum or maximum, and find its value and location.

Problem 23127

Problem 23128

Express v12v^{\frac{1}{2}}v21​ as a radical expression.

Problem 23129

Simplify 9329^{\frac{3}{2}}923​.

Problem 23130

Simplify the expression: z13z14z−34\frac{z^{\frac{1}{3}}}{z^{\frac{1}{4}} z^{-\frac{3}{4}}}z41​z−43​z31​​ using only positive exponents.

Problem 23131

Rewrite t34\sqrt[4]{t^{3}}4t3​ as an exponential expression.

Problem 23132

Simplify the expression: z−14z13z12\frac{z^{-\frac{1}{4}}}{z^{\frac{1}{3}} z^{\frac{1}{2}}}z31​z21​z−41​​ using only positive exponents.

Problem 23133

Simplify and write without exponents: (181)34=□ \left(\frac{1}{81}\right)^{\frac{3}{4}}=\square (811​)43​=□ and 32−35=□ 32^{-\frac{3}{5}}=\square 32−53​=□

Problem 23134

Simplify the expression y−12y−17y32y^{-\frac{1}{2}} y^{-\frac{1}{7}} y^{\frac{3}{2}}y−21​y−71​y23​ using only positive exponents.

Problem 23135

Simplify the expression: b−12b13b14\frac{b^{-\frac{1}{2}} b^{\frac{1}{3}}}{b^{\frac{1}{4}}}b41​b−21​b31​​ using only positive exponents.

Problem 23136

Simplify the expression (c2⋅a−45)15\left(c^{2} \cdot a^{-\frac{4}{5}}\right)^{\frac{1}{5}}(c2⋅a−54​)51​ without negative exponents.

Problem 23137

Simplify the expression (z−3⋅y54)15\left(z^{-3} \cdot y^{\frac{5}{4}}\right)^{\frac{1}{5}}(z−3⋅y45​)51​ without negative exponents.

Problem 23138

Simplify: −580+20-5 \sqrt{80} + \sqrt{20}−580​+20​.

Problem 23139

Simplify the expression x−13x−47\frac{x^{-\frac{1}{3}}}{x^{-\frac{4}{7}}}x−74​x−31​​ using only positive exponents.

Problem 23140

Simplify: 448×984 \sqrt{48} \times \sqrt{98}448​×98​.

Find $c$ using the formula $d=(r-c) t$ for $d=26$ , $r=15$ , and $t=2$ . $c=$

Solve the following equations: a. $5x - 6 = 0$ b. $25x^2 - 36 = 0$ c. $25x^2 - 36 = 589$ d. $25x^2 - 36 = 60x - 72$

Simplify the polynomial expression: $3(x+5)^{2}-3(x+5)+6$ .

A tennis ball hits a wall at $10.0 \mathrm{~m/s}$ and returns at $8.0 \mathrm{~m/s}$ . Find the average acceleration over $0.045 \mathrm{s}$ .

Simplify the polynomial expression: $2(x-4)^{2}+3(x-4)+1$ .

Find $y$ in the equation $6.4(3) + 2.8y = 44.4$ .

Expand $\left(\frac{5}{3} x+4\right)^{2}$ into a trinomial in simplest form.

Expand the expression to standard polynomial form: $(x-1)(-x^{2}+x+9)$ .

Expand $\left(\frac{5}{3} x-2\right)^{2}$ into a trinomial in simplest form.

Solve for $x$ in the equation $x^{4}-13x^{2}+36=0$ and factor it if possible.

Factor the expression $x^{4}-12 x^{2}+32$ .

Find the equation of a line parallel to $y=\frac{4}{5} x+2$ that goes through the point $(1,2)$ .

Convert the repeating decimal $0.\overline{51}$ into a fraction.

Solve for $x$ using the quadratic formula: $8 x^{2}-8 x-1=0$ . Provide solutions separated by commas. $x=$

Find $w$ in the equation $4 w^{2}+20 w=-25$ . List all solutions or state "No solution."

Find the discriminant and the real solutions for the equation: $-9 x^{2}-6 x-1=0$ .

Find a number to complete the expression as a perfect square: $x^{2}+6x+10$ .

Solve for $w$ : $w^{2}-9w+20=0$ . If multiple solutions, list them; if none, say "No solution."

Find the quadratic equation with roots 5 and -2, and leading coefficient 4. Use Yetter $x$ for the variable.

Plot five points on the parabola $y=-\frac{3}{4} x^{2}$ : the vertex and two points on each side of it.

Graph the solution to the inequality $(x+4)(x-6) \leq 0$ on a number line.

Select the factored form of the expression: $16 x^{2}-8 x+1=$

Choose the factored form for each expression: $16 x^{2}-8 x+1$ , $x^{2}-x-30$ , $9 x^{2}-49$ , $3 x^{2}+17 x-6$ .

Determine if the function $f(x)=-2 x^{2}+12 x-20$ has a minimum or maximum, and find its value and location.

Express $v^{\frac{1}{2}}$ as a radical expression.

Simplify $9^{\frac{3}{2}}$ .

Simplify the expression: $\frac{z^{\frac{1}{3}}}{z^{\frac{1}{4}} z^{-\frac{3}{4}}}$ using only positive exponents.

Rewrite $\sqrt[4]{t^{3}}$ as an exponential expression.

Simplify the expression: $\frac{z^{-\frac{1}{4}}}{z^{\frac{1}{3}} z^{\frac{1}{2}}}$ using only positive exponents.

Simplify and write without exponents:
$\left(\frac{1}{81}\right)^{\frac{3}{4}}=\square$ and $32^{-\frac{3}{5}}=\square$

Simplify the expression $y^{-\frac{1}{2}} y^{-\frac{1}{7}} y^{\frac{3}{2}}$ using only positive exponents.

Simplify the expression: $\frac{b^{-\frac{1}{2}} b^{\frac{1}{3}}}{b^{\frac{1}{4}}}$ using only positive exponents.

Simplify the expression $\left(c^{2} \cdot a^{-\frac{4}{5}}\right)^{\frac{1}{5}}$ without negative exponents.

Simplify the expression $\left(z^{-3} \cdot y^{\frac{5}{4}}\right)^{\frac{1}{5}}$ without negative exponents.

Simplify: $-5 \sqrt{80} + \sqrt{20}$ .

Simplify the expression $\frac{x^{-\frac{1}{3}}}{x^{-\frac{4}{7}}}$ using only positive exponents.

Simplify: $4 \sqrt{48} \times \sqrt{98}$ .

Simplify: $\sqrt{50}+2 \sqrt{98}$

Simplify $\sqrt{18} \times 2 \sqrt{98}$ .

Simplify: $\sqrt{54} \times 4 \sqrt{48}$

Simplify the expression: $\sqrt{32} \times 2 \sqrt{50}$ .

Find the common difference and the 20th term of the sequence: 1, 2, 5, 8, 11, ...; use $a_{20}$ .

Esther paints 7 faces in 21 minutes. Find the equation relating $f$ , the number of faces, and $m$ , the time in minutes.

Find the equation relating $p$ (hours parked) and $c$ (cost in dollars) if Alexandra paid \$7 for 3 hours.

Carlos harvests cassavas at a constant rate. If he takes 35 mins for 15 cassavas, find the equation for $t$ and $c$ .

Flannery made 6 identical arrangements with 30 lilies and 78 roses. Find the equation relating $l$ and $r$ .

Find the common difference and the 20th term of the sequence: $2, 5, 8, 11, \ldots$

Create an equation for $y$ (yellow paint) and $b$ (blue paint) where $y + b = 8$ liters for the Green Goober's paint.

Find the GCF of 48 and 30, then express $48 + 30$ as $GCF \cdot (a + b)$ .

Based on the equation $C=\frac{5}{9}(F-32)$ , which statements about temperature changes are true? A) I only B) II only C) III only D) I and II only

If $3x - y = 12$ , find the value of $\frac{8^x}{2^y}$ . A) $2^{12}$ B) $4^{4}$ C) $8^{2}$ D) Cannot determine.

Combine the terms in the expression: $-3x + y - y + 7x$ . What is the simplified result?

Simplify the expression $x + 5y + 3x$ .

Simplify the expression $-2x - 3y + 4x + 5yi$ .

Simplify the expression: $-2 x + (-3 y) - (-4 x) + 5 y$ .

Simplify the expression: $-3 x(-2 y - 5 z + 3 z)$ .

Choose the incorrect statement given $i>0, j>0, k>0$ : a. If $i>j$ then $i+k>j+k$ b. If $i<j$ then $j>i$ c. If $i>j$ then $i \times k>j \times k$ d. If $j<i$ and $i<k$ then $k<j$

Solve for $x$ in the equation $2 - \frac{x}{2} + 20 = 0$ .

Find $k$ if $k\%$ of 127 equals 32. A) 0.25 B) 0.55 C) 25 D) 55

Solve the equation $\frac{x}{2}+20=0$ for $x$ .

Solve the equation: $2 x^{2}-10 x=0$ for the variable $x$ .

Solve the equation $x^{2}+2x=5x$ .

Find $a_{23}$ given $a_{1}=-5$ and $d=4$ .

Choose the false statement about binomials: A binomial has two terms. Is $q^{5}+8 q-2$ a binomial? Is $q^{5}+8 q$ a binomial?

Find the linear function $f$ such that $f\left(\frac{3}{5}\right)=\frac{1}{2}$ and $f(2)=4$ .

What function represents the world's population P (in billions) $t$ years after 1975, given a 1.9% growth rate? A) $P(t)=4(1.019)^{t}$ B) $P(t)=4(1.9)^{t}$ C) $P(t)=1.19 t+4$

Choose the false statement about monomials:
1. A monomial is a number, variable, or product of a number and variables with whole number exponents.
2. $-3 x^{4} y$ is a monomial.
3. $-3 x^{4} y + 2 x y$ is a monomial.

Find $a_{71}$ using $a_{1}=0.1$ and common difference $d=-2$ .