Numbers & Operations

Problem 3001

Find $(x+y)^{-1 / 2}$ if $x=11$ and $y=25$ . Choices: a) 6 b) -6 c) $\frac{\sqrt{11}}{55}$ d) $\frac{1}{6}$ e) $-\frac{1}{6}$

See Solution

Problem 3002

Calculate the expression: $5^{5} \times e^{4} \times 4 \times 5^{5} \times 5 e^{3}$ .

See Solution

Problem 3003

Solve $\frac{1}{2 x+18}-\frac{x}{x^{2}-81}=$ for options a) to e).

See Solution

Problem 3004

Simplify the expression: $2^{5} \times 2^{8} \times a^{3}$ .

See Solution

Problem 3005

A paper is 0.01 cm thick. Each fold doubles its thickness. Find thickness after 4, 5 folds, and derive a formula $T = 0.01 \cdot 2^f$ .
(d) Thickness at $f=10$ ? (e) Thickness after 20 folds in meters? (f) Does it reach the Moon (384,000 km) after 40 folds? Show calculations.

See Solution

Problem 3006

Simplify the expression: $x^{2} y^{3} \div x y^{2}$ .

See Solution

Problem 3007

Factor $16 x^{4}-1$ . Choose the correct option from: a) $(2 x-1)^{2}(2 x+1)^{2}$ , b) $(4 x-1)^{2}(4 x+1)^{2}$ , c) $(2 x-1)(2 x+1)(4 x^{2}+1)$ , d) $(2 x-1)(2 x+1)(2 x^{2}-1)$ , e) $(2 x-1)(2 x+1)(2 x^{2}+1)$ .

See Solution

Problem 3008

Solve for $\frac{xy}{\frac{1}{x^2} - \frac{y}{x}}$ . Choose the correct option: a) $\frac{y}{x}$ , b) $\frac{x}{y}$ , c) $\frac{1-xy}{x}$ , d) $xy$ , e) $xy-1$ .

See Solution

Problem 3009

1. For the function $f(x)=10(2)^{x}$ , find $f(0)$ and its graph point. Is it increasing or decreasing? Compare average rates with $g(x)=10x+7$ . Sketch the graph.

See Solution

Problem 3010

Simplify the expression: $21 j^{8} k^{3} l^{3} \div 3 k^{2} l$ .

See Solution

Problem 3011

Simplify the expression: $2 r^{8} s^{5} t^{2} \div r^{2} s^{2}$ .

See Solution

Problem 3012

Simplify: $16 f^{7} g^{2} \div 4 f^{3} g$

See Solution

Problem 3013

Simplify the expression: $45 x^{9} y^{10} z^{5} \div 5 x^{12} y^{7}$ .

See Solution

Problem 3014

Simplify the expression: $\left(h^{4}\right)^{16}$ .

See Solution

Problem 3015

Calculate $\left(8^{9}\right)^{3}$ .

See Solution

Problem 3016

Solve for $z$ in the equation $283 - z = 15z + 11$ .

See Solution

Problem 3017

a) Calculate $-5-(-1)$ . b) Verify if $-5-(-7)=-12$ . c) Find the result of $4+(-10)$ .

See Solution

Problem 3018

Rewrite $\frac{4}{2+p}=\frac{3 p}{2-p}$ in general form and solve the resulting quadratic equation.

See Solution

Problem 3019

If $A$ and $B$ are invertible square matrices, find $(A B)^{-1}$ .

See Solution

Problem 3020

Find $f(x-1)$ if $f(x)=x^{2}-1$ . Choose the correct option: a) $x^{2}-2$ , b) $x^{2}-2 x-2$ , c) $x^{2}-x$ , d) $x^{2}-2 x$ , e) $x^{2}$ .

See Solution

Problem 3021

Solve for $x$ in the equation $\frac{5}{x+2}=\frac{5-x}{x-2}+1$ . Options: a) 2 b) -8 c) 8 d) -2 e) None.

See Solution

Problem 3022

Find $g(f(x))$ where $f(x)=x-2 x^{2}$ and $g(x)=1-2 x$ . Choices: a) $1-x-2 x^{2}$ , b) 0, c) $6 x-1-8 x^{2}$ , d) $x-2$ , e) $1-2 x+4 x^{2}$ .

See Solution

Problem 3023

Find the square matrix $B$ of order 2 such that $A B = I$ , where $A = \left(\begin{array}{cc}3 & -4 \\ -1 & 2\end{array}\right)$ .

See Solution

Problem 3024

Find the integral of $\frac{2}{3 x^{2}} - 2 \sec^{2}(5x)$ with respect to $x$ .

See Solution

Problem 3025

Evaluate the integral: $\int_{2}\left(\frac{2}{3 x^{2}}-2 \sec ^{2} 5 x\right) d x$

See Solution

Problem 3026

A cylinder has a radius of $x$ cm and height $x + 3$ cm. Its surface area is $130 \pi$ cm². Find the quadratic in $x$ .

See Solution

Problem 3027

$A B$ || $D E$ , $A C E$ and $B C D$ are straight lines. Given $A B=9$ cm, $A C=7.2$ cm, $C D=5.2$ cm, $D E=6$ cm. Find $B C$ .

See Solution

Problem 3028

Maria's hotel charge for $x$ nights is represented by which formula? $\$ 99.95$ night + $8\%$ tax + $\$ 5.00$ fee.

See Solution

Problem 3029

Find the integral: $\int 6 \operatorname{cosec} 2 x \cot 2 x \, dx$

See Solution

Problem 3030

The graph of $y=4-x$ is: a) parabola, b) parabola, c) line (slope -1, intercept 4), d) line (slope 4, intercept -1), e) circle.

See Solution

Problem 3031

Find the integral of $10^{3 x}$ with respect to $x$ .

See Solution

Problem 3032

The graph of $y=4-x^{2}$ is: a) down parabola at $(0,4)$ , b) down at $(4,0)$ , c) up at $(0,4)$ , d) up at $(4,0)$ , e) circle radius 2.

See Solution

Problem 3033

Solve $x^{2}+6 x+3=0$ using two methods: (a) Completing the Square, (b) Quadratic Formula. Simplify answers.

See Solution

Problem 3034

Find the line equation through points (-2,1) and (1,-2). Options: a) $y=x-1$ , b) $y=x+1$ , c) $y=-2x+1$ , d) $y=1-x$ , e) $y=-x-1$ .

See Solution

Problem 3035

Convert the decimal number 4025 to base 4.

See Solution

Problem 3036

Solve $\log _{2} x + \log _{2}(x-2) = 3$ for $x$ . Options: a) $4,-2$ b) 4 c) -2 d) $2,-4$ e) None.

See Solution

Problem 3037

Find the value of $\log _{5} \sqrt{5}$ . Options: a) 2 b) -2 c) $\frac{1}{2}$ d) $\frac{-1}{2}$ e) 0

See Solution

Problem 3038

Find the original price of an item that costs \$4.20 after a 20% price decrease. Options: a) \$4.40 b) \$5.04 c) \$5.00 d) \$4.96 e) \$5.25

See Solution

Problem 3039

Find the intersection points of the parabolas $y=x^{2}+2 x+2$ and $y=-2 x^{2}+8 x-7$ . Choose the correct pairs.

See Solution

Problem 3040

Tentukan nilai nombor $4025_{6}$ dalam basis sepuluh.

See Solution

Problem 3041

A ring of weight 8.5 N is on a string with tension $T$ . Show that $T \sin \theta = 12$ and $T \cos \theta = 3.5$ , then find $\theta$ .

See Solution

Problem 3042

If $4^{x}=40$ , find the value of $x$ : a) $10$ b) $\sqrt[40]{4}$ c) $\sqrt[4]{40}$ d) $\log_{4} 40$ e) $\log_{40} 4$ .

See Solution

Problem 3043

Simplify $e^{4x-2} e^{x+1}$ . What is the result? a) $e^{5x-1}$ b) $e^{4x^{2}+2x-2}$ c) $e^{3x-3}$ d) $e^{3x-1}$ e) $e^{3}$

See Solution

Problem 3044

Calculate the integral: $\int_{0}^{\frac{\pi}{4}} 4 \sin 2 x \, dx$

See Solution

Problem 3045

Calculate the sum: $412_{6}+3121_{6}$ .

See Solution

Problem 3046

Simplify $\log \left(x y^{2}\right)$ . Choose from: a) $2 \log (x y)$ b) $\log (x) \log \left(y^{2}\right)$ c) $2^{x y}$ d) $\log (x)+2 \log (y)$ e) none.

See Solution

Problem 3047

Circle the highlighted digit and state its value:
4. $2,850,12$ tens
5. $2,905,146$ hundred thousands

See Solution

Problem 3048

If $\log _{a} 64=2$ , find the value of $a$ . Options: a) -8 b) 32 c) 128 d) 4096 e) 8

See Solution

Problem 3049

Find the integral: $\int \frac{5-x-3 x^{2}}{4 \sqrt{x}} \, dx$

See Solution

Problem 3050

Trova il lato di un quadrato isoperimetrico a un rettangolo di base $15 \mathrm{~cm}$ e altezza $24 \mathrm{~cm}$ . R: $19,5 \mathrm{~cm}$ . Inoltre, la somma e la differenza di due lati consecutivi di un rettangolo sono $75 \mathrm{~cm}$ e $17 \mathrm{~cm}$ .

See Solution

Problem 3051

Solve for $x$ in the equation $4^{x+1}=8$ . What is $x$ ? a) 1 b) $\frac{1}{2}$ c) 2 d) -2 e) $\frac{-1}{2}$

See Solution

Problem 3052

Calculate $\log _{3} 81$ . Choose from: a) 3 b) 9 c) 27 d) 4 e) none of the above.

See Solution

Problem 3053

Find the area of a square (side 2) with a semi-circle on top. Options: a) $6+\pi$ , b) $2+\pi$ , c) $4+4\pi$ , d) $4+\frac{\pi}{2}$ , e) $4+\pi$ .

See Solution

Problem 3054

Un quadrato è isoperimetrico a un rettangolo con base $15 \mathrm{~cm}$ e altezza $4 \mathrm{~cm}$ . Trova il lato del quadrato. R: $19,5 \mathrm{~cm}$

See Solution

Problem 3055

36) Trova il lato di un quadrato isoperimetrico a un rettangolo di base $15 \mathrm{~cm}$ e altezza $24 \mathrm{~cm}$ . R: $19,5 \mathrm{~cm}$ 37) Due lati consecutivi di un rettangolo hanno somma $75 \mathrm{~cm}$ e differenza $17 \mathrm{~cm}$ .

See Solution

Problem 3056

What is the domain restriction for the equation $y=-a \sqrt{x-d}+c$ ?

See Solution

Problem 3057

Calculate $\frac{\left(2^{3}\right)^{2}-4^{-3}}{8^{-2}}$ .

See Solution

Problem 3058

Calcola il perimetro di un esagono con lati congruenti: $15 \mathrm{~cm}$ , $21 \mathrm{~cm}$ e $7 \mathrm{~cm}$ . R: $78 \mathrm{~cm}$

See Solution

Problem 3059

Calculate the value of $\square \cdot \frac{12^{4} \cdot 5^{-3} \cdot 9^{2}}{8 \cdot 3^{6} \cdot 135^{-1}}$ .

See Solution

Problem 3060

Find the number of intersection points for the system: $y=ax+8$ and $y=-x^{2}$ .

See Solution

Problem 3061

Trova due segmenti la cui somma è $57 \mathrm{~cm}$ e differenza è $7 \mathrm{~cm}$ . R: $32 \mathrm{~cm}$ e $25 \mathrm{~cm}$ .

See Solution

Problem 3062

Find the Discriminant of the equation $y=5 x^{2}-5 x+10$ .

See Solution

Problem 3063

Calculate the expression $8 \cdot 3^{6} \cdot 135^{-1}$ and simplify $2 \sqrt{50}$ .

See Solution

Problem 3064

Calcola due angoli sapendo che la loro somma è $90^{\circ} 30^{\prime}$ e la loro differenza è $10'30$ .

See Solution

Problem 3065

A car leaves Regina at 1 PM at 85 km/h. A 2nd car leaves at 1:30 PM at 110 km/h. When does it pass the first car?

See Solution

Problem 3066

Find the area of a triangle with sides 3, 4, and 5. Options: a) 6 b) 7.5 c) 10 d) 12 e) 15.

See Solution

Problem 3067

Adam shovels a driveway in 2 hours, Bev in 3 hours. How long for both to finish together? a) 2:30 b) 2:20 c) 0:48 d) 1:12 e) 1:36

See Solution

Problem 3068

Find the distance between points $(-1,2)$ and $(3,4)$ . Options: a) 5 b) $\sqrt{8}$ c) $\sqrt{10}$ d) $\sqrt{20}$ e) $\sqrt{40}$ .

See Solution

Problem 3069

Simplify the expression: $\frac{12^{4} \cdot 5^{-3} \cdot 9^{2}}{8 \cdot 3^{6} \cdot 135^{-1}}$ and find $2 \sqrt{50}$ .

See Solution

Problem 3070

36) Trova il lato di un quadrato isoperimetrico a un rettangolo di base $15 \mathrm{~cm}$ e altezza $24 \mathrm{~cm}$ . R: $19,5 \mathrm{~cm}$ 37) Due lati consecutivi di un rettangolo hanno somma $75 \mathrm{~cm}$ e differenza $17 \mathrm{~cm}$ . Trova i lati. R: $46 \mathrm{~cm}, 29 \mathrm{~cm}$

See Solution

Problem 3071

Find the standard form of a parabola with $x$ -intercepts at $\pm \sqrt{3}$ and a maximum value of 18.

See Solution

Problem 3072

Find the coefficients $a$ , $b$ , and $c$ for the quadratic function with roots $x=2$ , $x=5$ , and passing through $(7,-40)$ .

See Solution

Problem 3073

The nurse gives penicillin $750 \mathrm{mg}$ daily, every 6 hours. How much is each dose?

See Solution

Problem 3074

If $S(t)=250(1.045)^{t}$ , which statement is true about the initial deposit and interest rate?

See Solution

Problem 3075

If a triangle is scalene, then all side lengths are different. Choose the equivalent statement: A, B, or C.

See Solution

Problem 3076

Find the inverse of the function $f(x)=3 x^{2}-6 x+1$ .

See Solution

Problem 3077

If $S(t)=250(1.045)^{t}$ , which statement about the initial deposit and interest rate is true?

See Solution

Problem 3078

Model the depth of water in a pool draining at $20\%$ per hour from an initial depth of 12 feet. Find $D(t)$ for $t=1, 2, 3$ hours.

See Solution

Problem 3079

Find $w$ for one $x$ -intercept in $f(x)=w x^{2}+(2 w-6) x+(w-10)$ .

See Solution

Problem 3080

Find the number of sides $n$ in a polygon if the interior angles sum to $1080^{\circ}$ . Use $=(n-2)180$ .

See Solution

Problem 3081

Determine which sets can be side lengths of a triangle: A. $9,5,15$ B. $10,3,7$ C. $8,5,7$

See Solution

Problem 3082

A child weighing 50 lbs needs tetracycline at $8 \mathrm{mg} / \mathrm{kg} /$ day, 4 times daily. Find: a. Dose in mg? b. mL per dose if supplied at $50 \mathrm{mg} / 7 \mathrm{~mL}$ ? c. Total daily mg?

See Solution

Problem 3083

Find the Discriminant of the quadratic equation $y=3 x^{2}-5 x+2$ .

See Solution

Problem 3084

Правоъгьлен паралелепипед с размери $a, b, c$ има отношение $a:b=4:3$ и $b:c=2:5$ . Сборът на ръбовете е $232 \mathrm{~cm}$ . Какъв е обемът му?

See Solution

Problem 3085

Identify the domain restriction for the function $y=-a \sqrt{x-d}+c$ . What is the restriction?

See Solution

Problem 3086

Find the limit of $f(x)=\frac{\sin 4x}{4 \sin 3x}$ as $x$ approaches 0.

See Solution

Problem 3087

What is the domain restriction for the function $y=\frac{a}{x-d}+c$ ?

See Solution

Problem 3088

Find the limit of $f(x)=\frac{\sin 4x}{4\sin 3x}+\frac{\sin (x/3)}{9x}$ as $x \to 0$ .

See Solution

Problem 3089

Find the reflection of the point $P=(-4,-1)$ across the x-axis. What are the new coordinates?

See Solution

Problem 3090

Find the number that completes the translation rule $T(x, y)=(x-5, y+[?])$ given points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

See Solution

Problem 3091

Identify the quadrilateral formed by the points $(-5,0),(0,4),(5,0),(0,-4)$ . Options: A. Trapezoid B. Rhombus C. Square D. Rectangle.

See Solution

Problem 3092

Find the translation rule $\mathrm{T}(\mathrm{x}, \mathrm{y})=(\mathrm{x}-[?], \mathrm{y}+[\mathrm{]})$ for points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

See Solution

Problem 3093

Giải hệ phương trình: $-2mx + y = 5$ và $mx + 3y = 1$ . Tìm nghiệm khi $m=1$ và giá trị $m$ để hệ có nghiệm duy nhất.

See Solution

Problem 3094

Solve the proportion $\frac{3}{4}=\frac{6}{x}$ for $x$ .

See Solution

Problem 3095

Find the new coordinates of $(-1,3)$ after moving 2 units down and rotating $270^{\circ}$ counterclockwise around the origin.

See Solution

Problem 3096

Find the scale factor of the side lengths of two similar squares with areas $16 \mathrm{~m}^{2}$ and $49 \mathrm{~m}^{2}$ .

See Solution

Problem 3097

Find the number of edges in a polyhedron with 6 faces and 6 vertices using Euler's formula: $F + V = E + 2$ .

See Solution

Problem 3098

If $1=3$ , $2=3$ , $3=5$ , $4=4$ , $5=4$ , what is $6$ ?

See Solution

Problem 3099

Find the parabola equation with focus $(3,4)$ and directrix $y=2$ .

See Solution

Problem 3100

Calculate the area of a regular 7-sided polygon with an apothem of 8 m and side length of 7.7 m. Round to the nearest tenth. [?] $\mathrm{m}^{2}$

See Solution

1 ...28 29 30 31 32 33 34 ...118

Numbers & Operations

Problem 3001

Find (x+y)−1/2(x+y)^{-1 / 2}(x+y)−1/2 if x=11x=11x=11 and y=25y=25y=25. Choices: a) 6 b) -6 c) 1155\frac{\sqrt{11}}{55}5511​​ d) 16\frac{1}{6}61​ e) −16-\frac{1}{6}−61​

Problem 3002

Calculate the expression: 55×e4×4×55×5e35^{5} \times e^{4} \times 4 \times 5^{5} \times 5 e^{3}55×e4×4×55×5e3.

Problem 3003

Solve 12x+18−xx2−81=\frac{1}{2 x+18}-\frac{x}{x^{2}-81}=2x+181​−x2−81x​= for options a) to e).

Problem 3004

Simplify the expression: 25×28×a32^{5} \times 2^{8} \times a^{3}25×28×a3.

Problem 3005

Problem 3006

Simplify the expression: x2y3÷xy2x^{2} y^{3} \div x y^{2}x2y3÷xy2.

Problem 3007

Problem 3008

Solve for xy1x2−yx\frac{xy}{\frac{1}{x^2} - \frac{y}{x}}x21​−xy​xy​. Choose the correct option: a) yx\frac{y}{x}xy​, b) xy\frac{x}{y}yx​, c) 1−xyx\frac{1-xy}{x}x1−xy​, d) xyxyxy, e) xy−1xy-1xy−1.

Problem 3009

1. For the function f(x)=10(2)xf(x)=10(2)^{x}f(x)=10(2)x, find f(0)f(0)f(0) and its graph point. Is it increasing or decreasing? Compare average rates with g(x)=10x+7g(x)=10x+7g(x)=10x+7. Sketch the graph.

Problem 3010

Simplify the expression: 21j8k3l3÷3k2l21 j^{8} k^{3} l^{3} \div 3 k^{2} l21j8k3l3÷3k2l.

Problem 3011

Simplify the expression: 2r8s5t2÷r2s22 r^{8} s^{5} t^{2} \div r^{2} s^{2}2r8s5t2÷r2s2.

Problem 3012

Simplify: 16f7g2÷4f3g16 f^{7} g^{2} \div 4 f^{3} g16f7g2÷4f3g

Problem 3013

Simplify the expression: 45x9y10z5÷5x12y745 x^{9} y^{10} z^{5} \div 5 x^{12} y^{7}45x9y10z5÷5x12y7.

Problem 3014

Simplify the expression: (h4)16\left(h^{4}\right)^{16}(h4)16.

Problem 3015

Calculate (89)3\left(8^{9}\right)^{3}(89)3.

Problem 3016

Solve for zzz in the equation 283−z=15z+11283 - z = 15z + 11283−z=15z+11.

Problem 3017

a) Calculate −5−(−1)-5-(-1)−5−(−1). b) Verify if −5−(−7)=−12-5-(-7)=-12−5−(−7)=−12. c) Find the result of 4+(−10)4+(-10)4+(−10).

Problem 3018

Rewrite 42+p=3p2−p\frac{4}{2+p}=\frac{3 p}{2-p}2+p4​=2−p3p​ in general form and solve the resulting quadratic equation.

Problem 3019

If AAA and BBB are invertible square matrices, find (AB)−1(A B)^{-1}(AB)−1.

Problem 3020

Find f(x−1)f(x-1)f(x−1) if f(x)=x2−1f(x)=x^{2}-1f(x)=x2−1. Choose the correct option: a) x2−2x^{2}-2x2−2, b) x2−2x−2x^{2}-2 x-2x2−2x−2, c) x2−xx^{2}-xx2−x, d) x2−2xx^{2}-2 xx2−2x, e) x2x^{2}x2.

Problem 3021

Solve for xxx in the equation 5x+2=5−xx−2+1\frac{5}{x+2}=\frac{5-x}{x-2}+1x+25​=x−25−x​+1. Options: a) 2 b) -8 c) 8 d) -2 e) None.

Problem 3022

Find g(f(x))g(f(x))g(f(x)) where f(x)=x−2x2f(x)=x-2 x^{2}f(x)=x−2x2 and g(x)=1−2xg(x)=1-2 xg(x)=1−2x. Choices: a) 1−x−2x21-x-2 x^{2}1−x−2x2, b) 0, c) 6x−1−8x26 x-1-8 x^{2}6x−1−8x2, d) x−2x-2x−2, e) 1−2x+4x21-2 x+4 x^{2}1−2x+4x2.

Problem 3023

Find the square matrix BBB of order 2 such that AB=IA B = IAB=I, where A=(3−4−12)A = \left(\begin{array}{cc}3 & -4 \\ -1 & 2\end{array}\right)A=(3−1​−42​).

Problem 3024

Find the integral of 23x2−2sec⁡2(5x)\frac{2}{3 x^{2}} - 2 \sec^{2}(5x)3x22​−2sec2(5x) with respect to xxx.

Problem 3025

Evaluate the integral: ∫2(23x2−2sec⁡25x)dx\int_{2}\left(\frac{2}{3 x^{2}}-2 \sec ^{2} 5 x\right) d x∫2​(3x22​−2sec25x)dx

Problem 3026

A cylinder has a radius of xxx cm and height x+3x + 3x+3 cm. Its surface area is 130π130 \pi130π cm². Find the quadratic in xxx.

Problem 3027

ABA BAB || DED EDE, ACEA C EACE and BCDB C DBCD are straight lines. Given AB=9A B=9AB=9 cm, AC=7.2A C=7.2AC=7.2 cm, CD=5.2C D=5.2CD=5.2 cm, DE=6D E=6DE=6 cm. Find BCB CBC.

Problem 3028

Maria's hotel charge for xxx nights is represented by which formula? $99.95\$ 99.95$99.95 night + 8%8\%8% tax + $5.00\$ 5.00$5.00 fee.

Problem 3029

Find the integral: ∫6cosec⁡2xcot⁡2x dx\int 6 \operatorname{cosec} 2 x \cot 2 x \, dx∫6cosec2xcot2xdx

Problem 3030

The graph of y=4−xy=4-xy=4−x is: a) parabola, b) parabola, c) line (slope -1, intercept 4), d) line (slope 4, intercept -1), e) circle.

Problem 3031

Find the integral of 103x10^{3 x}103x with respect to xxx.

Problem 3032

The graph of y=4−x2y=4-x^{2}y=4−x2 is: a) down parabola at (0,4)(0,4)(0,4), b) down at (4,0)(4,0)(4,0), c) up at (0,4)(0,4)(0,4), d) up at (4,0)(4,0)(4,0), e) circle radius 2.

Problem 3033

Solve x2+6x+3=0x^{2}+6 x+3=0x2+6x+3=0 using two methods: (a) Completing the Square, (b) Quadratic Formula. Simplify answers.

Problem 3034

Find the line equation through points (-2,1) and (1,-2). Options: a) y=x−1y=x-1y=x−1, b) y=x+1y=x+1y=x+1, c) y=−2x+1y=-2x+1y=−2x+1, d) y=1−xy=1-xy=1−x, e) y=−x−1y=-x-1y=−x−1.

Problem 3035

Convert the decimal number 4025 to base 4.

Problem 3036

Solve log⁡2x+log⁡2(x−2)=3\log _{2} x + \log _{2}(x-2) = 3log2​x+log2​(x−2)=3 for xxx. Options: a) 4,−24,-24,−2 b) 4 c) -2 d) 2,−42,-42,−4 e) None.

Problem 3037

Find the value of log⁡55\log _{5} \sqrt{5}log5​5​. Options: a) 2 b) -2 c) 12\frac{1}{2}21​ d) −12\frac{-1}{2}2−1​ e) 0

Problem 3038

Find the original price of an item that costs \$4.20 after a 20% price decrease. Options: a) \$4.40 b) \$5.04 c) \$5.00 d) \$4.96 e) \$5.25

Problem 3039

Find the intersection points of the parabolas y=x2+2x+2y=x^{2}+2 x+2y=x2+2x+2 and y=−2x2+8x−7y=-2 x^{2}+8 x-7y=−2x2+8x−7. Choose the correct pairs.

Problem 3040

Tentukan nilai nombor 402564025_{6}40256​ dalam basis sepuluh.

Problem 3041

Find $(x+y)^{-1 / 2}$ if $x=11$ and $y=25$ . Choices: a) 6 b) -6 c) $\frac{\sqrt{11}}{55}$ d) $\frac{1}{6}$ e) $-\frac{1}{6}$

Calculate the expression: $5^{5} \times e^{4} \times 4 \times 5^{5} \times 5 e^{3}$ .

Solve $\frac{1}{2 x+18}-\frac{x}{x^{2}-81}=$ for options a) to e).

Simplify the expression: $2^{5} \times 2^{8} \times a^{3}$ .

Simplify the expression: $x^{2} y^{3} \div x y^{2}$ .

Solve for $\frac{xy}{\frac{1}{x^2} - \frac{y}{x}}$ . Choose the correct option: a) $\frac{y}{x}$ , b) $\frac{x}{y}$ , c) $\frac{1-xy}{x}$ , d) $xy$ , e) $xy-1$ .

1. For the function $f(x)=10(2)^{x}$ , find $f(0)$ and its graph point. Is it increasing or decreasing? Compare average rates with $g(x)=10x+7$ . Sketch the graph.

Simplify the expression: $21 j^{8} k^{3} l^{3} \div 3 k^{2} l$ .

Simplify the expression: $2 r^{8} s^{5} t^{2} \div r^{2} s^{2}$ .

Simplify: $16 f^{7} g^{2} \div 4 f^{3} g$

Simplify the expression: $45 x^{9} y^{10} z^{5} \div 5 x^{12} y^{7}$ .

Simplify the expression: $\left(h^{4}\right)^{16}$ .

Calculate $\left(8^{9}\right)^{3}$ .

Solve for $z$ in the equation $283 - z = 15z + 11$ .

a) Calculate $-5-(-1)$ . b) Verify if $-5-(-7)=-12$ . c) Find the result of $4+(-10)$ .

Rewrite $\frac{4}{2+p}=\frac{3 p}{2-p}$ in general form and solve the resulting quadratic equation.

If $A$ and $B$ are invertible square matrices, find $(A B)^{-1}$ .

Find $f(x-1)$ if $f(x)=x^{2}-1$ . Choose the correct option: a) $x^{2}-2$ , b) $x^{2}-2 x-2$ , c) $x^{2}-x$ , d) $x^{2}-2 x$ , e) $x^{2}$ .

Solve for $x$ in the equation $\frac{5}{x+2}=\frac{5-x}{x-2}+1$ . Options: a) 2 b) -8 c) 8 d) -2 e) None.

Find $g(f(x))$ where $f(x)=x-2 x^{2}$ and $g(x)=1-2 x$ . Choices: a) $1-x-2 x^{2}$ , b) 0, c) $6 x-1-8 x^{2}$ , d) $x-2$ , e) $1-2 x+4 x^{2}$ .

Find the square matrix $B$ of order 2 such that $A B = I$ , where $A = \left(\begin{array}{cc}3 & -4 \\ -1 & 2\end{array}\right)$ .

Find the integral of $\frac{2}{3 x^{2}} - 2 \sec^{2}(5x)$ with respect to $x$ .

Evaluate the integral: $\int_{2}\left(\frac{2}{3 x^{2}}-2 \sec ^{2} 5 x\right) d x$

A cylinder has a radius of $x$ cm and height $x + 3$ cm. Its surface area is $130 \pi$ cm². Find the quadratic in $x$ .

$A B$ || $D E$ , $A C E$ and $B C D$ are straight lines. Given $A B=9$ cm, $A C=7.2$ cm, $C D=5.2$ cm, $D E=6$ cm. Find $B C$ .

Maria's hotel charge for $x$ nights is represented by which formula? $\$ 99.95$ night + $8\%$ tax + $\$ 5.00$ fee.

Find the integral: $\int 6 \operatorname{cosec} 2 x \cot 2 x \, dx$

The graph of $y=4-x$ is: a) parabola, b) parabola, c) line (slope -1, intercept 4), d) line (slope 4, intercept -1), e) circle.

Find the integral of $10^{3 x}$ with respect to $x$ .

The graph of $y=4-x^{2}$ is: a) down parabola at $(0,4)$ , b) down at $(4,0)$ , c) up at $(0,4)$ , d) up at $(4,0)$ , e) circle radius 2.

Solve $x^{2}+6 x+3=0$ using two methods: (a) Completing the Square, (b) Quadratic Formula. Simplify answers.

Find the line equation through points (-2,1) and (1,-2). Options: a) $y=x-1$ , b) $y=x+1$ , c) $y=-2x+1$ , d) $y=1-x$ , e) $y=-x-1$ .

Solve $\log _{2} x + \log _{2}(x-2) = 3$ for $x$ . Options: a) $4,-2$ b) 4 c) -2 d) $2,-4$ e) None.

Find the value of $\log _{5} \sqrt{5}$ . Options: a) 2 b) -2 c) $\frac{1}{2}$ d) $\frac{-1}{2}$ e) 0

Find the intersection points of the parabolas $y=x^{2}+2 x+2$ and $y=-2 x^{2}+8 x-7$ . Choose the correct pairs.

Tentukan nilai nombor $4025_{6}$ dalam basis sepuluh.

A ring of weight 8.5 N is on a string with tension $T$ . Show that $T \sin \theta = 12$ and $T \cos \theta = 3.5$ , then find $\theta$ .

If $4^{x}=40$ , find the value of $x$ : a) $10$ b) $\sqrt[40]{4}$ c) $\sqrt[4]{40}$ d) $\log_{4} 40$ e) $\log_{40} 4$ .

Simplify $e^{4x-2} e^{x+1}$ . What is the result? a) $e^{5x-1}$ b) $e^{4x^{2}+2x-2}$ c) $e^{3x-3}$ d) $e^{3x-1}$ e) $e^{3}$

Calculate the integral: $\int_{0}^{\frac{\pi}{4}} 4 \sin 2 x \, dx$

Calculate the sum: $412_{6}+3121_{6}$ .

Simplify $\log \left(x y^{2}\right)$ . Choose from: a) $2 \log (x y)$ b) $\log (x) \log \left(y^{2}\right)$ c) $2^{x y}$ d) $\log (x)+2 \log (y)$ e) none.

Circle the highlighted digit and state its value:
4. $2,850,12$ tens
5. $2,905,146$ hundred thousands

If $\log _{a} 64=2$ , find the value of $a$ . Options: a) -8 b) 32 c) 128 d) 4096 e) 8

Find the integral: $\int \frac{5-x-3 x^{2}}{4 \sqrt{x}} \, dx$

Solve for $x$ in the equation $4^{x+1}=8$ . What is $x$ ? a) 1 b) $\frac{1}{2}$ c) 2 d) -2 e) $\frac{-1}{2}$

Calculate $\log _{3} 81$ . Choose from: a) 3 b) 9 c) 27 d) 4 e) none of the above.

Find the area of a square (side 2) with a semi-circle on top. Options: a) $6+\pi$ , b) $2+\pi$ , c) $4+4\pi$ , d) $4+\frac{\pi}{2}$ , e) $4+\pi$ .

Un quadrato è isoperimetrico a un rettangolo con base $15 \mathrm{~cm}$ e altezza $4 \mathrm{~cm}$ . Trova il lato del quadrato. R: $19,5 \mathrm{~cm}$

36) Trova il lato di un quadrato isoperimetrico a un rettangolo di base $15 \mathrm{~cm}$ e altezza $24 \mathrm{~cm}$ . R: $19,5 \mathrm{~cm}$ 37) Due lati consecutivi di un rettangolo hanno somma $75 \mathrm{~cm}$ e differenza $17 \mathrm{~cm}$ .

What is the domain restriction for the equation $y=-a \sqrt{x-d}+c$ ?

Calculate $\frac{\left(2^{3}\right)^{2}-4^{-3}}{8^{-2}}$ .

Calcola il perimetro di un esagono con lati congruenti: $15 \mathrm{~cm}$ , $21 \mathrm{~cm}$ e $7 \mathrm{~cm}$ . R: $78 \mathrm{~cm}$

Calculate the value of $\square \cdot \frac{12^{4} \cdot 5^{-3} \cdot 9^{2}}{8 \cdot 3^{6} \cdot 135^{-1}}$ .

Find the number of intersection points for the system: $y=ax+8$ and $y=-x^{2}$ .

Trova due segmenti la cui somma è $57 \mathrm{~cm}$ e differenza è $7 \mathrm{~cm}$ . R: $32 \mathrm{~cm}$ e $25 \mathrm{~cm}$ .

Find the Discriminant of the equation $y=5 x^{2}-5 x+10$ .

Calculate the expression $8 \cdot 3^{6} \cdot 135^{-1}$ and simplify $2 \sqrt{50}$ .

Calcola due angoli sapendo che la loro somma è $90^{\circ} 30^{\prime}$ e la loro differenza è $10'30$ .

Find the distance between points $(-1,2)$ and $(3,4)$ . Options: a) 5 b) $\sqrt{8}$ c) $\sqrt{10}$ d) $\sqrt{20}$ e) $\sqrt{40}$ .

Simplify the expression: $\frac{12^{4} \cdot 5^{-3} \cdot 9^{2}}{8 \cdot 3^{6} \cdot 135^{-1}}$ and find $2 \sqrt{50}$ .

Find the standard form of a parabola with $x$ -intercepts at $\pm \sqrt{3}$ and a maximum value of 18.

Find the coefficients $a$ , $b$ , and $c$ for the quadratic function with roots $x=2$ , $x=5$ , and passing through $(7,-40)$ .

The nurse gives penicillin $750 \mathrm{mg}$ daily, every 6 hours. How much is each dose?

If $S(t)=250(1.045)^{t}$ , which statement is true about the initial deposit and interest rate?