Solve.

$√(x-1)+3=x$

Answers

Answer 1

Answer: $√(x-1)+3=x;\ Domain:x-1\geq0\ \wedge\ x\geq3\to x\geq1\ \wedge\ x\geq3\nD:x\in[3;\ \infty)\n\n√(x-1)=x-3\ \ \ \ |square\ both\ sides\n\nx-1=(x-3)^2\ \ \ \ |use\ of\ the\ formula:(a-b)^2=a^2-2ab+b^2\n\nx-1=x^2-6x+9\n\nx^2-6x+9=x-1\n\nx^2-6x-x+9+1=0\nx^2-7x+10=0\ \ \ \ |use\ quadratic\ formula$

$a=1;\ b=-7;\ c=10\n\n\Delta=b^2-4ac\to\Delta=(-7)^2-4\cdot1\cdot10=49-40=9\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=\sqrt9=3\n\nx_1=(7-3)/(2\cdot1)=(4)/(2)=2\notin D\n\nx_2=(7+3)/(2\cdot1)=(10)/(2)=5\in D\n\nSolution:x=5$

Answer 2

Answer: $√(x-1)+3=x\n √(x-1)=x-3\n D:x-1\geq0 \wedge x-3\geq0\n D:x\geq1 \wedge x\geq3\n D:x\geq3\n x-1=(x-3)^2\n x-1=x^2-6x+9\n x^2-7x+10=0\n x^2-2x-5x+10=0\n x(x-2)-5(x-2)=0\n (x-5)(x-2)=0\n x=5 \vee x=2\n 2\not \in D \Rightarrow x=5$

Answer:

A.) 2x+6=2

B.) 2(x-4)=6x

Step-by-step explanation:

A.) 2x+6=2:

Move all terms that don't contain x to the right side and solve.

x=−2

B.) 2(x-4)=6x:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=−2

C.) 3x+1/2=1/4x+6:

Solve for x by cross multiplying.

x=2

D.) 3x+15=2x+9:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=−6

a school is buying jerseys for their baskett ball team that cost $35 each. how many jerseys were purchased if she school spent $560

Answers

Answer: 16

Step-by-step explanation:

560 divided by 35=16

560/35=16

16 jerseys would be purchased

a money bag contains ten 5-dollar notes and thirty 10-dollar notes. if a note is randomly selected from the bag, what is the probability of a 5-dollar note being selected?

Answers

Total no. of notes = 10+30 =40
5 dollars note = 10

probability = 10/40 =1/4

$67 answer from my oppinon

in japan, farmers have created watermelons in the shape of rectangular prisms. find the volume of a prism-shaped watermelon in cubic inches if its length is 10 inches, its width is 2/3 foot, and its height is 9 inches

Answers

Given:
rectangular prism.
length = 10 inches
width = 2/3 foot
height = 9 inches

convert width from foot to inches. 1 foot = 12 inches
2/3 foot * 12inches/ft = 2/3 * 12 inches = 2*12/3 = 24/3 = 8 inches

Volume of rectangular prism = length * width * height
V = 10 inches * 8 inches * 9 inches
V = 720 in³

Danny charges $35 for 3 hours of swimming lessons.Martin charges $24 for 2 hours of swimming lessons. Who offers a better deal?