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Can you help me solve x^2+7x=0   Answer: x = {0, -7} Step-by-step explanation: Given: x² + 7x = 0 Factor: (x) (x + 7) = 0 Equate each factor to 0 to solve for the roots: x = 0 and x+7 = 0 x = - 7 The solution or roots of the quadratic equation: x = {0, -7}  ⇒  there are  two real solutions. The solution {0, 7} lie on x-axis where the parabola or graph of the quadratic equation opening upward passes through.

What is the square root of 468?   Answer: 6√13 Step-by-step explanation: Without using a calculator: 1) Factor the radicand where one of the factors is a perfect number. Factors of radicand: √9 × √4 × √13 2) Simplify: (3)(2)√13 6√13

The school day begins at 7:30 AM and ends at 3:45 PM. How many minutes are there in a school day? ( Assuming that the break time is 1 1/2 hour)   There are 405 minutes in a school day. From 7:30AM to 3:45PM, there are 8 hours and 15 minutes. Covertn 8 hours to minutes (1 hour = 60 minutes), the result will be 480 minutes plus 15 minutes, 495 minutes. Since there is a 1 1/2 hour break which is equal to 90minutes, subtract this from 495 minutes, the result now is 405 minutes.

Rectangle has an area of 8x^5y^3 and a length of 4x^2y^3 what is the width   Answer: Formula for area of rectangle: Finding the width: Substitute: Cancel: Divide:

Given that 20=20+18+16 + . . . +x, how many terms are on the right side of the equation? Find the sum of −100–99–98–97 – . . . +100+101+102 Please answer these 2 questions.   Answer: Step-by-step explanation: Sum of arithmetic sequence: Sn = n/2 2a₁ + (n-1)(d) Where: Sn = sum of the sequence n = number of terms a₁ = first term d = common difference Given: 20 = 20+18+16+...+ x Sn = 20 a₁ = 20 d = -2  (the sequence decreases by 2 per term) x = nth term Find n, the number of terms: 20 = n/2 2(20) + (n-1)(-2) 20 = n/2 {40 + 2 - 2n 20 = n 21 - n) 20 = -n² + 21n Arrange the quadratic equation in standard form: n² - 21n + 20 = 0 Factor: (n - 20) (n - 1) = 0 n - 20 = 20 n = 20 n - 1 = 0 n = 1 Choose n = 20. ANSWER: There are 20 terms. Find the 20th term: a₂₀ = 20 + (20-1)(-2) a₂₀ = 20 + (19)(-2) a₂₀ = 20 - 38 a₂₀ = -18 The 20th term x = -18. Check: Sn = n/2 (a₁ + an) 20 = 20/2 (20 + (-18)) 20 = 10 (2) 20 = 20  (True) ---- Find the sum of  −100–99–98–97 – . . . +100+101+102 Where: a₁...

Do you like to sleep ___ the stars? to on under at   Do you like to sleep "under" the stars Because the word " under" means "below" so "below the stars"

Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The balls height (in meters above the ground), xxx seconds after Antoine threw it, is modeled by: h(x)=-2x^2+4x+16h(x)=−2x 2 +4x+16h, left parenthesis, x, right parenthesis, equals, minus, 2, x, start superscript, 2, end superscript, plus, 4, x, plus, 16 How many seconds after being thrown will the ball hit the ground?   Answer: The ball hit the ground after 4 seconds. Step-by-step explanation: Model of parabola of the ball thrown to the dog from the balcony: h(x)=-2x²+4x+16 Where: h(x) is the height of the ball from the balcony at x seconds y-intercep t is the height of the balcony from the ground ⇒ 16 meters To solve for the time the ball reaches the dog on the ground, solve for x. Set h(x) at 0 meters on ground level. -2x²+4x+16 = 0 Factor the equation: -2(x - 4) (x + 2) = 0 Find the x, the time in seconds: x - 4 = 0 x = 4 x +2 = 0 x = -2 Choose the positive value for time: The ball...