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liberstina [14]

3 years ago

12

Jayden is filling his 290 gallon pool with a garden hose. The garden hose produces 29 gallons of water per hour. How long will i

t take for Jayden to fill up his pool?

1 answer:

astra-53 [7]3 years ago

4 0

Answer:

10 hours

Step-by-step explanation:

290 divided by 29 = 10

check to see if its correct 29 multiple by 10 is 290

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Malik earned $2,344.55 fixing computers. He charged $35.50 per hour. Which expression does NOT use appropriate compatible number

Mademuasel [1]

I will say b 2,400 and some else

3 0

3 years ago

Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

<u>Answer</u><u> </u><u>Check</u>

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

<u>Answer</u>

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

8 0

3 years ago

A country will produce 3000 missiles this year. Each of the short-range missiles cost $200000 to produce. Each of the medium-ran

Lynna [10]

Answer:

$350,000

Step-by-step explanation:

Let's define:

s: amount of short-range missiles produced

m: amount of medium-range missiles produced

l: amount of long-range missiles produced

From the total production and the ratios we can write the following equations:

s + m + l = 3000

s/m = 3/3 = 1 = m/s

s/l = 3/4 or l/s = 4/3

Dividing the first equation by s, we get:

s/s + m/s + l/s = 3000/s

1 + 1 + 4/3 = 3000/s

10/3 = 3000/s

s = 3000*3/10 = 900

m = 900

l = 4/3*900 = 1200

From the money that the countries plans to use and each missile cost, we can write the following equation:

200,000*s + 300,000*m + cost*l = 870,000,000

Replacing with previous result:

200,000*900 + 300,000*900 + cost*1200 = 870,000,000

cost = (870,000,000 - 200,000*900 - 300,000*900)/1200 = 350,000

3 0

3 years ago

Find the equation of the line passing through point (4,2) and perpendicular to AB

Setler [38]

Answer:

a. -⅓

b. 3

c. y = 3x - 10

Step-by-step explanation:

a. Gradient of line AB:

A(1, 3), B(7, 1)

$Gradient = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{7 - 1} = \frac{-2}{6} = -\frac{1}{3}$

Gradient (m) = -⅓

b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.

Thus, the negative reciprocal of -⅓ = 3

Gradient of the line perpendicular to line AB = 3

c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:

We can write the equation using the point-slope form equation, y - b = m(x - a), where,

(a, b) represents a point on the line, and,

m = gradient/slope

We know that the gradient/slope (m) = 3

Also, a point, (a, b) = (4, 2).

Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)

Thus:

y - 2 = 3(x - 4)

y - 2 = 3x - 12

Add 2 to both sides

y = 3x - 12 + 2

y = 3x - 10

5 0

3 years ago

M-15=9 inverse operation

zheka24 [161]

Answer: 24

Step-by-step explanation:

m - 15 + 15 = 9 + 15

m = 24

6 0

3 years ago