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3 years ago

Solve the simultaneous equations x2 + y2 = 10 and x – 3y + 10 = 0.

Mathematics

1 answer:

ch4aika [34]3 years ago

3 0

Answer:

x = - 1, y = 3 or (-1 , 3)

Step-by-step explanation:

x – 3y + 10 = 0 x = 3y - 10 ... plug in

x² + y² = 10

(3y-10)² + y² = 10

10y² - 60y +90 = 0

y² - 6y + 9 = 0

(y - 3)² = 0

y = 3

x = - 1

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Jen picked 3/4 of a gallon of strawberries in a half an hour.If she keeps picking strawberries at the same rate, how many gallon

sp2606 [1]

Answer:

3 gallons.

Step-by-step explanation:

We have been given that Jen picked 3/4 of a gallon of strawberries in a half an hour.

Let us convert our given time in minutes.

1 hour= 60 minutes.

1/2 hour= 30 minutes.

So 2 hours= 120 minutes.

Let us find the number of gallons of strawberries picked by Jen in 30 minutes by dividing 3/4 by 30.

$\text{The number of gallons of strawberries picked by Jen in 30 minutes}=\frac{\frac{3}{4} }{30}$

$\text{The number of gallons of strawberries picked by Jen in 30 minutes}=\frac{3}{4*30}$

$\text{The number of gallons of strawberries picked by Jen in 30 minutes}=\frac{1}{40}$

Now let us multiply 1/40 by 120 to find the number of gallons of strawberries picked by Jen in 120 minutes(2 hours).

$\text{The number of gallons of strawberries picked by Jen in 30 minutes}=120*\frac{1}{40}$

$\text{The number of gallons of strawberries picked by Jen in 30 minutes}=3$

Therefore, Jen picked 3 gallons of strawberries in 2 hours.

8 0

3 years ago

What is the solution to this system?

Elza [17]

Answer:

Equation Form: x=−2,y=−2

Step-by-step explanation:

Eliminate the equal sides of each equation and combine.

3/2x+1=−x−4

Solve 3/2x+1=−x−4

for x. x=−2

Evaluate y when x=−2.

y=−2

The solution to the system is the complete set of ordered pairs that are valid solutions.

(−2,−2)

The result can be shown in multiple forms.

Point Form:

(−2,−2)

Equation Form:

x=−2,y=−2

7 0

3 years ago

Use the equation Y= 11 - 5X to find y when x=7.

kap26 [50]

Plug in x = 7. Then use the order of operations (PEMDAS) to simplify
y = 11 - 5*x
y = 11 - 5*7 .... x has been replaced with 7 (since x = 7 is given)
y = 11 - 35
y = -24

7 0

3 years ago

Read 2 more answers

13. For what value of b would the following system of equations have an infinite number of solutions?

tiny-mole [99]

Answer:

b=2

Step-by-step explanation:

we have

9x+12y=21 -----> equation A

6x+8y=7b ----> equation B

we know that

If the system of equations have an infinite number of solutions then the equation A must be equal to the equation B

Multiply equation B by 1.5 both sides

1.5*[6x+8y[=7b*1.5

9x+12y=10.5b ----> equation C

Compare equation A and equation C

9x+12y=21 -----> equation A

9x+12y=10.5b ----> equation C

For the equations to be equal it must be fulfilled that

21=10.5b

solve for b

b=21/10.5

b=2

5 0

4 years ago

The volume of a hemisphere is 144 pi. Find the radius and total surface area.

sineoko [7]

Formula of the Volume of a hemisphere:
V = $\frac{2}{3}$ $\pi$ r³
144 $\pi$ = $\frac{2}{3}$ $\pi$ r³
Multiply by 3 to cancel fraction in the right side
144 $\pi$ × 3 = 2 $\pi$ r³
432 $\pi$ = 2 $\pi$ r³
Divide by 2 $\pi$ on either sides to isolate r³
$\frac{432 \pi }{2 \pi }$ = $\frac{2 \pi }{2 \pi }$ r³
2 $\pi$ and $2 \pi$ cancel out
216 = r³
Take cube root to find the radius
$\sqrt[3]{216}$ = $\sqrt[3]{r^3}$
6 = r
Radius is 6 units

The formula of the surface area of a hemisphere is:
S.A = 2 $\pi$ r² + $\pi$ r²
= $2\pi$ (6)² + $\pi$ (6)²
=2 $\pi$ × 36 + 36 $\pi$
= 72 $\pi$ + 36 $\pi$
= 108 $\pi$ units² (in terms of $\pi$ )
≈ 339.12 units²

Surface area = 108 $\pi$ units

8 0

3 years ago