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valentina_108 [34]
1 year ago
9

the value of a varies directly as the square of the value of b, and b=3 when a=10. Find the value of a when b=9.

Mathematics
1 answer:
Charra [1.4K]1 year ago
4 0

Answer:

answer = 90

Step-by-step explanation:

General equation:  a = k*b^2

Specifically:          10 = k*(3)^2 = 9 k

Solving for k:  k = 10/9

Then a = (10/9)b^2.    If b = 9, then a = (10/9)(9)^2 = 90 (answer)

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A 7 kg ham costs $19/kg. Find the cost per pound.
stepan [7]

Answer: \$8.62/\text{Pound}

Step-by-step explanation:

Given

There is 7\ kg of ham available which costs

cost=\$\ 19/kg

i.e.

1\ kg\ \text{costs}\ \$19

and we know

1\ kg=2.204\ \text{pound}

So, 2.204\ \text{Pound costs}\ \$19

thus 1\ \text{Pound costs}\ \dfrac{19}{2.204}=\$8.62/\text{Pound}

4 0
2 years ago
2. A machine burns m gallons of oil each hour on weekends and ngallons each hour on weekdays. How many gallons of oil are burned
Lynna [10]

The question says the machine uses up m gallons of oil each hour on weekends.

This means that if the machine works for 24 hours each day, it implies that:

\text{Total amount of oil used up in a day = 24}\times m=24m

There are only two days on weekends i.e. Saturday and Sunday.

This means that if the amount of oil used in 1 day in the weekend is 24m, then we can say:

Saturday: oil used is 24m

Sunday: oil used is 24m

Total oil used during the weekend is:

24m+24m=48m

4 0
10 months ago
Which pair of triangles can be proven congruent by SAS?
ivolga24 [154]

Answer:

Second option

Step-by-step explanation:

They have two congruent pairs of sides and one congruent pair of angles.

4 0
2 years ago
A metalworker has a metal alloy that is 25% copper and another alloy that is 60% copper.How many kilograms of each alloy should
Neporo4naja [7]

Answer:

20kg of 25% copper alloy

30kg of 60% copper alloy

Step-by-step explanation:

There are 2 kinds of metal, first metal(A) have 25% copper while the second metal(B) has 60% copper. The metalworker want to create 50kg of metal, which means the total weight of both metals is 50kg (A+B = 50). The metalworker also want the metal made of a 46% which is 23kg(0.25A + 0.6B = 0.46*50). From these sentences, we can derive 2 equations. We can solve this with substitution.

A+B = 50

A= 50-B

Let's put the first equation into the second.

0.25A + 0.6B = 0.46 *50

0.25(50-B) + 0.6B =23

12.5 - 0.25B + 0.6B =23

0.35B=23 -12.5

B= 10.5/ 0.35= 30

Then we can solve A

A= 50-B

A= 50-30

A=20

8 0
3 years ago
Find the center and the radius of the circle with the equation: <br> x2+6x+y2+4y+12=0
Andrews [41]

Answer:

centre = (- 3, - 2) , radius = 1

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + 6x + y² + 4y + 12 = 0 ( subtract 12 from both sides )

x² + 6x + y² + 4y = - 12

Use the method of completing the square on the x and y terms

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(3)x + 9 + y² + 2(2)y + 4 = - 12 + 9 + 4

(x + 3)² + (y + 2)² = 1 ← in standard form

with centre = (- (- 3), - (- 2)) and r² = 1, that is

centre = (- 3, - 2) and radius = 1

8 0
3 years ago
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