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pantera1 [17]
3 years ago
7

Which number is a solution of the inequality? 6 ≥ 6k?

Mathematics
1 answer:
german3 years ago
8 0
This isnt a inequality
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Philip made a total of 9 bracelets and necklaces from 120 inches of cord. He used 8 inches of cord for each bracelet and 20 inch
Viktor [21]

Answer:

So Philip made 5 bracelets and 4 necklaces.

Step-by-step explanation:

Let x = number of bracelets and y = number of necklaces.

Since we have a total of 9 bracelets and necklaces,

x + y = 9 (1)

Also, we have 8 inches of cord for each bracelet and 20 inches of cord for each necklace, then the total length for the bracelet is 8x and that for the necklace is 20y.

So, the total length for both is 8x + 20y. Since the total length of cord used is 120 inches,

8x + 20y = 120 (2)

Simplifying it we have

2x + 5y = 30  (3).

Writing equations (1) and (3) in matrix form, we have

\left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}9\\30\end{array}\right]

Using Cramer's rule to solve for x and y,

x = det \left[\begin{array}{ccc}9&1\\30&5\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

x = (9 × 5 - 30 × 1) ÷ (1 × 5 - 1 × 2)

x = (45 - 30) ÷ (5 - 2)

x = 15 ÷ 3

x = 5

y = det \left[\begin{array}{ccc}1&9\\2&30\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

y = (30 × 1 - 9 × 2) ÷ (1 × 5 - 1 × 2)

y = (30 - 18) ÷ (5 - 2)

y = 12 ÷ 3

y = 4

So Philip made 5 bracelets and 4 necklaces.

3 0
3 years ago
What is the percent equation for 46% of 127?
Brut [27]

Answer:

46% of 127 is 58.42

Step-by-step explanation:

46/100 = x/127

Cross multiply

46 × 127 = 100 × x

5,842 = 100x

Divide both sides by 100

58.42 = x

3 0
3 years ago
In sunlight, a vertical stick has a height of 5 ft and casts a shadow 3 ft long at the same time that a nearby tree casts a shad
leva [86]
The tree is 25 feet tall. Given the height of the stick and the shadow it cast, the angle formed by the sun and the stick's height can be obtained by taking the Inverse Tangent of 3/5. This is equal to 30.93. This angle is equal to the angle formed by the sun and the tree's height. Using the tangent formula, Tan (30.93)=tree's shadow (15 ft)/ height of the tree, giving the answer 25 feet.
7 0
3 years ago
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the volume V of a gas at a constant temperature varies inversely with the pressure P. when the volume is 100 cubic inches the pr
fiasKO [112]

Answer:

The pressure is 20\ psi

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form y*x=k or y=k/x

In this problem we have

V*P=k

where

V is the volume of a gas at a constant temperature

P is the pressure

we have

For V=100\ in^{3},P=25\ psi

step 1

Find the value of k

substitute the values of V and P

100*25=k

k=2,500

The equation is equal to  V*P=2,500

step 2

Find the pressure when the volume is 125 cubic inches

For V=125\ in^{3}

substitute in the equation and solve for P

125*P=2,500

P=2,500/125=20\ psi

8 0
3 years ago
Find the probability of rolling an even number on a standard number cube.
inn [45]

Answer:

D as likely as not.

Step-by-step explanation:

......

7 0
3 years ago
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