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2 years ago

Algebraically show that each of the given combinations are equivalent to the given functions.

Mathematics

1 answer:

BlackZzzverrR [31]2 years ago

6 0

Answer:

Yes they ate Equivalent

Step-by-step explanation:

Given the expression

h(x) = - 3x – 1;j(x) = – 7x + 11 ; k(x) = 21.22 – 262 – 11

H(x)•j(x) = (-3x-1)(-7x+11)

H(x)•j(x) = (-3x)(-7x)-3x(11)-1(-7x)(-1)(11)

H(x)•j(x) = 21x²-33x+7x-11

H(x)•j(x) = 21x²-26x-11

This shows that H(x)•j(x) = k(x)

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There are three different cubes such that the first cube is 64 times the volume of the second, and the volume of the second cube

tankabanditka [31]

Answer:

4/3

Step-by-step explanation:

If the ratio between the volumes of the first and the second cube is 64, the ratio between the sides is the cubic root of the ratio between the volumes, so:

$V1 / V2 = 64$

$s1 / s2 = \sqrt[3]{64} = 4$

Doing the same for the second and third cubes, we have:

$V2 / V3 = 1/27$

$s2/ s3 = \sqrt[3]{1/27} = 1/3$

So the ratio of the first cube side and the third cube side is:

$s1 / s3 = (s1/s2) * (s2/s3) = 4 * (1/3) = 4/3$

5 0

2 years ago

Suppose the current cost of gasoline is

Elodia [21]

Answer:

The current price index number is $604.2.

Step-by-step explanation:

The index value is the ratio between the current value and the reference value, multiplied by 100.

In this problem, we have that:

Current value = $3.48

Reference value: $0.576

Index price = (3.48/0.576)*100 = $604.2.

The current price index number is $604.2.

4 0

3 years ago

Find the number of permutations of the letters in twelve<br>

kifflom [539]

Answer:

360

Step-by-step explanation:

Six letters in twelve with a repeated e would be 6! ÷ 2

6 0

2 years ago

Bethany opened a store credit card to purchase a TV for $589. She put the entire purchase on the credit card. Her APR is 29.99%

7nadin3 [17]

Original debt = $589
APR = 29.99%
The monthly rate is 0.2999/12 = 0.02499

After 1 month:
Amount owed = 589*1.02499 = $603.72
5% payment = 0.05*603.72 = $30.187
New balance = $603.72 - 30.187 = $573.53

After 2 months:
Amount owed = 573.53*1.02499 = $587.87
5% payment = 0.05*587.87 = $29.39
New balance = 587.87 - 29.39 = $558.48

After 3 months:
Amount owed = 558.48*1.02499 = $572.44
5% payment = 0.05*572.44 = $28.62
New balance = 572.43 - 28.62 = $543.82

Answer: $543.82

4 0

2 years ago

Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands

Black_prince [1.1K]

When the rock hits the ground, y = 0

-.005x^2 +0.41x -5.1 = 0

Multiply equation by (-200)

x^2 -82x +1020 = 0

Use quadratic formula:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{82 \pm \sqrt{82^2 -4(1)(1020)}}{2} \\ \\ x = \frac{82 \pm 51.4198}{2} \\ \\ x = 15.29 , 66.71$

Since the ball is initially below the ground, on its way up it will reach the point where y=0 but still be in the air, therefore the ball lands the second time y=0 or when x is larger.

Answer: 66.71 feet

6 0

3 years ago

Read 2 more answers