Choose the polynomial written in standard form.

H(x) = x^2+6 g(x) = 8x-5 show that hg(x)=19 simplifies to 16x^2 - 20x + 3 = 0

Studentka2010 [4]

Answer:

h(x)=x²+6 and g(x)=8x-5

prove that hg(x)=19

Step-by-step explanation:

step 1: hog(x)=h[g(x)]

step 2: h(8x-5)

step 3: h(8x-5)= (8x-5)²+6

step 4: (8x-5)(8x-5)+6

step 5: 16x² +15x +6

6 0

3 years ago

A pet store sells goldfish and hermit crabs,

Elis [28]

Answer:

$Cost = \$28$

Step-by-step explanation:

Given

Represent Goldfish with g and hermit crabs with h.

The first statement, we have:

$7g + 3h = 26$

The second statement, we have:

$4g + 5h = 28$

Required

Determine the selling price of 6 goldfish and 4 hermit crabs

The equations are:

$7g + 3h = 26$ --- (1)

$4g + 5h = 28$ --- (2)

Make g the subject in (2)

$4g + 5h = 28$

$4g = 28 - 5h$

Divide both sides by 4

$g = \frac{1}{4}(28 - 5h)$

Substitute $\frac{1}{4}(28 - 5h)$ for g in (1)

$7g + 3h = 26$

$7(\frac{1}{4}(28 - 5h)) + 3h = 26$

$\frac{7}{4}(28 - 5h) + 3h = 26$

Multiply through by 4

$4 * \frac{7}{4}(28 - 5h) + 4*3h = 26*4$

$7(28 - 5h) + 4*3h = 26*4$

Open bracket

$196 - 35h + 12h = 104$

$196 -23h = 104$

Collect Like Terms

$-23h = 104-196$

$-23h = -92$

Make h the subject

$h = \frac{-92}{-23}$

$h = \frac{92}{23}$

$h = 4$

Substitute 4 for h in $g = \frac{1}{4}(28 - 5h)$

$g = \frac{1}{4}(28 - 5*4)$

$g = \frac{1}{4}(28 - 20)$

$g = \frac{1}{4}(8)$

$g = 2$

This implies that:

1 goldfish = $2

1 hermit crab = $4

The cost of 6 goldfish and 4 hermit crabs is:

$Cost = 6g + 4h$

$Cost = 6*\$2 + 4*\$4$

$Cost = \$12 + \$16$

$Cost = \$28$

5 0

3 years ago

What’s the common multiples for 12 and 30

jasenka [17]

Hi!

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 30: 1, 2, 3, 5, 6, 10, 30

Explanation: This question is super super easy. This question should be the least common multiples. First find the prime factorization of 12. It gave us 2*2*3=12. Then the prime factorization of 30. It gave us 2*3*5=30. You can also multiply each factors the greater number of times and it occurs to in steps 1 or step 2 and it gave us LCM=2*2*3*5=60. The least common multiple factors is 60 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie

6 0

3 years ago

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Paula has her own business making cakes for

djverab [1.8K]

Answer:

Since Paula has her own business of making cakes for special occasions, and the total price (P) of one of Paula's cakes is represented by the equation P = 0.75S +10, where S is the number of people the cake serves, for determine what does the 0.75 represent in this situation and what does the 10 represent in this equation, the following mathematical reasoning must be carried out:

P is the price of the cake

S is the number of servings

Therefore, 0.75 is the value of each serving, which can be variable (the number of servings can vary)

In turn, 10 is the fixed cost of each cake.

4 0

3 years ago

west palm beach, florida, gets rain about 16 percent of the time. on how many days out of 400 can residents of west palm beach p

Lubov Fominskaja [6]

Remember that 16%=16/100=0.16

If it rains 16% of the time, out of 400 days...

400*0.16=64days

you can predict they'll get 64days of rain

Answer=64days

4 0

3 years ago

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