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Lady bird [3.3K]
3 years ago
8

Matthew is going to drive from Salt Lake City, Utah, to Las Vegas, Nevada. His car travels a consistent

Mathematics
1 answer:
Eddi Din [679]3 years ago
5 0

Answer: 14 gallons of gasoline.

Step-by-step explanation:

given data:

25(x + 3) = 424

where x is the number of gallon of gasoline needed to purchase.

Solution.

25(x + 3) = 424

first we open the bracket

25x + 75 = 424

collect like terms

25x = 424 – 75

25x = 349

divide both sides by 25

25x/25 = 349/25

x = 13.96

x = 14

mathew needs to get 14 gallons of gasoline.

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What is In 7 days, a group of workers can plant 21 acres. What is their rate in acres per day?
FromTheMoon [43]
So do 21/7 to give you how much they do in a day. The answer is three so they do 3 aceres in a day.
8 0
3 years ago
Explain why there can be no infinite geometric series with a first term of 12 and a sum of 5.
Iteru [2.4K]

Answer:

Step-by-step explanation:

When you find the sum of a number you are adding two or more numbers together. therefore the only answer that you could use to get a sum of 5 when your first term is 12 would be -7

3 0
3 years ago
4: Please help. What is the equation for ⨀C?
TEA [102]
It’s the second option
7 0
3 years ago
Read 2 more answers
List all possible rational roots. Then use synthetic division to confirm which rational roots exist:
Kisachek [45]

Answer:

\boxed{(1) \, x = \, \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10; (2) \, x = -2}

Step-by-step explanation:

2x³+ 6x² - x - 10 = 0

(1) Possible roots

The Rational Roots Theorem states that, if a polynomial has any rational roots, they will have the form p/q, where p is a factor of the constant term  and q is a factor of the leading coefficient.

\text{Possible rational root} = \dfrac{ p }{ q } = \dfrac{\text{factor of constant term}}{\text{factor of leading coefficient}}

In your function, the constant term is -10 and the leading coefficient is 2, so

\text{Possible root} = \dfrac{\text{factor of 10}}{\text{factor of 2}}

Factors of 10 = ±1, ±2, ±5, ±10

Factors of 2 = ±1, ±2

\text{Possible roots are } \large \boxed{\mathbf{x = \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10}}

(2) Synthetic division

Rather than work through all 12 possibilities, I will do one that works.

\begin{array}{r|rrrr}-2 & 2 & 6 & -1 & -10\\& & -4& -4 & 10\\& 2 & 2& -5 & 0\\\end{array}

So, x = -2 is a root, and the quotient is 2x² + 2x - 5.

(3) Check for other rational roots

2x² + 2x - 5 = 0

D = b² - 4ac =2²- 4(2)(-5) = 4 + 40 = 44

√44 = 2√11, which is irrational.

Since irrational roots come in pairs, the cubic equation has two real, irrational roots and one rational root at x = -2.

6 0
3 years ago
Factor: 9x^2 + 15x.
slega [8]

Answer:

3(3x^2 + 5)

Step-by-step explanation:

step 1: find out the greatest common factor (GCF) of the number 9 and 15

ex: 9x^2 + 15x   (3 * 3x^2 + 3 * 5)

step 2: factor out the common term 3

ex: 3 * 3x^2 + 3 * 5   (3 * 3x^2 + 5)

step 3: simplify the equation

3 * 3x^2 + 5   [3(3x^2 + 5)]

6 0
2 years ago
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