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3 years ago

{y=2x+3 y=x+3 Solve the system of equations by graphing.

Mathematics

1 answer:

Vlad1618 [11]3 years ago

6 0

To solve this, graph both lines and the ordered pair where they intersect is your answer. (0, 3)

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Wyatt is working two summer jobs, making $8 per hour walking dogs and making $14 per hour tutoring. In a given week, he can work

VLD [36.1K]

Answer:

he spends 7 hours walking a dog and 6 hours tutoring

Step-by-step explanation:

you multiple 8 by 7 and get 56

then multiple 14 by 6 and get 84

you add 6 and 7 together and get 13 hours

you add 56 and 84 together and get 140

3 0

4 years ago

Which number line models the solution set of the following problem? One less than twice a number is no less than five. What is t

Nadya [2.5K]

Answer:

Option 1.

The solution set is: {n|n is a real number, n≥3}

Step-by-step explanation:

1. You must read carefully the information given in the problem: "One less than twice a number" indicates that you must write a number $n$ multiplied by 2 and subtract 1 from this term, as following:

$2n-1$

2. "is not less than five" indicates that the result must be equal or greater than 5. Then, you obtain the following expression:

$2n-1\geq5$

3. Now, you can solve for $n$ . Then, you obtain:

$2n-1\geq5\\2n\geq6\\n\geq\frac{6}{2}\\n\geq3$

4. Then, the solution set is: {n|n is a real number, n≥3}.

5. The correct plot on the number line must show a circle on 3 (You must fill in the circle if the sign is $\leq$ or $\geq$ ) with a line from that circle to the right.

5. Therefore, the answer is the first option.

7 0

3 years ago

Standard 6 sided die is weighted so that the probabilities of rolling 2,3,4,5 or 6 are equal and the probability of rolling 1 is

bulgar [2K]

There are 6 sides of the die, let us say that side 1 is S1, side 2 is S2 and so on.

Assigning a value of 3 to S1, so the probabilities are:

Probability

S1 = 3 3/8

S2 = 1 1/8

S3 = 1 1/8

S4 = 1 1/8

S5 = 1 1/8

S6 = 1 1/8

total = 8

The combinations that the sum of the two rolls will be 4 are:

S1 and S3

S3 and S1

S2 and S2

So the total probability is:

P = (3/8) * (1/8) + (1/8) * (3/8) + (1/8) * (1/8)

P = 0.1094 = 10.94%

So there is about 0.1094 or 10.94% probability that the sum will be 4.

6 0

3 years ago

Mark is playing baseball after school. He wants to find the total distance he will need to ride his bike from school to the park

Ymorist [56]

Use the distance formula (derived from Pythagorean Theorem:
$d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ = \sqrt{ {(10 - 8)}^{2} + {(11 - 7)}^{2} } \\ = \sqrt{ {(2)}^{2} + {(4)}^{2} } = \sqrt{4 + 16} \\ d = \sqrt{20}$
$d = \sqrt{20} = \sqrt{4} \times \sqrt{5} = 2 \sqrt{5}$

4 0

3 years ago

Read 2 more answers

The weight of Jane and Jessica was in the ratio of 8 : 9. Jane gained 2 kg while Jessica lost 4 kg. They then had the same weigh

postnew [5]

Answer:

48 kg

Step-by-step explanation:

The given relations can be used to write a system of equations for the two weights. Those can be solved to find Jane's weight.

<h3>setup</h3>

Let x and y represent Jane's and Jessica's original weight, respectively. The ratio of weights was ...

x/y = 8/9

After the changes in weight, they were equal:

x+2 = y-4

<h3>solution</h3>

Adding 4 to the second equation, we have an expression for y that can be substituted into the first equation.

y = x +6 . . . . . . . . . . solve the second equation for y

x/(x+6) = 8/9 . . . . . . substitute for y in the first equation

9x = 8(x +6) . . . . . . . multiply by 9(x+6)

x = 48 . . . . . . . . . . . simplify and subtract 8x

Jane weighed 48 kg at first.

_____

<em>Alternate solution</em>

The original difference in "ratio units" was 9-8 = 1 ratio unit. We find that this corresponds to 6 kg after the weight changes make the weights equal. Then 8 ratio units will be 8(6 kg) = 48 kg—Jane's original weight.

(This mental solution is virtually the same as the solution using equations shown above.)

3 0

2 years ago