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3 years ago

Solve the simultaneous equation:2x+3y=13X+2y=9

Mathematics

1 answer:

Neko [114]3 years ago

8 0

Answer:

2x + 3y = 13

4x - y = -2

In the second equation, subtract 4x from both sides.

-y = -2 - 4x

Divide both sides by -1.

y = 2 + 4x

Put this into the first equation in place of y.

2x + 3(2 + 4x) = 13

Multiply everything in the parenthesis by 3.

2x + 6 + 12x = 13

Combine like terms.

14x + 6 = 13

Subtract 6 from both sides.

14x = 7

Divide 14 on both sides.

x = 7 / 14

x = 0.5

Put this into the second equation in place of x.

4(0.5) - y = -2

2 - y = -2

Subtract 2 from both sides.

-y = -4

Divide both sides by -1.

y = 4

So x = 0.5 and y = 4.

Step-by-step explanation:

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A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise

DiKsa [7]

Answer:

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, we failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.

Step-by-step explanation:

Refer to the attached data.

The Null and Alternate hypothesis is given by

Null hypotheses = H₀: μ₁ = μ₂

Alternate hypotheses = H₁: μ₁ ≠ μ₂

The test statistic is given by

$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }$

Where $\bar{x}_1$ is the sample mean of people who do not exercise regularly.

Where $\bar{x}_2$ is the sample mean of people who do exercise regularly.

Where $s_1$ is the sample standard deviation of people who do not exercise regularly.

Where $s_2$ is the sample standard deviation of people who do exercise regularly.

Where $n_1$ is the sample size of people who do not exercise regularly.

Where $n_2$ is the sample size of people who do exercise regularly.

$t = \frac{72.7 - 69.7}{\sqrt{\frac{10.9^2}{16} + \frac{8.2^2}{12} } }$

$t = 0.83$

The given level of significance is

1 - 0.95 = 0.05

The degree of freedom is

df = 16 + 12 - 2 = 26

From the t-table, df = 26 and significance level 0.05,

t = 2.056 (two-tailed)

Conclusion:

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, We failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.

4 0

3 years ago

OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME I A

natka813 [3]

Answer:

3. The equivalent fractions are presented as follows;

$\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}$

4. The equivalent fractions are presented as follows;

$\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}$

5. The reason why it works is because $\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}$

Step-by-step explanation:

3. Based on the shaded region of the given figures, the two fractions are equivalent

Mathematically, we can show the equivalency of the two fractions as follows;

$\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{2}{3} \times \dfrac{2}{2} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}$

Therefore;

$\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}$

4. From the shaded region of the given figure, the fractions are equivalent

Mathematically, we have;

$\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{4}{4} \times \dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}$

Therefore;

$\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}$

5. The amount of salt required by the recipe = 1/4 teaspoon of salt

The measure of the spoon Jonas has = 1/8 teaspoon

When Jonas adds two 1/8 teaspoons, he gets;

$\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1 + 1}{8} = \dfrac{2}{8} = \dfrac{2 \times 1}{2 \times 4} = \dfrac{2}{2} \times \dfrac{1}{4} = 1 \times \dfrac{1}{4} = \dfrac{1}{4}$

Therefore;

$\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}$

Two 1/8 measuring teaspoons are equivalent to one 1/4 teaspoons and therefore Jonas is able to get the 1/4 teaspoons of salt the recipe asks for b combining two 1/8 measuring teaspoons of salt he has because 1/8 + 1/8 = 1/4.

6 0

3 years ago

The rule which allows us to change the sign of an exponent is called the ____ rule.

Bogdan [553]

Answer:

The rule which allows us to change the sign of an exponent is called the negative exponent rule.

Step-by-step explanation:

Consider the provided information.

The negative exponent rule is the rule which allows to change the sign of an exponent.

$x^{-1}=\frac{1}{x}$

According to negative exponent rule: A negative exponents in the numerator moved to the denominator and become positive exponents.

If A negative exponents in the denominator moved to the numerator and become positive exponents.

Hence, the required statement is: The rule which allows us to change the sign of an exponent is called the negative exponent rule.

6 0

3 years ago

Find the area of the circle

vlada-n [284]

Answer:

A = 1.77 ft^2

Step-by-step explanation:

The circle has a diameter of 1.5 ft

We need the radius

r = d/2 = 1.5/2 = .75 ft

The area of a circle is

A = pi r^2

A = 3.14 ( .75)^2 = 1.76625

To the nearest hundredth

A = 1.77 ft^2

3 0

3 years ago

Twice c is at least 19

Sliva [168]

<h3>The value of c is greater than or equal to the value 9.5</h3>

2c ≥ 19

We can treat this inequality like a standard algebraic equation.

Divide both sides by 2.

c ≥ 9.5

7 0

3 years ago

Solve the simultaneous equation:2x+3y=13X+2y=9​

Solve the simultaneous equation:2x+3y=13X+2y=9