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3 years ago

Solve each given equation and show your work

Mathematics

1 answer:

vekshin13 years ago

6 0

Answer:

(b) $INFINITELY\: MANY\: SOLUTIONS$

(a) $30 = x;\: ONE\: SOLUTION$

Step-by-step explanation:

* If two expressions have the exact same <em>rate</em><em> </em><em>of</em><em> </em><em>change</em><em> </em>[<em>slope</em>], automatically, there is no solution.

4x + 8 = 2x + <u>7</u> + 2x <u>- 20</u>

4x + 8 = −13 + 4x

-4x - 4x

_________________

8 ≠ −13; NO SOLUTION

__________________________________________________________

25 - 4x = <u>15</u> - 3x + <u>10</u> - x

25 - 4x = −4x + 25; INFINITELY MANY SOLUTIONS

__________________________________________________________

6x + 4x - 6 = 24 + 9x

10x - 6 = 24 + 9x

-10x - 10x

_________________

−6 = 24 - x

-24 - 24

___________

−30 = −x

30 = x; ONE SOLUTION

I am joyous to assist you anytime.

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Solve the system of equations algebraically.

nordsb [41]

Answer: D

Step-by-step explanation:

$4x-3y=8\\5x-4y=5$

Let's take one of the equations and solve for a variable to use the substitution method.

$5x-4y=5\\5x=5+4y\\x=\frac{5+4y}{5}$

Now replace this in the first equation.

$4x-3y=8\\4(\frac{5+4y}{5})-3y=8\\\frac{20+16y}{5}-3y=8$

Separate the terms.

$\frac{20}{5}+\frac{16y}{5}-3y=8$

Solve 20/5

$4+\frac{16y}{5}-3y=8$

Subtract 4 from both sides to isolate y.

$4-4+\frac{16y}{5}-3y=8-4$

$\frac{16}{5}y-3y=4$

Solve the difference.

$\frac{16-(3)(5)}{5}y=4\\$

$\frac{16-15}{5} y=4$

$\frac{1}{5}y=4$

Multiply by the reciprocal or the inverted fraction that is next to y to isolate it.

$(\frac{5}{1} )(\frac{1}{5})y=4(\frac{5}{1})$

$y=20$

Now, in order to find x, replace y in any of the two equations.

$5x-4y=5\\5x-4(20)=5\\5x-80=5\\5x=5+80\\5x=85\\x=\frac{85}{5}\\x=17$

7 0

3 years ago

Michael ran 655 feet in 19 seconds jasmine ran 1 mile in 4 minutes and 24 seconds in miles per hour and to the nearest tenth how

Natalka [10]

Answer:

Step-by-step explanation:

<h3>Step 1: Convert miles to feet</h3>

First, we need to convert the miles to feet keeping in mind that:

1 mile = 5,280 feet

655 ft 19 sec

5,280 ft 4 min 24 sec

<h3>Step 2: Divide the distance by the time to find the unit rate</h3>

3,447 feet per minute

1,245 feet per minute

<h3>Step 3: Convert minutes to hours</h3>

206,820 feet per hour

74,700 feet per hour

<h3>Step 4: Convert feet to miles</h3>

39.17 miles per hour

14.15 miles per hour

To find how much faster Michael ran, we need one more step.

<h3>Step 5: Subtract smaller amount from larger amount</h3>

39.17 - 14.15 = 25

I'm always happy to help :)

4 0

3 years ago

Alicia earns $9.00 per hour working T a part-time job. She wants to earn more than $180 this week. How many hours does Alicia ha

Helga [31]

20 hours times $9 is $180. She would have to work over 20 hours to earn more than $180.

I would say 21 hours.

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4 years ago

Read 2 more answers

Sailboats use block and tackle systems to reduce the effort needed to move or raise the sails. If a block and tackle has five ro

nata0808 [166]

The mechanical advantage of the block and tackle is that it is easier to lift a lock using multiple parts of the rope that go around the system of pulleys. If there are no friction, the mechanical advantage is exactly equal to the number of parts of the rope that are attached to the load.

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3 years ago

Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 9 havi

QveST [7]

Answer: $(-0.48,\ -0.04)$

Step-by-step explanation:

The confidence interval for the difference of two population proportion is given by :-

$(p_1-p_2)\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}$

Given : The first sample consists of 20 people with 9 having a common attribute.

Here, $n_1=20$ , $p_1=\dfrac{9}{20}=0.45$

$n_2=2100$ , $p_1=\dfrac{1492 }{2100}\approx0.71$

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

A 95% confidence interval for the difference of two population proportion will be :-

$(0.45-0.71)\pm z_{\alpha/2}\sqrt{\dfrac{0.45(1-0.45)}{20}+\dfrac{0.71(1-0.71)}{2100}}\\\\\approx -0.26\pm0.22\\\\=(-0.26-0.22,-0.26+0.22)\\\\=(-0.48,\ -0.04)$

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4 years ago