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3 years ago

12

To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before ad

ding the equations together? First Equation: 5x − 4y = 28 Second equation: 3x - 9y = 30

2 answers:

jek_recluse [69]3 years ago

8 0

Answer:

The first equation should be multiplied by 9 and the second equation by −4.

Step-by-step explanation:

vovikov84 [41]3 years ago

6 0

Answer:

use -9 to multiply the first equation

use -4 to multiply the second equation.

Step-by-step explanation:

5x-4y=28.....eqn (1)×-9

3x-9y=30....eqn(2)×-4

-45x+36y=-252

-(-12x+36y=-120)

therefore, -33x÷33 =-132÷-33

x=4.

substitute (x=4) in any of the equation. I'm just going to use eqn 1.

5x-4y=28

5(4)-4y=28

20-4y=28

-4y =28-20

-4y÷-4 = 8÷-4

y=-2

so, x=4, y=-2

Note: for proof of answers substitute the answers for x and y and see if you have the same result...e.g

5(4)-4(-2)=28.

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A point moves along the curve y = √ x in such a way that the y-component of the position of the point is increasing at a rate of

Eduardwww [97]

Answer:

The value of x component changes at a rate of $\frac{dx}{dt}=4\sqrt{x}$ units per second

Step-by-step explanation:

We are given that $y=x^{\frac{1}{2}}$

Differentiating on both sides with respect to time we get

$\frac{dy}{dt}=\frac{d\sqrt{x}}{dt}\\\\\frac{dy}{dt}=\frac{1}{2}x^{\frac{-1}{2}}(\frac{dx}{dt})\\\\\frac{dy}{dt}=\frac{1}{2\sqrt{x}}\frac{dx}{dt}$

It is given that $\frac{dy}{dt}=2units/sec$

Solving for $\frac{dx}{dt}$ we get

$\frac{dx}{dt}=\frac{dy}{dt}\times 2\sqrt{x}\\\\\frac{dx}{dt}=4\sqrt{x}$

5 0

3 years ago

Which is NOT true?<br> A. 16 + 3 = 11 + 8<br> B. 16 = 16<br> C. 16 - 4 = 7 + 6<br> D. 16 = 19 - 3

Yuliya22 [10]

Answer:

A

Step-by-step explanation:

16+3:19

11+8:19

19=19

6 0

3 years ago

Read 2 more answers

It is 3{:}32\text{ p.M.}3:32 p.M.3, colon, 32, start text, space, p, point, m, point, end text and Emma has gymnastics lessons a

Verizon [17]

Answer:

148 minutes

Step-by-step explanation:

It is 3{:}32\text{ p.M.}3:32 p.M.3, colon, 32, start text, space, p, point, m, point, end text and Emma has gymnastics lessons at 6{:}00\text{ p.M.}6:00 p.M.6, colon, 00, start text, space, p, point, m, point, end text How many minutes are there until Emma's gymnastics lessons?\

The time is 3:32 pm

Emma's gymnastics lesson is at 6:00 pm

6:00 pm - 3:32 pm = 2 hours 28 minutes

That is, we have 28 minutes before 4:00 pm

And 2 hours from 4:00 pm to 6:00 pm making a total of 2 hours 28 minutes

How many minutes are there until Emma's gymnastics lessons?

Convert 2 hours 28 minutes to minutes

1 hour = 60 minutes

2 hours = 60 minutes × 2 = 120 minutes

120 minutes + 28 minutes = 148 minutes

2 hours 28 minutes to minutes = 148 minutes

4 0

3 years ago

Solve the proportional<br> equation below:<br> x/4 = x-6/3

aleksandrvk [35]

<h2><u>PROPORTIONAL EQUATION</u></h2><h3>Exercise</h3>

Apply the means-extremes property of proportions: this allows you to cross multiply:

$\boxed{\mathsf{\dfrac{x}{4} = \dfrac{x - 6}{3}}}$

$\mathsf{\dfrac{x}{4} \searrow \dfrac{x - 6}{3}}$ ‏‏‎ ‏‏‎‎ $\mathsf{\dfrac{x}{4} \nearrow \dfrac{x-6}{3}}$ ‏‏‎‎

$\boxed{\mathsf{3x = 4(x - 6)}}$

Apply the distributive property:

$\mathsf{3x = 4(x-6)}$

$\mathsf{3x = 4(x) - 4(6)}$

$\mathsf{3x = 4x - 24}$

Add 24 to both sides:

$\mathsf{3x + 24 = 4x - 24 + 24}$

$\mathsf{3x + 24 = 4x}$

Substract 3x to both sides

$\mathsf{3x - 3x + 24 = 4x - 3x}$

$\mathsf{24 = 4x - 3x}$

$\large{\boxed{\mathsf{24 = x}}}$

‎ ‏‏‎

<h3><u>Answer</u>. The value of x = 24.</h3>

‎ ‏‏‎

8 0

3 years ago

According to a polling organization, 24% of adults in a large region consider themselves to be liberal. A survey asked 200 resp

Varvara68 [4.7K]

Answer:

$z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47$

Now we can calculate the p value based on the alternative hypothesis with this probability:

$p_v =P(z>4.47)=0.00000391$

The p value is very low compared to the significance level of $\alpha=0.05$ then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24

Step-by-step explanation:

Information given

n=200 represent the random sample taken

X=75 represent the number of people Liberal

$\hat p=\frac{75}{200}=0.375$ estimated proportion of people liberal

$p_o=0.24$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true proportion of adults liberal is higher than 0.24:

Null hypothesis: $p \leq 0.24$

Alternative hypothesis: $p > 0.24$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47$

Now we can calculate the p value based on the alternative hypothesis with this probability:

$p_v =P(z>4.47)=0.00000391$

The p value is very low compared to the significance level of $\alpha=0.05$ then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24

6 0

3 years ago