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3 years ago

Solve the following system of equations -2x+y=1 -4x+y=-1

Mathematics

2 answers:

Setler [38]3 years ago

6 0

Answer:

(1, 3).

Step-by-step explanation:

-2x + y = 1

-4x + y = -1 Subtract :

-2x - (-4x) = 1 - (-1)

-2x + 4x = 2

2x = 2

x = 1.

Substitute x = 1 in the first equation:

-2(1) + y = 1

-2 + y = 1

y = 1 + 2

y = 3.

VladimirAG [237]3 years ago

4 0

Answer:

x = 1

y =

Step-by-step explanation:

-2x + y=1

-4x + y=-1

-2 (2) x + (2) y = (2) 1 (multilply by 2)

-4x + y=- 1

-4x + 2y = 2

-4x + y = -1

minus side by

y = 3

x =

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What is the value of x?

Phantasy [73]

Answer:

value of x = 5.8 mm

Step-by-step explanation:

We have given,

Two right triangles EDH and EDG.

In right triangle EDH, EH = 56mm , DH = 35 mm

Using Pythagoras theorem we can find ED.

i.e EH² = ED²+DH²

56²=ED²+35²

ED²=56²-35²

ED = √(56²-35²) = 7√39 = 43.71 mm

Now, Consider right triangle EDG

Here, EG=44.8mm , GD = x+4 and ED = 7√39

Again using Pythagoras theorem,

EG² = ED² + DG²

44.8²= (7√39)²+ (x+4)²

(x+4)² = 44.8² - (7√39)²

x+4 = √(44.8² - (7√39)²)

x+4 = 9.8

or x = 9.8 - 4 = 5.8 mm

Hence we got the value of x = 5.8 mm

6 0

3 years ago

A researcher tests five individuals who have seen paid political ads about a particular issue. These individuals take a multiple

devlian [24]

Answer:

$t=\frac{46-40}{\frac{5.148}{\sqrt{5}}}=2.606$

The degrees of freedom are given by:

$df=n-1=5-1=4$

The p value wuld be given by:

$p_v =2*P(t_{(4)}>2.606)=0.060$

For this case the p value is higher than the significance level so then we can conclude that the true mean is not significantly different from 40

The distribution with the critical values are in the figure attached

Step-by-step explanation:

Information given

48, 41, 40, 51, and 50

The sample mean and deviation can be calculated with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=46$ represent the mean height for the sample

$s=5.148$ represent the sample standard deviation

$n=5$ sample size

$\mu_o =40$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test

Hypothesis to test

We want to test if the true mean for this case is equal to 40, the system of hypothesis would be:

Null hypothesis: $\mu = 40$

Alternative hypothesis: $\mu \neq 40$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing we got:

$t=\frac{46-40}{\frac{5.148}{\sqrt{5}}}=2.606$

The degrees of freedom are given by:

$df=n-1=5-1=4$

The p value wuld be given by:

$p_v =2*P(t_{(4)}>2.606)=0.060$

For this case the p value is higher than the significance level so then we can conclude that the true mean is not significantly different from 40

The distribution with the critical values are in the figure attached

6 0

3 years ago

What is the standard for of (1 7i)(3-i)?

marissa [1.9K]

3 -1i + 21i -7i2 now you have to fix the last factore because you have to change the imaginery i this would give you the answer of 3 - 1i + 21i +7 now add common factor which would give you the final answer of 3 +20i +7

7 0

3 years ago

37. The sum of first three terms in an arithmetic progression is 24 and the sum of their squares is 224. Find the first three te

Airida [17]

Answer:

12, 8, and 4

Step-by-step explanation:

Given

a + d + a + a - d = 24

3a = 24 ⇒ [ a = 8 ]

and (a + d)² + a² + (a - d)² = 224

3a² + 2d² = 224

2d² = 224 - 192 = 32

d² = 16

[ d = ±4 ]

∴ The first three terms to A.P are

a + d = 8 + 4 = 12

a - = 8

a - d = 8 - 4 = 4

∴ Three terms are 12 , 8, and 4

8 0

2 years ago

The high school is hosting an event for seniors but will also allow some juniors to attend. The principal approved the event for

Flura [38]

Answer:

Step-by-step explanation:

The total is 200 and 25% are juniors so u multiply 200 by 25%

Hope this helps

Correct me if this is wrong

8 0

3 years ago

Read 2 more answers