Solve: negative 1 over 2 x + 2 = −x + 7 (5 points)

True or false: arc measure is the same length as arc length

STatiana [176]

Answer:

true

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Solve the system of linear equations for x and y.(cos θ)x + (sin θ)y=1(−sin θ)x + (cos θ)y = 0x=y=

lys-0071 [83]

Answer:

$\bold{x =cos\theta}\\\bold{y=sin\theta}$

Step-by-step explanation:

The given system of linear equations is:

$(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0$

We have to solve the equations for the values of $x, y$ .

Let us use elimination method in which we eliminate one of the variables from the two variables.

For this, let us multiply the first equation by $sin\theta$ and second equation by $cos\theta$

Now, the equations become:

$(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)$

Now, let us add (1) and (2):

$(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta$

Using the equation:

$(-sin\theta)x+(cos\theta)y=0$

Putting value of $y$ :

$\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta$

So, the answer to the system of linear equations is:

$\bold{x =cos\theta}\\\bold{y=sin\theta}$

7 0

3 years ago

F(x) = x5 + (x + 3)2 x=-1

sveticcg [70]

Hello!

You put -1 in for x

F(-1) = (-1)^5 + (-1 + 3)^2

F(-1) = -1 + (2)^2

F(-1) = -1 + 4

F(-1) = 3

The answer is 3

Hope this helps!

8 0

3 years ago

To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of t

ivolga24 [154]

Answer:

$p_v =P(t_{(29)}>1.42)=0.0831$

For this case the p value calculated is higher than the significance level used of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and the best conclusion for this case would be:

a) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100

Step-by-step explanation:

Information given

We want to verify if he mean IQ of employees in an organization is greater than 100 , the system of hypothesis would be:

Null hypothesis: $\mu \leq 100$

Alternative hypothesis: $\mu > 100$

The statistic for this case is given by:

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

The statistic calculated for this case $t_{calc}= 1.42$

The degrees of freedom are given by:

$df=n-1=30-1=29$

Now we can find the p value using tha laternative hypothesis and we got:

$p_v =P(t_{(29)}>1.42)=0.0831$

For this case the p value calculated is higher than the significance level used of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and the best conclusion for this case would be:

a) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100

5 0

3 years ago

Factor 24g - 36h. Remember that your answer needs to be factored completely.

Diano4ka-milaya [45]

Answer:

<h2>The completed factor is $=12(2g- 3h)$ </h2>

Step-by-step explanation:

To factor the expression we need to look for a value that is unique to both terms in the expression.

Given the expression

$24g - 36h$

The available factors common to both terms are 2,3,4,6,8,12. but since we are expected to factor the expression completely we will use the greatest common factor (gcf) to find the solution

The greatest but common factor is 12, hence we have

$=12(2g- 3h)$

5 0

3 years ago