What is the perimeter and area of the figure?

Finding angles June 23,2022

nikitadnepr [17]

Answer:

61 degrees

Step-by-step explanation:

Considering angle <GJI and <IKD, these two angles are corresponding angles. Recall that corresponding angles are equal hence,

m<GJI = m<IKD = 119 degrees

Again

m<GJI and m<AJG are on a straight line at a point. Recall that the sum of angles on a straight line is 180 degrees. Hence

m<GJI + m<AJG = 180

119 + m<AJG = 180

m<AJG = 180 - 119

= 61 degrees

8 0

3 years ago

Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form ModifyingBelow lim With h

Gre4nikov [31]

Answer:

$\dfrac{1}{2\sqrt{x}}$

Step-by-step explanation:

$f(x) = \sqrt{x} = x^{\frac{1}{2}}$

$f(x+h) = \sqrt{x+h} = (x+h)^{\frac{1}{2}}$

We use binomial expansion for $(x+h)^{\frac{1}{2}}$

This can be rewritten as

$[x(1+\dfrac{h}{x})]^{\frac{1}{2}}$

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}$

From the expansion

$(1+x)^n=1+nx+\dfrac{n(n-1)}{2!}+\ldots$

Setting $x=\dfrac{h}{x}$ and $n=\frac{1}{2}$ ,

$(1+\dfrac{h}{x})^{\frac{1}{2}}=1+(\dfrac{h}{x})(\dfrac{1}{2})+\dfrac{\frac{1}{2}(1-\frac{1}{2})}{2!}(\dfrac{h}{x})^2+\tldots$

$=1+\dfrac{h}{2x}-\dfrac{h^2}{8x^2}+\ldots$

Multiplying by $x^{\frac{1}{2}}$ ,

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}=x^{\frac{1}{2}}+\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots$

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}=\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots$

$\dfrac{x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}}{h}=\dfrac{1}{2x^{\frac{1}{2}}}-\dfrac{h}{8x^{\frac{3}{2}}}+\ldots$

The limit of this as $h\to 0$ is

$\lim_{h\to0} \dfrac{f(x+h)-f(x)}{h}=\dfrac{1}{2x^{\frac{1}{2}}}=\dfrac{1}{2\sqrt{x}}$ (since all the other terms involve $h$ and vanish to 0.)

8 0

3 years ago

1. If x = 2 and 3x + y = 5, what is the value of y?

Flura [38]

Answer:

y = -1

Step-by-step explanation:

3(2) + y = 5

6 + y = 5

-6

y = 5 -6

y = -1

3 0

3 years ago

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A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars

motikmotik

Answer:

$t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value for this case is given by:

$p_v =P(t_{(7)}$

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Step-by-step explanation:

Information given

$\bar X=25.5$ represent the sample mean

$s=1$ represent the sample standard deviation

$n=8$ sample size

$\mu_o =26$ represent the value to verify

$\alpha=0.06$ represent the significance level

t would represent the statistic (variable of interest)

$p_v$ represent the p value

Hypothesis to est

We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:

Null hypothesis: $\mu \geq 25.5$

Alternative hypothesis: $\mu < 25.5$

The statistic for this case is given by;

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

Replacing the info given we got:

$t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value for this case is given by:

$p_v =P(t_{(7)}$

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

3 0

4 years ago

Long division 25 dived by 2550

Elina [12.6K]

Answer:

25 divided by 2550 = 0.009803922

2550 divided by 25 = 102

Step-by-step explanation:

6 0

3 years ago

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