All categories

3 years ago

Which property is used in the statement? If z=3+1, then 3+1=z

1 answer:

4 0

This is the symmetric property of equality, and in a more general form it can be written as: if a=b then b=a.

This is not to be confused with communicative property, which says that the order doesn't matter in some operations, such as addition, and can be written as a+b=b+a

You might be interested in

Pleasssseeee hellllpllllllppppp???????

olchik [2.2K]

Answer:

f(x) and g(x) are inverse functions

Step-by-step explanation:

In the two functions f(x) and g(x) if, f(g(x)) = g(f(x)) = x, then

f(x) and g(x) are inverse functions

Let us use this rule to solve the question

∵ f(x) = 3x²

∵ g(x) = $\sqrt{\frac{x}{3}}$

→ Find f(g(x)) by substitute x in f(x) by g(x)

∴ f(g(x)) = 3( $\sqrt{\frac{x}{3}}$ )²

→ Cancel the square root with power 2

∴ f(g(x)) = 3( $\frac{x}{3}$ )

→ Cancel the 3 up with the 3 down

∴ f(g(x)) = x

→ Find g(f(x)) by substitute x in g(x) by f(x)

∴ g(f(x)) = $\sqrt{\frac{3x^{2}}{3}}$

→ Cancel the 3 up with the 3 down

∴ g(f(x)) = $\sqrt{x^{2}}$

→ Cancel the square root with power 2

∴ g(f(x)) = x

∵ f(g(x)) = g(f(x)) = x

→ By using the rule above

∴ f(x) and g(x) are inverse functions

5 0

2 years ago

Given: PRST is a square

xxTIMURxx [149]

Answer:

$(1-\sqrt{2})a^2$

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

$PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a$

Thus,

$MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a$

Consider isosceles triangle MSC. In this triangle

$MS=MC=(\sqrt{2}-1)a.$

The area of this triangle is

$A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}$

Consider right triangle PTS. The area of this triangle is

$A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}$

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

$A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2$

5 0

3 years ago

Can u guys pls help me on this question and pls explain how u got the answer

Lady_Fox [76]

Answer:

55.75

Step-by-step explanation:

find the area of 1 side using the base and height and divide that answer by 2

5x6=30 30 divided by 2=15

all sides are equal so each side is 15

the base you do the same thing.

base is 5, height is 4.3

4.3 x 5= 21.5

divide it by 2 10.75

side 1=15

side 2= 15

side 3=15

base 1= 10.75

add all together

55.75

8 0

2 years ago

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 900 vot

Stells [14]

Answer:

$z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00$

Now we can calculate the p value. Since is a bilateral test the p value would be:

$p_v= P(Z>2) =0.0228$

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%

Step-by-step explanation:

Information given

n=900 represent the random sample selected

$\hat p=0.75$ estimated proportion of residents favored annexation

$p_o=0.72$ is the value that we want to test

represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

The political strategist wants to test the claim that the percentage of residents who favor annexation is above 72%.:

Null hypothesis: $p\leq 0.72$

Alternative hypothesis: $p > 0.72$

The statistic for this case is given by:

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

Replacing the data given we got:

$z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00$

Now we can calculate the p value. Since is a bilateral test the p value would be:

$p_v= P(Z>2) =0.0228$

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%

3 0

3 years ago

I need help on this.

liraira [26]

If the triangles are similar, the proportion of the legs on the left to the legs on the right will be equal. This proportion would look like:

$\frac{2x+1}{3x}=\frac{10}{14}$

(You needed to combine the orange segment and the yellow segment to find the total length of the large triangle).

Now, cross multiply and solve for x:

28x+14=30x

*Subtract 28x from both sides to isolate the variable*

14=2x

*Divide both sides by 2*

7=x

Hope this helps!!

7 0

3 years ago