Guided Practice
CPCTC
Given
KGK
H is the midpoint of GK
Prove:
Side FG - Side JK
Statement
Reason
es

The value of k in which a line is has a slope 1/4 passing through the points (4,6) and (12,k) is 8.The option is A.8

Slope of straight line(m) which is passing through the point is y=mx+c, where m= slope of the line c is the intercept and x and y are distance from the respective x-axis and y-axis.

The line is passing through the 2 points say (\(x_{1}\),\(y_{1}\)) and (\(x_{2}\), \(y_{2}\)) then m=\(\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\)we are having the points (4,6) and (12,k)( \(x_{1}\),\(y_{1}\)) and (\(x_{2}\),\(y_{2}\))and slope m=1/4.

Now substitute the values of( \(x_{1}\),\(y_{1}\)) and (\(x_{2}\),\(y_{2}\)) in m=\(\frac{x_{2}-x_{1} }{y_{2}-y_{1} }\).

\(\frac{1}{4}\)= \(\frac{k-6}{12-4}\),

4(k-6)= 8

4k-24=8

4k=32

k=\(\frac{32}{4}\)

k=8

The value of k in which a line is has a slope 1/4 passing through the points (4,6) and (12,k) is 8.The option is A.8

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Answer:

Step-by-step explanation:

No; it is rational.  25/9 is the ratio of two integers.

Explanation:

We have a fraction of two integers, so 25/9 is rational. A rational number is any fraction of two integers (as long as the denominator is not zero).

Something that is irrational would be pi = 3.14159... where we cannot write it as a fraction of two integers. We can get approximations such as 22/7, but we cannot land exactly on pi with a fraction like this. Another irrational value is sqrt(2).

Something like sqrt(25) is rational though because sqrt(25) = 5 = 5/1.

Using the graphical method for limits, it is found that:

\(\lim_{x \rightarrow 3} f(x) = 1\)

\(\lim_{x \rightarrow a} f(x) = \lim_{x \rightarrow a^+} f(x) = \lim_{x \rightarrow a^-} f(x)\)

In this problem, the definition as x goes to 3 is the same, hence:

\(\lim_{x \rightarrow 3} f(x) = \lim_{x \rightarrow 3^+} f(x) = \lim_{x \rightarrow 3^-} f(x) = 1\)

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Answer:

360 million written in scientific notation is 3.6 × 108.

Step-by-step explanation:

Answer: 450

Step-by-step explanation: 95+115+240=450

The classification of the ordered pairs as functions and not functions are as follows;

{(2, 2), (4, 4), (6, 6), (8, 8)} is a function

{(0, 3), (3, 5), (5, 6), (8, 4)} is a function

{(1, 2), (3, 3), (4, 8), (6, 3)} is a function

{(3, 4), (5, 2), (5, 6), (7, 3)} is not a function

A function is a rule, law or definition that maps the elements of a set of values known as the input, to the elements of a set of values known as the output, such that each element of the input element is mapped to exactly one output element.

The values in each of the set of ordered pairs can be arranged into an input and output set as follows;

{(2, 2), (4, 4), (6, 6), (8, 8)}

Input   \({}\) Output

2  \({}\)     ⇒    2

4      \({}\) ⇒    4

6 \({}\)      ⇒    6

8 \({}\)      ⇒    8

In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.

{(0, 3), (3, 5), (5, 6), (8, 4)}

Input   \({}\) Output

0  \({}\)     ⇒    3

3      \({}\) ⇒    5

5 \({}\)      ⇒    6

8 \({}\)      ⇒    4

In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.

{(1, 2), (3, 3), (4, 8), (6, 3)}

Input   \({}\) Output

1  \({}\)     ⇒    2

3      \({}\) ⇒    3

4 \({}\)      ⇒    8

6 \({}\)      ⇒    3

In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.

{(3, 4), (5, 2), (5, 6), (7, 3)}

Input   \({}\) Output

3  \({}\)     ⇒    4

5      \({}\) ⇒    2

5 \({}\)      ⇒    6

7 \({}\)      ⇒    3

In the above mapping, the input value of 5 has two output values of 2 and 6, therefore, the input, 5 maps to two values of the output, 2 and 6, which indicates that the relationship is not a function

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The solutions are where the two lines cross over each other.

(0,3) and (4,-5)

Answer:

-80

Step-by-step explanation:

Let's take this problem step-by-step:

If a line is parallel to each other:

 ⇒ their slope must be equal

Thus the line parallel to: \(y=\frac{3}{4}x-4\)

 ⇒ that line's slope: 3/4

The point-slope form is: \((y-y_1)=m(x-x_1)\)

Let's put that line into the point-slope form:

 \((y-7)=\frac{3}{4}(x+1)\)  <== Answer

Hope that helps!

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Answer:

\(y - 7 = \frac{3}{4} (x+1)\)

Step-by-step explanation:

We are given the equation y = 3/4x-4, and we want to write an equation of a line that is parallel to y=3/4x-4, and that also passes through (-1, 7), in point-slope form.

Point-slope form is written as \(y-y_1=m(x-x_1)\), where \(m\) is the slope, and \((x_1, y_1)\) is a point

If two lines are parallel to each other, it means they have the same slope.

The line y = 3/4x-4 is written in the form slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.

As 3/4 is in the place of where m is, 3/4 is the slope of this line.

It is also the slope of our new line.

So we can substitute 3/4 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=\frac{3}{4} (x-x_1)\)

Now, we need to replace the values of \(x_1\) and \(y_1\) with a point.

Since we are given (-1, 7), and that it passes through the line, it means that we can use its values in the equation.

Note that we have subtraction in this equation, so when we use a negative number, we still write the subtraction sign in front of the minus sign the negative number has. Just because the number is already negative doesn't mean we ignore the minus sign the formula gives.

\(y-7=\frac{3}{4} (x--1)\)

We can simplify this equation, as --1 is the same as +1.

\(y-7=\frac{3}{4} (x+1)\)

Answer:

fdsfskdfdsjg,dgkdfjkgjkdfgjkfjkdghdkj

Step-by-step explanation:

Explanation

the distributive property is that multiplying a number by a sum is the same as doing each multiplication separately

Step 1

get the factors of each term

the commom factor is 3y

hence factorize 3y

I hope this helps you

Answer:

The function is an odd function.

Step-by-step explanation:

A function f is odd if the following equation holds for all x and −x in the domain of f : −f(x)=f(−x) − f ( x ) = f ( − x ).

This equation holds for the function in the question.

Also, the function is a sin function so it is known to be odd.

The solution of the given expression will be 9/16.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²

= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²

= 9/16

Hence, The solution of the given expression will be 9/16.

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Answer:

The value of test statistic

   |Z| = |-2.2883| = 2.2883

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 57.7miles/gallon

The standard deviation of the Population = 1.9

The mean of sample x⁻ = 57.4

Given that the sample size 'n' =210

level of significance = 0.1

Step(ii):-

Test statistic

        \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

       \(Z = \frac{57.4-57.7}{\frac{1.9}{\sqrt{210} } }\)

      Z = -2.2883

  |Z| = |-2.2883| = 2.2883

Final answer:-

The value of test statistic

   |Z|  = 2.2883

Answer:

about 50 degrees

Step-by-step explanation:

To find the angle you would first subtract 180 - 90 (Since a triangle always equals 180) and that would be 90 and then divide by 2 to equal 45. I believe they wanted to round to nearest tenth so then the answer would change to 50. (Tell me if this is wrong; its been a while since I have done this)

I hope this helps :)

Answer:

(4x - 3)(3x + 2)

Step-by-step explanation:

(4x - 3)(3x + 2)

Answer:

You need to have 538 people in your study.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.94}{2} = 0.03\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.03 = 0.97\), so Z = 1.88.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

You practiced on the people at work and found a standard deviation of about 0.37 seconds.

This means that \(\sigma = 0.37\)

You want to get a 94% confidence interval that is only 0.06 in width.

This means that \(M = \frac{0.06}{2} = 0.03\)

How many people do you need to have in your study?

This is n for which M = 0.03. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.03 = 1.88\frac{0.37}{\sqrt{n}}\)

\(0.03\sqrt{n} = 1.88*0.37\)

\(\sqrt{n} = \frac{1.88*0.37}{0.03}\)

\((\sqrt{n})^2 = (\frac{1.88*0.37}{0.03})^2\)

\(n = 537.6\)

Rounding up:

You need to have 538 people in your study.

Answer:

Addition = 3656999

Step-by-step explanation:

Predecessor of number = (Number - 1)

Predecessor of 365000 = 365000 - 1

                                         = 364999

Successor of a number = (Number + 1)

Successor of 3291999 = 3291999 + 1

                                      = 3292000

Now we have have to add the predecessor of 365000 and successor of 3291999,

364999 + 3292000 = 3656999

In other words addition of predecessor of any number and successor of other number will be same as the sum of both the numbers.

Answer:

height = 6 mm

Step-by-step explanation:

The prism is a rectangular prism. The base area of the prism is 24 mm². The volume of the prism is given as 144 mm³.

The height of the prism can be solved as follows.

Volume of the rectangular prism = Bh

where

B = base area

h = height

Volume = 144 mm³

B = 24 mm²

volume = Bh

144 = 24 × h

144 = 24h

divide both sides by 24

h = 144/24

h = 6 mm

Answer:

c

Step-by-step explanation:

edg 2022

Answer:

ax^2 + bx + c = 0

Step-by-step explanation:

a, b, are the coefficients, c is the constant term, and x is the variable

Hope that helps

Answer:

A) less than

Step-by-step explanation:

4 times 6 is 20

24 inches is 2 feet

So, it is A because 20 is less than 24.

Answer:

No

Step-by-step explanation:

19.795 is smaller than 19.8 because since the whole number is the same (19), we have to look at the decimal. In 19.795, the tenth place has a 7. In 19.8, the tenth place has an 8. Since eight is bigger than 7, we know that 19.8 is larger than 19.795.

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The denominator of the fraction at point Y is equal to 24.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Let the variable d represent the denominator of the fraction at point Y and since point Y is the same distance from 0 as point X, which is at 2/3 on a number line, this can be modeled by this mathematical expression:

8/d = 1 - 2/3

8/d = 1/3

Cross-multiplying, we have:

d = 8 × 3

d = 24.

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The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.

To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.

We shade the area where the circles for D and E overlap because the equation (D ⋃ E)  denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.

The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.

The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.

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Answer:

1700 meters / hour

Step-by-step explanation:

160x20 = 3200

3200/ 2 = 1700

When S =  {−2,−1, 0, 1, 2, 3}, the coressponding values of f(S) are {4/3, 1/3, 0, 1/3, 4/3, 1/3, 4/3, 3}

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given f (x) = |x² ∕3| and  S = {−2,−1, 0, 1, 2, 3}

To find f(S), we are going to substitute the values of S (one after the other) into the function f(x)  = |x² ∕ 3|

For S = -2:  f(-2) = |(-2)² ∕ 3| = |4/3| = 4/3

For S = -1:   f(-1) = |(-1)² ∕ 3| = |1/3| = 1/3

For S = 0:   f(0) = |(0)² ∕ 3| = |0/3| = 0

For S = 1:   f(1) = |(1)² ∕ 3| = |1/3| = 1/3

For S = 2:  f(2) = |(2)² ∕ 3| = |4/3| = 4/3

For S = 3:  f(3) = |(3)² ∕ 3| = |9/3| = 9/3 =3

The values of f(S) are 4/3, 1/3, 0, 1/3, 4/3, 1/3, 4/3 and 3 when S= {−2,−1, 0, 1, 2, 3} respectively

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Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484