Determine if the statements are true or false
The standard form of 4.4 x 10-4 is 0.00044.
The standard form of 6.39 x 105 is 63,900,000.
The standard form of 3.02 x 10° is 3,020,000,000.

A line that intersects two or more lines at a distinct point is known as a transversal line.

A transversal is a line in geometry that connects two lines in the same plane at two different places. When determining whether two or more other lines in the Euclidean plane are parallel, transversals are important. Consecutive interior angles, consecutive exterior angles, corresponding angles, and alternate angles are only a few examples of the several pairings of angles that can be formed when a transversal intersects two lines. Euclid’s parallel postulate states that if two lines are parallel, then comparable interior angles are equal, alternate interior angles are equal, and successive interior angles are supplementary.

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Answer:

182 [tex]in^{2}[/tex]

Step-by-step explanation:

Bottom:

12 x 4 = 48

Left side:

5x4= 20

Front:

[tex]\frac{12x5}{2}[/tex]= 30

Back

[tex]\frac{12x5}{2}[/tex] = 30

Top

13x4 =54

Add together:

48+ 20+ 30+30+54 = 182

The rectangular coordinate form of a complex number is represented by the formula z=a+bi. The real axis is the horizontal one, and the imaginary axis is the vertical one. In terms of r and, where r is the vector's length and is the angle it makes with the real axis, we determine the real and complex components.

Rectangular form;-

Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides.

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Answer:

y=1.5x-3

Step-by-step explanation:

(0,-3) => x=0, y=-3

(2,0) => x=2, y=0

y=ax+b

-3=a*0+b

0=2*a+b

-3=b

0=2a+b

2a-3=0

2a=3

a=1.5

b=-3

y=1.5x-3

Answer:

[tex]y = \dfrac{3x}{2} -3[/tex]

Step-by-step explanation:

Before we identify the equation of the line in slope intercept form, we must identify the slope intercept form equation. The slope intercept form equation is y = (m)x + (b) ⇒ m = slope of line; b = y-intercept of line.

To identify the equation of the line shown in slope intercept form, according to the slope intercept form equation, we need to identify the slope of the line and the y-intercept of the line. The slope of a line is the rate of a line, which advances up/down/side-to-side at a constant rate. The y-intercept of a line is the intersection of the line at the y-axis.

There is a specific formula for identifying the slope:

[tex]\boxed{\text{Slope} = \dfrac{\text{y coordinate of 2nd point - y coordinate of 1st point}}{\text{x coordinate of 2nd point - x coordinate of 1st point}}}[/tex]

Some facts about slope: The slope of a line will also depend on the graph. If the graph ascends upward to somewhere in Quadrant 1 or 2, the slope of the line will be positive. If the graph descends downward to somewhere in Quadrant 3 or 4, the slope will be negative. If the line horizontal and it passes perfectly through the x-axis, the slope of the line is 0. If the slope of the line is vertical, then the slope will be undefined.

Location of plotted points: First point: (0, -3); Second point: (2, 0)

Let us now identify the x and y coordinates of the plotted points:

[tex]\boxed{\text{y-coordinate of 2nd point = 0; y-coordinate of 1st point = -3}} \\ \boxed{\text{x-coordinate of 2nd point = 2; x-coordinate of 1st point = 0 }}[/tex]

Plug the coordinates into the slope formula to determine the slope:

[tex]\implies {\text{Slope} = \dfrac{\text{0 - (-3)}}{\text{2 - 0}}} = \dfrac{0 + 3}{2} = \dfrac{3}{2}[/tex]

Plug the slope of the line into the slope intercept form equation:

[tex]\implies y = (m)x + (b)[/tex]

[tex]\implies y = \huge\text{(}\dfrac{3}{2} \huge\text{)}x + (b)[/tex]

[tex]\implies y = \dfrac{3(x)}{2} + b[/tex]

Let us plug any point (that is on the line) for x and y. This will help us find the y-intercept (b). I will plug in the first point because it is my preference.

[tex]\implies y = \dfrac{3(x)}{2} + b[/tex]

[tex]\implies -3 = \dfrac{3(0)}{2} + b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{First point: (0, -3)} \implies x = 0; y = -3]}[/tex]

[tex]\implies -3 = 0 + b[/tex]

[tex]\implies -3 = b[/tex]

Finally, let us substitute the slope of the line and the y-intercept of the line into the slope-intercept form equation. Then, we can simplify both sides of the equation and isolate the y-variable completely on the other side.

[tex]\implies y = (m)x + (b)[/tex]

[tex]\implies y = \huge\text{(}\dfrac{3}{2} \huge\text{)}x + (-3)[/tex]

[tex]\implies y = \dfrac{3x}{2} -3[/tex]

Therefore, the equation of the line in slope intercept form is y = 3x/2 - 3.

The expression (√z√y√x)^8 is simplified to zyx

Square root of a number can be defined as a value, which by multiplying itself, gives the original number.

It is represented with the symbol " √ ".

The square root of a number is the direct opposite of squaring a number.

Given the expression;

Find the square root of z

[tex]{\sqrt{z\sqrt{y\sqrt{x} } }}^8[/tex]

Square root can be expressed as the power of 1/2

Then, we have'

[tex]z\sqrt{y\sqrt{x} } ^ 4[/tex]

Find the square root of y

[tex](zy\sqrt{x} )^2[/tex]

Find the square root of x

zyz

Hence, the expression is xyz

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Answer:

This is a V-shaped function that opens downward. The vertex of the V is point (1, 12).

Step-by-step explanation:

This is a V-shaped function that opens downward. The vertex of the V is point (1, 12).

The line m passing through the points (2, -7) and (4, -9) is parallel to the line y = -x + 2 , the correct option is (c) .

In the question ,

it is given that ,

the Line m passes through the points (2,-7) and (4,-9),

So , the slope of the line will be = (-9 + 7)/(4 - 2)

= -2/2

= -1

We know that the if two lines are parallel then they will have same slope ,

the slope of the line should be -1,

from the given options , we can see that only option (c) has the slope = -1

on comparing equation y = -x + 2 with the general equation of the line y = mx + c , we get

slope(m) = -1

hence , the line m is parallel to y = -x + 2 .

Therefore , the line m passing through the points (2, -7) and (4, -9) is parallel to the line y = -x + 2 .

The given question is incomplete , the complete question is

Line m passes through the points (2, -7) and (4, -9). Line m is parallel to which line?

(a) 8x + 2y = -10

(b) x = 5

(c) y = -x + 2

(d) y = x - 9

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Answer:

≈ 4,22 m

Step-by-step explanation:

volume = 20000L = 20000 dm^3 = 20 m^3

diameter = 2,4m

the volume of a cilinder is π * r^2 * h (height)

20 = π * 1,2^2 * h

h = [tex]\frac{20}{\pi * 1,44} \\[/tex] ≈ 4,42 m

Answer: ∠1 = 90°

Step-by-step explanation:

      There are a few steps we will take to solve this problem. In each step, I will write an equation to help us solve, then use inverse operations to solve.

      First, we will use the exterior angles theorem to find the measurement of ∠3 (this will help us solve for ∠2, then for ∠1).

89° = 51° + ∠3

∠3 = 38°

      Next, we will find the measurement of ∠2 since we know ∠2 plus ∠3 is 90 degrees, as shown by the perpendicular lines and the box.

90° = ∠3 + ∠2

90° = 38° + ∠2

∠2 = 52°

      Lastly, we will solve for ∠1. We know that there are 180 degrees in a triangle.

180° = 38° + ∠1 + ∠2

180° = 38° + ∠1 + 52°

180° = 90° + ∠1

∠1 = 90°

Answer:

90

Step-by-step explanation:

I started by finding angle 5

180 - 89 = 91  Supplemental angles

Then I found angle 3

The sum of the interior angles of a triangle is 180

180-89-91 = 38

Angle2 and 3 are complementary angles

90- 38 =52

the sum of the interior angles of a triangle is 180

Angle 1

180 - 52 - 38 = 90

The amount Erica owed for the 6 years if 5300 dollars was loaned at the rate of 8% is $8,551.56.

The amount Erica owes for 6 years if 5300 dollars is loaned to her at the rate of 8% compounded monthly can be computed as follow:

Therefore,

[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]

where

Therefore,

p = 5300 dollars

t = 6 years

n = 12

r = 8%

Therefore,

[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]

[tex]A = 5300(1+ \frac{0.08}{12} )^{(12)(6)}[/tex]

A = 5,300(1 + 0.0066666666666667)⁷²

Therefore,

A = $8,551.56

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Answer:

jenny earned a total of $103.05.

Step-by-step explanation:

jenny charges 9.15 an hour to babysit todllers and 7.4 an hour to babysit school -aged children. if jenny babysat toddlers for 9 hours and school -aged childrenfor 6, she earned in all 83.55.

Answer:

  x = -0.5, -3.5

Step-by-step explanation:

You want the solution to 4x² +16x +7 = 0 using the quadratic formula.

Comparing the given equation to the standard form quadratic, you can identify the coefficients as ...

Substituting these values into the quadratic formula, you find the solutions to be ...

  [tex]x=\dfrac{-16\pm\sqrt{16^2-4(4)(7)}}{2(4)}=\dfrac{-16\pm\sqrt{144}}{8}\\\\x=\dfrac{-16\pm12}{8}=\dfrac{-4\pm3}{2}\\\\x=\left\{-\dfrac{7}{2},\ -\dfrac{1}{2}\right\}[/tex]

The possible values of x are -3.5 and -0.5.

         then it becomes, [tex]y=-\frac{1}{2} x^2[/tex].

                                                                            [tex]y = -\frac{1}{4} (x+2)^2[/tex]

        [tex]y = -\frac{1}{4} (x+2)^2[/tex]

What do you mean by graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

What do you mean by Factor?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.

What is whole number?

The positive integers are another name for the whole numbers or the nonnegative integers, if zero is included.

What is integer?

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

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The correct algebraic form is b. k/-9 + 7 = 17

There are four components in division namely divisor, dividend, quotient and remainder. The significance and meaning of each is evident from their name. The dividend is the number that is being divided. And the number which is used to divide the dividend is divisor. The result of dividing the dividend by divisor is termed as quotient. Remainder is the left over amount.

So, multiplying the divisor and quotient and adding the product with remainder will give us the desired algebraic expression. Seven is remainder. The quotient of k and negative nine implies k is dividend and negative nine is divisor. So, algebraic expression -> k/-9 + 7 = 17

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The Answer is 25.12 I know this because I used a calculator. Hope this helped! :)

Answer: 25.12

Step-by-step explanation:

The Answer is 25.12 I did a test and got it right. I hope this helps!

The number is 115.

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = [tex]\frac{a}{b}[/tex] x 100

We have,

Number = M

40% of M = 46

[tex]\frac{40}{100}[/tex] x M = 46

M = (46 x 100) / 40

M = 115

Thus,

The number is 115.

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Answer: 0.286

Step-by-step explanation:

1.657−2.397(5.968x−0.27)=4.193x−3

Use the distributive property to multiply −2.397 by 5.968x−0.27.

1.657−14.305296x+0.64719=4.193x−3

Add 1.657 and 0.64719 to get 2.30419.

2.30419−14.305296x=4.193x−3

Subtract 4.193x from both sides.

2.30419−14.305296x−4.193x=−3

Combine −14.305296x and −4.193x to get −18.498296x.

2.30419−18.498296x=−3

Subtract 2.30419 from both sides.

−18.498296x=−3−2.30419

Subtract 2.30419 from −3 to get −5.30419.

−18.498296x=−5.30419

Divide both sides by −18.498296.

x=

−18.498296

−5.30419

Expand  

−18.498296

−5.30419

​by multiplying both the numerator and the denominator by 1000000.

x=

−18498296

−5304190

Reduce the fraction  

−18498296

−5304190

 to lowest terms by extracting and canceling out −2.

x=

9249148

2652095

​

and then round

If we compute a 92% confidence interval in  excel command the critical value will be 1.750686.

Level of confidence c = 0.92

level of significance α = 1 - c = 0.08

A 92% confidence interval has goes from  8/2 = 4% to 100%–(8/2)% = 96%

Leaving 92% in the middle (96%–4%) = 92 %

So look up z-score for 96% or p =0.96

The two closest value in a z-table are

P(z< 1.75) = 0.95994

P(z< 1.76) = 0.96080

Based on this online table

( https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf )

So critical value Z = 1.75 is the closest value , but just barely.

But if you want a more accurate , use the normal function on Excel or from an online calculator or interpolate

If you interpolate

1.75 + (0.96–0.959954)*0.01/ (0.9608–0.95994)

Critical value Z= 1.750535

If you round to four digits,  critical value Z = 1.7505

So the interpolation isn’t that much more accurate

Excel function says critical value Z= 1.750686

=normsinv(0.96)

= 1.750686 which is probably more accurate.

By using the word interval, you have implied you are talking about a two-sided test.

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The length of the other leg of the right angles triangle is 3. Option D

The Pythagorean theorem states that the square of the hypotenuse side is equal to the square of the other two sides in a right angled triangle.

We have;

a² = b² + c²

Where;

Now, substitute the values

4² = (√7)² + c²

Find the square values

16 = 7 + c ²

collect like terms

c² = 9

Find the square root of both sides

c = 3

Hence, the value is 3

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Answer:The length of the other leg of the right angles triangle is 3. Option D

Step-by-step explanation:

If the a has 15 boys and 20 girls, then the boy to girls ratio in simplest form is 3 : 4

Number of boys in the class = 15 boys

Number of girls in the class = 20 girls

The ratio can be defined as the a number that can be used to express one quantity as a fraction of the other ones. That means we are comparing them by dividing those numbers

Here the ratio will be

Number of boys in the class : Number of girls in the class

Substitute the values in the ratio

= 15 : 20

Divide both numbers by 5

= (15/5) : (20/5)

= 3 : 4

Hence, if the a has 15 boys and 20 girls, then the boy to girls ratio in simplest form is 3 : 4

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The property of the equality is a method to perform a operation both sides of the equal sign which will not affect the equation. Property of equality which is needed to isolate a variable and solve a given equation is use inverse relationships to "undo" the operation. Thus the option A is the correct option.

Property of equality

The property of the equality is a method to perform a operation both sides of the equal sign which will not affect the equation.

Inverse means to revere something which has been done earlier. An undo operation in mathematics is the operation of undoes what was done by the previous operation.

For example suppose the given expression is no 5. Then by adding 4 and again subtracting 4 keeps the system isolate.

Hence the property of equality which is needed to isolate a variable and solve a given equation is use inverse relationships to "undo" the operation. Thus the option A is the correct option.

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Answer:

Step-by-step explanation:0495-46y7467-6686-745676-5

Answer:

there fore y = 1/8x-1   it can be write as 8xy+8x-1 = 0

and -5x+4y=-3 can be write it as -5x+4y+3 = 0

Step-by-step explanation:

given that

pair y = 1/8x-1   ------ equation (1)

and -5x+4y=-3   ------ equation (2)

you can write it as

you can write equation (1) as

y = 1/8x-1

y = 1-8x/8x

8xy = 1-8x

there fore

y = 1/8x-1   it can be write as 8xy+8x-1 = 0

you can write equation (2) as

-5x+4y = -3

-5x+4y+3 = 0

there fore

-5x+4y=-3 can be write it as -5x+4y+3 = 0

Answer:

20/1

Step-by-step explanation:

2000 divided by 100 = 20

100 divided by 100 = 1

The graph of the function graph (a) and the table in the figure represents the actual table of the function

From the question, we have the following equation that can be used in our computation:

f(x) = (3/4)^x

This equation can be re-expressed as

f(x) = (3/4)ˣ

The x values on the table of values are given as: x = -2, -1, 0, 1 and 2

The next step is to substitute these values

So, we have the following equations

f(-2) = (3/4)⁻² = 16/9

f(-1) = (3/4)⁻¹ = 4/3

f(0) = (3/4)⁰ = 1

f(1) = (3/4)¹ = 3/4

f(2) = (3/4)² = 9/16

When these equations are represented on a table of values, we have the following table:

x  -2       -1      0     1      2

y  16/9   4/3   1     3/4   9/16

Next, we represent the values on a graph

From the table, we have

y = 1 when x = 0

This means that it crosses the y-axis at (0, 1)

This is represented by graph (a)

So, the graph of the function is graph (a)

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The operations being done in each step are:

(1) Use the distributive property

(2) Subtraction property of equality.

(3) Addition property of equality.

(4) Division property of equality.

Two or more expressions with an equal sign are defined as an equation.

3(-3x-4) = 5x+2

Use distributive property:

-9x -12 = 5x + 2

Subtract 5x from both sides of the equation:

-14x -12 = 2

Add 12 to both sides of the equation:

-14x = 14

Divide both sides by -14:

x = -1

Hence, the operations being done in each step are:

(1) Use the distributive property

(2) Subtraction property of equality.

(3) Addition property of equality.

(4) Division property of equality.

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Answer: Yes

Step-by-step explanation:

Because a=b, we can use the Substitution Property of Equality to substitute a for b. Now our equation looks like this:

a+a=a+a

Using the Reflexive Property, we know that this equation is true. We can use an example by setting a=2. This is what that would look like:

a=2

a=b          transitive property

b=2

a+a=a+b  substitution property

2+2=2+2

4=4          true

Therefore, yes, it is possible for a+a=a+b when a=b