Given: Ray BD bisects prove: <1 and <3 are supplementary

We have to do a diagram with the following characteristics.

• VX has to intersect UW at V.

• VX is perpendicular to UW.

• U, V, and W are collinear.

Based on the given information, we have the following diagram

The image above shows the answer.

Given:

Ethan is 23 years older than Evan

So, let Ethan is (x) years old

And Evan is (y) years old

So, the difference between them is 23 years old

so, x - y = 23

And the sum of Ethan and Evan's age is 43

so, x + y = 43

So, we have the following system of equations:

add the equations to eliminate (y):

Now, substitute with (x) into the second equation to find (y):

So, the answer will be:

Ethan's age = x = 33

Evan's age = y = 10

Since we have that y = 10, then:

Then

In the first part, we need to sum 15 to both sides of the equation.

In the second part, we divide both sides by 5.

Then, x = 19.

Answer:

[tex]f(x) = - 2x - 1 \\ h(x) = - x + 5 \\ \\ The \: \: value \: \: of \: \: \: f(6) = ( - 2) \times 6 - 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 13 \\ \\ as \: we \: know ,\: \\➪(hf)(x) = h(f(x)) \\ so \:➪( hf)(6) = h(f(6)) \\ \\ put \: the \: value \: \: of \: f(6) \: we \: \: get \\ \\➪ (hf)(6) \: = h( - 13) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - ( - 13) + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 13 + 5 \\ \: \: \: \: \: \: \: = 18[/tex]

2a³ - 3a² - 45a + 50 is the simplified form of the expression ( 2a² + 7a - 10 )( a - 5 ) using FOIL method.

Given the expression in the question;

( 2a² + 7a - 10 )( a - 5 )

To expand ( 2a² + 7a - 10 )( a - 5 ), multiply each term in the first expression by each term in the second expression.

( 2a² + 7a - 10 )( a - 5 )

a( 2a² + 7a - 10 ) -5( 2a² + 7a - 10 )

a×2a² + a×7a + a×-10 -5×2a² -5×7a -5×-10

Multiply a and 2a²

2a³ + a×7a + a×-10 -5×2a² -5×7a -5×-10

Multiply a and 7a

2a³ + 7a² + a×-10 -5×2a² -5×7a -5×-10

Multiply a and -10

2a³ + 7a² - 10a -5×2a² -5×7a -5×-10

Multiply -5 and 2a²

2a³ + 7a² - 10a - 10a² -5×7a -5×-10

Multiply -5 and 7a

2a³ + 7a² - 10a - 10a² - 35a -5×-10

Multiply -5 and -10

2a³ + 7a² - 10a - 10a² - 35a + 50

Collect and add like terms

2a³ + 7a² - 10a² - 10a  - 35a + 50

2a³ - 3a² - 45a + 50

Therefore, the simplified form of the expression is 2a³ - 3a² - 45a + 50.

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We need to find the average termperature change per hour during January 2008.

We have the information that Minnesota fell from 41 degrees to -13 degrees over 24 hours.

Then, 41 degrees to -13 degrees, there is a difference of 41+13 = 54 degrees over 24 hours.

If the difference is over 24 hours, then:

54 degrees / 24 hours =2.25 F is the rate of change.

However, the termperature is decreasing, so the rate of change must be negative.

Hence, the rate of change = -2.25 F.

The correct answer is the third option.

Reflection:

A reflection is a transformation that flips a figure across a line.

Properties of reflection:

• The length remains the same, the angles remain the same.

• This means that the image and the pre-image have the same size and shape only the orientation changes.

• The line segment which connects the corresponding parts of the image and pre-image is perpendicular to the line of reflection.

• The distance from the line of reflection of the corresponding parts of the image and pre-image is the same.

Following is an example of a reflection

This is called a horizontal reflection since the image and the pre-image is flipped across the x-axis. The line of reflection is the vertical line.

Answer:

Step-by-step explanation:

y = -|x|

The graph is facing downwards, meaning it is negative.

The situation describes an exponential growth, which can be expressed using the general formula:

Where

a is the initial value

r is the growth rate, expressed as a decimal value

x is the number of times intervals

y is the final value after x time intervals

For the studied population, the growth rate is 2.5%, to express this number as a decimal value you have to divide it by 100:

The initial value is the current population of the town: a=50000

You can express the equation of exponential growth for this population as follows:

We know that after x years the population will be y=100000, to determine how many years it will take to reach this value you have to equal the equation to 100000 and solve for x:

-Divide both sides of the expression by 50000

-Apply logarithm to both sides of the equal sign:

-Divide both sides by the logarithm of 1.025

After approximately 28 years the population of the town will be 100,000.

The percent tip which Ai mi added to the $9 dinner as required in the task content is; 31%.

It follows from the task content that the percent tip which Ai mi added to the dinner is to be determined by evaluation.

Since the dinner itself costs; $9 and she paid $11.79 after adding tip, it follows that the percent tip is the percentage change in price paid per unit original price as follows;

Percent tip = { ( 11.79 - 9 ) / 9} × 100%

Percent tip = 2.79/9 × 100%

Percent tip = 31%.

Therefore, the percent tip added by Ai mi to the original price of dinner is ; 31%.

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Given that:

- The triangle is isosceles.

- Its base is 49.96 meters.

- Each base angle is 31.43°.

You can draw the triangle. See the picture shown below (it is not drawn the scale):

Notice that the Isosceles Triangle can be divided into two equal Right Triangles. Then, you know that:

Since it is isosceles, the sides AB and AC have equal length.

Then, you can choose one of the equal Right Triangles and use the following Trigonometric Function in order to find the length of each equal side:

In this case, you can set up that:

Therefore, substituting values and solving for AC, you get:

Hence, the answer is:

The length of the two equal sides of the triangle is:

To answer this question, we need to expand the original equation, and then simplify to obtain the equivalent expression as follows:

We used the distributive property for -5 (1 + 5).

Then, we have:

Adding like terms:

In summary, therefore, the equivalent expression is:

The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13

From the table given, we have

The balance of the credit card from May 1 - May 5 was 2000 which is 5 days, from may 6- may 10 was 1600, which is again 5 days, from may 11 to may 20 was 1350, the interval is 10 days and 21 to may 31, 11 days the balance was 1550.

The avergae daily balance was

=[tex]\frac{(Balance (number of days))}{Total number of days}[/tex]

= [tex]\frac{2000(5)+1350(10)+1550(11)}{5+5+10+11}[/tex]

=[tex]\frac{48550}{31}[/tex]

=1566.13

So The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13

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Generally, one should not write down values such as this directly from a calculator. √2 is an irrational number, which means that instead of writing it as a terminating decimal, it is best to write it in its exact form (√2) to ensure accuracy for further calculations.

Multiplication:

Lisa, Bret, and Gary harvested apples. If they each harvested 3 carts of apples, how many carts did they harvest in total?

--> 3 * 3 = 9 carts in total

Division:

Lisa, Bret, and Gary harvested apples. If all three of them harvested 9 carts of apples in total, how many carts did each person harvest.

--> 9 / 3 = 3 carts per person

we have the following

sin of an angle is the same as:

therefore we can create the following right triangle:

we can calculate the adjacent side using the pythagorean theorem

where h is the hypotenuse, a is the adjacent side and b the opposite side to the angle.

thus, the adjacent side is:

Using that value, we can now calculate cos of the angle

which can't be simplify, thus that is the answer for the exact value

Solve the system using substitutions:

x has a value of 1. Use this value to find the value of y.

y has a value of 1.

x=1

y=1

what the??????????????

At an animal shelter, 3/8 of the animals are dogs, of the dogs, 2/5 have spots, 3/20 portion of the animals at shelter are dogs that have spots. A fraction, which derives from Latin word fractus, which means "broken," is a portion of whole or, more broadly, any number of equal pieces.

A fraction, which derives from Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator that is displayed below (or after) line on which the numerator is shown. Compound fractions, complicated fractions, and mixed numeral fractions are the examples of uncommon fractions that use numerators and denominators.

The numerator and the denominator of positive common fractions are both natural integers. The denominator shows how many of numerator's equal parts make up a unit or whole, and the numerator reflects the number of equal parts. Since there can never be zero components in a whole, denominator cannot be zero. For instance, numerator 3 in the fraction 3/4 denotes that the fraction is made up of 3 equal parts, while denominator 4 denotes that the fraction is made up of 4 parts altogether.

Let, [tex]\frac{3}{8} x[/tex] animals are dogs,

[tex]\frac{2}{5} * \frac{3}{8}x = \frac{3}{20}x[/tex]

Therefore, [tex]\frac{3}{20}[/tex] of the animals at shelter are dogs that have spots.

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A 90 degree counterclockwise rotation about point A, a reflection across the y-axis, and a translation 20 units down may be used on quadrilateral ABCD to demonstrate that it is congruent to quadrilateral GHIJ.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners. A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English term quadrilateral. A four-sided polygon with four angles is known as a quadrilateral. Parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid are the seven different forms of quadrilaterals.

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Answer:

Solutions below.

Step-by-step explanation:

This question is asking us to find the points of intersection, which means its asking to find the x-intercept abd y-intercept.

To find the x-intercept, we know that y = 0.

Therefore we can substitute y = 0 into the line equation:

[tex]0 = - \frac{1}{4} x + 2 \\ - \frac{1}{4} x = - 2 \\ x = - 2 \div - \frac{1}{4} \\ = 2 \times 4 \\ = 8[/tex]

Therefore the point of the x-intercept is (8,0).

Likewise to find the y-intercept, we know x = 0.

Therefore we can substitute x = 0 into the line equation:

[tex]y = - \frac{1}{4} (0) + 2 \\ = 0 + 2 \\ = 2[/tex]

Therefore the point of the y-intercept is (0,2).

Answer:

x-intercept:  (8, 0)

y-intercept:  (0, 2)

Step-by-step explanation:

Given equation:

[tex]y=-\dfrac{1}{4}x+2[/tex]

The graph intersects the y-axis when x = 0.  

To find the graph's y-intercept, substitute x = 0 into the equation and solve for y:

[tex]\begin{aligned}x=0 \implies y&=-\dfrac{1}{4}(0)+2\\y&=0+2\\y&=2\end{aligned}[/tex]

Therefore, the coordinates of the point of intersection with the y-axis are:

The graph intersects the x-axis when y = 0.  

To find the graph's x-intercept, substitute y = 0 into the equation and solve for x:

[tex]\begin{aligned}y=0\implies \-\dfrac{1}{4}x+2&=0\\-\dfrac{1}{4}x&=-2\\x&=8\end{aligned}[/tex]

Therefore, the coordinates of the point of intersection with the x-axis are:

The equation of the linear function represented by the table below in slope-intercept form is y = -3x + 5

The linear function that will be obtained by using these values of x and y will be a Equation of line.

The slope-intercept form of line looks like this,

y = mx + c

where,

m is the slope.

c is the y intercept,

Firstly, to find the slope we can use any two points,

we will use (1,2) and (2,-1)

Hence, slope m,

m = (-1-2)/(2-1)

m = -3

Putting the value of slope in equation y = mx + c,

y = -3x + c

To fin the value of c,

Using the coordinate (1,2) and putting the values of x and y,

2 = -3 + c

c = 5.

Putting the values of c and m in the equation,

we get,

y = -3x + 5.

The required equation of the line in slope-intercept form is y = -3x + 5

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The total amount (in dollars) saved using both plans combined is T = 50 + 101.1N.

Based on the information, the function = 50+20.55N.

where N is the number of weeks she has been saving.

For the second function, this is illustrated as:

function B = 80.55 N.

Therefore, the total of the plans combined will be:

T = 50 + 20.55N + 80.55N

T = 50 + 101.1N

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Given the function below;

The x-intercept is the point where f(x) = 0 as shown:

The x-intercept of the graph will be at (5.66, 0) and (-5.66, 0)

The y-intercept occurs at the. point where x = 0 to have:

The y-intercept is (0, 4)

The equivalent graphis as shown below

The graph shows that the function has a maxmum point at (0, 4) with no minimum point.

To determine the arc length of the shaded area you have to use the following formula:

"θ" represents the measure of the central angle, in degrees

"r" represents the radius of the circle

We know that the arc measure is 126º, the central angle has the same measure as the intercepted arc, then its measure is also θ=126º

The radius of the circle is r=15cm

The values of x and y are 26° and 54° respectively.

Consider the triangle with x is triangle 1

Triangle with y is triangle 2

In triangle 1

Since it is a right angled triangle one angle is already known

Another angle is 64°

We know the sum of interior angles of a triangle is equal to 180

Hence 90 + 64 +x = 180°

154 + x = 180°

x= 180 - 154

x = 26°

From triangle 2 it is evident that x and y are complementary angles which means they sum up to 90°

Hence  x + y = 90°

26 + y = 90

y = 90 - 26

y = 54°

Hence the value of x and y are 26° and 54° respectively

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The smallest whole number is 750,000, while the largest whole number is 849,999.

Consider the facts offered.

We must determine the smallest whole integer that, when rounded to the nearest hundred thousands, equals 800,000

Rounding a numerical rule

If the number on the right side of the rounding digit is 0, 1, 2, 3, 4, there is no need to modify the rounding digit and replace the remainder of the digit on the right with 0.

If the number on the right side of the rounding digit is 5, 6, 7, 8, 9, the rounding digit rounds up by one number and replaces the remainder of the digit on the right with 0.

Consider the number 800,000 for a moment.

Because we want the smallest number possible, the number at the hundred thousand place should be 7.

As a result, the smallest whole number is 750,000.

We now want the largest whole number that rounds to 800,000

Similarly, the biggest whole number must be bigger than 800,000 We don't want to raise the number at the hundred thousand place, hence the best ten thousand place option is 4. Put 9 at the rest locations to get the highest number.

As a result, the biggest whole number is 849,999.

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