Algebraic fraction equations
Solving question

It is given that AD = AC is the midpoint of the segment DC.  Therefore, DB = BC by the definition of the midpoint making the segment AB as a bisector. Additionally, ∠D is congruent to the angle ∠C by the definition of the vertical angle theorem. Triangle ΔADB is congruent to triangle ΔACB by SAS theorem.

Since angles like ∠ ABD and ∠ABC are a linear pair adding up to 180 and congruent by linear pair postulate. This means that the angle ABD and ABC each measures 90 degrees. Therefore, segment AB is perpendicular to segment DC by midpoint isosceles theorem making segment AB both as a bisector and perpendicular to the segment DC.

What is midpoint theorem?

Midpoint theorem defines the center point of a line segment which forms the triangle. And the sides of the triangle are equal with one side is parallel to the remaining sides.

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Answer: 168

Step-by-step explanation:

Answer:

5 tomato and 14 pineapples

Based on the Alternate Interior Angles Theorem, the degree measure of angle 3 is equal to 153.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Since line a and m are parallel lines, angle 4 and 6 are alternate interior angles. By applying the supplementary angle theorem, the measure of angle 6 is given by:

Q + R = 180°

153° + m<6 = 180°

Angle 6 = 180° - 153°

Angle 6 ≡ Angle 4 = 17°

Now, we can determine the degree measure of angle 3 by applying the supplementary angle theorem:

Q + R = 180°

17° + m<3 = 180°

Angle 3 = 180° - 17°

Angle 3 = 153°

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Answer:

If there is no additional contribution during these 8 years your balance will be $352.23

Step-by-step explanation:

He has been practicing in sports and drama for 208hours and 130 hours respectively in 52 weeks using unitary method.

It is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given Data

We can solve this by unitary method.

Time spent on sports in 2 weeks= 8 hours

Time spent on sports in 1 week= 4 hours

Time spent on sports in 52 weeks = 4×52 hours

That is Palmer has spent 208 hours practicing in sports for 52 weeks.

Similarly, we can calculate for his participation in drama.

Time spent in drama for 2 weeks= 5 hours

Time spent in drama for 1 week= 2.5 hours

Time spent in drama for 52 weeks= 2.5 × 52

That is, Palmer spent 130 hours practicing in drama for 52 weeks.

Collectively, he has been practicing in sports and drama for (208+ 130=)338 hours in 52 weeks using unitary method.

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f(t)=3t^2-2t+1

Evaluating a function means finding the value of f(x) that corresponds the given value of x To do this we replace all x variable with the assigned value of x. then evaluate the function by following order of operation

This means to substitute 5 for x and simplify. It is recommended that the value being substituted be placed inside parentheses.

In this question asked to evaluate f(t), then x has been assigned the value of t. here we replace x with t.

f(x) = 3x^2-2x+1

To evaluate the function substitute t in place of x we get

f(t)= 3t^2-2t+1

[tex]f(t)=3t^2-2t+1\\f(t)=3t^2-3t-1t+1\\f(t)=3t(t-1)-1(t-1)\\f(t)=(3t-1)(t-1)[/tex]

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Answer:

520,000,000

Step-by-step explanation:

Answer:

520,000,000

Step-by-step explanation:

The amount of wheat produced by the world = 5.2 × 10⁸ metric tons.

We know that 5.2 × 10⁸ = 520,000,000

The circumference and the area of the circular flower bed is 31.4285 feet and .

The space a circle takes up in a two-dimensional plane is known as the area of the circle.

given that A gardener makes a new circular flower bed the bed is 10 feet in diameter.

so, the diameter of circular flower bed is 10 feet.

the radius of the circular flower bed is 5 feet.

Now find the circumference of the circular flower bed .

the circumference of Circle formula is

circumference (C) = 2πr

C = 2 X 22/7 X 5

C = 31.4285 feets.

so, 31.4285 feets is the circumference of the circular flower bed.

now, find the area of circular flower bed.

The area of the circle formula is

[tex]A = \pi \: {r}^{2} [/tex]

[tex]A = \frac{22}{7} \times {5}^{2} [/tex]

A = 78.5714 feets.

so, 78.5714 feets is the area of the circular flower bed.

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The rectangle will have a 548.1 square foot size and a 94.2-foot periphery.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L×W square units

The length is 21 feet and the width is 26.1 feet.

The perimeter of the rectangle will be

P = 2 (21 + 26.1)

P = 2 x 47.1

P = 94.2 feet

The area of the rectangle will be

A = 21 x 26.1

A = 548.1 square feet

The rectangle will have a 548.1 square foot size and a 94.2-foot periphery.

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Hence , on solving 7x - 3 < - 52 the value of x lies in interval (-∞ , 7) and on solving -5x - 2 < 28 the value of x lies in interval (-6 , ∞)  .

We have given two inequalities 7x - 3 < - 52 and -5x - 2 < 28

On solving 7x - 3 < - 52 , we get

      7x < 3 - 52

      7x < 49

       x < 7

Therefore, x could be any number less than 7.

In interval notation , it is given by (-∞ , 7) .

On solving -5x - 2 < 28 , we get

      -5x < 2 + 28

      -5x < 30

       -x < 6

Multiplying by negative sign , inequality changes

 x > -6

Therefore, x could be any greater than -6.

In interval notation , it is given by (-6 , ∞) .

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In the expression 4b³ - 14c²b⁵⁶m⁹ + 34 we have total three terms -  4b³ ,  14c²b⁵⁶m⁹ ,  34.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given in the question is a expression as follows -

4b³ - 14c²b⁵⁶m⁹ + 34

In order to identify the number of terms in this expression, it is important to keep in mind that the terms of an expression are separated from one another by the following → + (Addition),  - (Subtraction). In some cases, (equal to) '=' , (less than) '<' , (greater than) '>' are also used. Now, the given expression given is -

4b³ - 14c²b⁵⁶m⁹ + 34

It has three terms -  4b³, 14c²b⁵⁶m⁹, 34

Therefore, in the expression 4b³ - 14c²b⁵⁶m⁹ + 34 we have total three terms -  4b³ ,  14c²b⁵⁶m⁹ ,  34.

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Answer:

Can you please add the image for I can help you?

Step-by-step explanation:

The length of RS is 58 when S is the midpoint of RT.

Distance is measured in length. According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units' fundamental unit of length is the meter.

In geometry, a line segment's midpoint is referred to as the midpoint. It serves as both the segment's and the ends' centroid, and it is equally spaced from both. It cuts the section in half.

If S is the midpoint of the line segment  RT then , from the definition we can say that RS = ST

Now we can put the values and solve the equation to find the length of RS .

7x - 5 = 6x + 4

or, x = 9

Therefore RS = 7x - 5 = 7 × 9 - 5 = 58

Hence the length of RS is 58 units.

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answer:

the solution is

The numbers should be matched to each of the expression on the left with its product on the right as follows:

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In Mathematics, a significant figure can be defined as the number of digits in a numerical data (value), typically a measurement, which enhances its degree of accuracy.

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Answer:

thanks

Step-by-step explanation:

In the given picture there are 5 questions.

1. What are the name of the segments?

We have 3 points on a line we get 3 segment that are [tex]\bar{AB},\bar{AC}and \bar{BC}[/tex].

2.What are the names of a rays?

The names of the rays are[tex]\overrightarrow{AB},\overrightarrow{AC},\overrightarrow{CB},\overrightarrow{BA},\overrightarrow{BC}and \overrightarrow{CA}[/tex].

3. Name a pair of opposite rays.

The pair of opposite rays are [tex]\overrightarrow{CB},and \overrightarrow{CA}[/tex].

4. What is the intersection of plane AEF and plane HGF

[tex]\overrightarrow{EF}[/tex].

5. Name two planes that intersect  [tex]\overline{CB}[/tex].

plane BFG and plane ADC.

1. Given there is a line with 3 points A,B and C.

The segment is the ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.

If there are 2 points on a line = 1 line segment; 3 points on a line = 3 segments.

We have 3 points on a line we get 3 segment that are [tex]\bar{AB},\bar{AC}and \bar{BC}[/tex].

2. Given there is a line with 3 points A,B and C.

A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.

The names of the rays are

[tex]\overrightarrow{AB},\overrightarrow{AC},\overrightarrow{CB},\overrightarrow{BA},\overrightarrow{BC}and \overrightarrow{CA}[/tex].

3. Opposite rays are the two rays which has same end point that when kind of combined together create a straight line.

So, here we have an end point as C and the reason being is if my endpoint C i can have a ray go to right point B and it can go to the left point A.

If we choose the point A it can go to right point but not left and if we choose the point B it can go to left point but not right.

That's why the end point is C.

The pair of opposite rays are [tex]\overrightarrow{CB},and \overrightarrow{CA}[/tex].

4. the intersection of plane AEF and plane HGF is [tex]\overrightarrow{EF}[/tex].

5. the planes that intersect  [tex]\overline{CB}[/tex].

plane BFG and plane ADC.

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Answer:

  a. h(4) = -207

  b. h(-2y) = 24y³ +12y +9

  c. h(5b+3) = -375b³ -675b² -435b -90

Step-by-step explanation:

You want the simplified form of h(y) = -3y³ -6y +9 for using 3 different values of y.

The expression is evaluated by putting the argument where y is, then simplifying the resulting expression.

  [tex]h(4)=-3(4)^3 -6(4) +9 = -3(64) -24 +9\\\\\boxed{h(4) = -207}[/tex]

  [tex]h(-2y)=-3(-2y)^3-6(-2y)+9=-3(-8y^3+12y+9\\\\\boxed{h(-2y)=24y^3+12y+9}[/tex]

  [tex]h(5b+3)=-3(5b+3)^3-6(5b+3)+9=-3(125b^3+225b^2+135b +27) -30b-18+9\\\\\boxed{h(5b+3)=-375b^3-675b^2-435b-90}[/tex]

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Additional comment

It can be useful to remember that ...

  (a +b)³ = a³ +3a²b +3ab² +b³

Answer:

  a.  29

  b.  g(p) = 2p² -3

  c.  4x +2h

Step-by-step explanation:

You want to evaluate g(x) = 2x²-3 for different values of x.

Substituting -4 for x, we have ...

  [tex]g(-4)=2(-4)^2-3 =2(16)-3\\\\\boxed{g(-4)=29}[/tex]

Substituting p for x, we have ...

  [tex]\boxed{g(p)=2p^2-3}[/tex]

The given expression simplifies to ...

  [tex]\dfrac{g(x+h)-g(x)}{h}=\dfrac{(2(x+h)^2-3)-(2x^2-3)}{h}\\\\=\dfrac{2(x^2+2hx+h^2))-3-2x^2+3}{h}=\dfrac{2x^2+4hx+2h^2-3-2x^2+3}{h}\\\\=\boxed{4x+2h}[/tex]

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Additional comment

The square of a real number is always positive. That should be your first clue that (-4)² = 16 ≠ -16.

Sometimes it helps to remember that an exponent signifies repeated multiplication:

  (-4)² = (-4)(-4) . . . . . . has an even number of minus signs, so is positive.

Please note that this is different from -4² = -(4²) = -16.

is this a test? if not let me know

Answer:

4400

Step-by-step explanation:

to solve this we should first put them in an equation

0.55 * 8000

because there are 3 zeros after the second number we can first put three 0s

?000

then multiply 8 by 55

440

then add that to the 000

440000

now because the first number as 2 decimal points we take the invisible decimal point at the end and move it to the left two

440000. --> 4400.00

which is also

4,400

that is your answer

Answer:

10 degree will be the answer.. buddy..

Answer:

Step-by-step explanation:

She would work 20 hours. If you do 320 divided by 16 you get 20.

a) the minimum number of hikers who could have walked between 6 miles and 17 miles is 9 as it lies in the common interval of 10 ≤ x ≤ 15.

b)  the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

When the derivative equals 0, rearrange the function using elementary algebraic principles to find the value for x. The x-coordinate of the function's vertex, which is where the maximum or lowest will occur, is provided in this answer. the solution back into the original function to determine the minimum or maximum.

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Answer:

3

Step-by-step explanation:

Dividing both sides by 4, we get 3(x-6)=y+3.

From here, it is clear the coefficient of x after isolating y, or the slope, is 3.