There is a rope running from the top of a flagpole to a hook in the ground. The flagpole is 21 feet high, and the hook is 20 feet from its base. How long is the rope?

The length of a side must be less than the sum of the other two sides. Here, that means x < 10+13, or x < 23.

In addition, remember that the length of a side must be greater than the difference of the other two sides. That means x > 13 - 10, or x > 3.

Therefore we have two limits for the value of x: 3 and 23.

3 < x < 23

We know that the height of the rectangular shape is BC=AD= 4 feet and the the area is A=29.2 ft^2. Since the area of our rectangle is given by

we get

By moving the number 4 to the left hand side, we have

which also is the lenght of one side of our parallelogram.

Now, the area of our parallelogram is given by

where the base is given by segment DC=7.3 ft and the height FG=2 BC. Then, we get

by substituting our previous result and BC=4 ft, we obtain

Then, the answer is 58.4 ft^2

Daley, this is the solution:

We have: x² = 196

√x² = √196

x = +/- 14

Thus,

• 14 * 14 = 196

• -14 * -14 = 196

• 14² = 196

• -14² = 196

Any of these options could be taken to explain why +/- 14 is an acceptable value for x.

Answer:

70degrees

Explanation:

The diagrammatical representation of the statement is as shown;

Since the sum of angles on a straight line is 180degrees, then;

m8x+2 + 5x = 180

13x + 2 = 180

13x = 180 + 2

13x = 182

x = 182/13

x = 14

Get mmmmHence the measure of m

Answer: the answer is -5/6

Step-by-step explanation:

The coordinates of the image of the point (-6, -7) after translation is (-20,-3).

a pair of figures used to specify a point's location on a coordinate plane using the horizontal and vertical separations from the two reference axes. They are typically expressed by the x-value and y-value pair (x,y). Always, the x-coordinate comes before the y-coordinate.

An ordered group of numbers known as coordinates is used to specify a point's location. In the event that the point is on a plane, two numbers are used.

The horizontal and vertical addresses of a point in any two-dimensional (2D) space, such as a sheet of paper or a computer display screen, are called the X and Y coordinates, respectively. These coordinates work as a pair to pinpoint a point's precise location.

A point located at (x,y), translated by (a,b) maps to the point (x+a,y+b).

If we know the location of the point (x,y) and the location of its image (x',y'), we can know the values of (a,b) by subtracting:

(a,b) = (x',y') - (x,y)

We know the coordinates of the point (9,9) and the coordinates of its image (-5,13). Calculate the translation:

(a,b) = (-5,13) - (9,9) = (-14,4)

If the point (-6,-7) is translated under the same conditions, then it will map to the point (-6,-7) + (-14,4) = (-20,-3).

The coordinates of the image are (-20,-3)

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Answer:

[tex]a^{6}[/tex]

Step-by-step explanation:

[tex]a^{0}[/tex] × [tex]a^{6}[/tex] = [tex]a^{0+6}[/tex]

          = [tex]a^{6}[/tex]

step 1

Find the unit rate

divide the total miles by the total gallons of gas

so

476/14=34 miles/gal

Let

y ------> the distance in miles

x -----> the number of gal

we have that

the linear equation is equal to

y=34x

part 2

If y=578 miles

Find the value of x

substitute in the equation

578=34x

solve for x

x=578/34

x=17 gallons

ANSWER

b = 13

EXPLANATION

We want to solve the equation:

To do this, simplify the equation:

Isolate b:

That is the answer.

x = 4

The area of the figure can be found below.

The size of the farm is a rectangle therefore, we use the area of a rectangle to find the area of the farm.

The value of the fraction 3/7 × 14/15 × 10/18 is 2/9.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

The value of the fraction will be:

= 3/7 × 14/15 × 10/18

= 3/7 × 14/15 × 5/9

= 3/1 × 2/3 × 1/9

= 1 × 2 × 1/9

= 2/9

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To graph the ellipse, connect  (-2, -3), (6, 2), (14, -3), and (6, -8) with a smooth curve

The standard form of the equation of an ellipse with center (h, k) and major axis parallel to the x-axis is:

(x-h)²/a² + (y-k)²/b² = 1

When a>b

Major axis length = 2a

Coordinates of the vertices are (h±a, k)

Minor axis length is 2b

Coordinates of covertices are (h, k±b)

Coordinates of foci are (h±c, k). Also c²= a²-b²

Given: the equation (x-6)²/64 + (y+3)²/25 = 1

Comparing the given equation with (x-h)²/a² + (y-k)²/b² = 1:

h = 6, k = -3 => (h, k ) = (6, -3)

Thus, the center of the ellipse is (6, -3)

Coordinates of the vertices are (h±a, k)

Since a² = 64, a = √64 = 8

Thus, the endpoints of the major axis are 8 units from the center

(h±a, k) implies (h-a, k) or (h+a, k). Thus:

(h±a, k) = (6-8, -3) = (-2, -3) or (6+8, -3) = (14, -3)

Coordinates of covertices are (h, k±b)

Since b² = 25, a = √25 = 5

Thus, the endpoints of the minor axis are 5 units from the center

(h, k±b) implies  (h, k-b) or  (h, k+b). Thus:

(h, k±b) = (6, -3-5) = (6, -8) or  (6, -3+5) = (6, 2)

Therefore:

The center of the ellipse is (6, -3). The endpoints of the major axis are 8 units from the center. The endpoints of the minor axis 5 are units from the center.

To graph the ellipse, connect  (-2, -3), (6, 2), (14, -3), and (6, -8) with a smooth curve.

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Answer:

A

Step-by-step explanation:

(7 / 12) × 4 = 28 / 12 = 2 and 4 twelfths

Answer:

6

Step-by-step explanation:

Using the factor theorem, the expression evaluated at [tex]x=1[/tex] will equal [tex]0[/tex].

[tex]1^3+3(1^2)+k(1)-10=0 \\ \\ 1+3+k-10=0 \\ \\ k=6[/tex]

The 106° measure of arc [tex]m\widehat{HJ}[/tex] and the length of the chords [tex]\widehat{FH}[/tex] and [tex]\widehat{JH}[/tex], which are the same, indicates that m∠G = 21° and ΔFGH is not isosceles. The correct option is option C;

C. The measure of ∠G is 21°, and triangle FGH is not isosceles

An isosceles triangle is a triangle that have two sides of the same length and two angles of the same measure.

According to the outside angle to a circle theorem, the measure of the outside angle ∠G formed by the secant GJ and the tangent GF is equal to the difference of the measures of the arcs [tex]m\widehat{F'KJ}[/tex], and arc [tex]m\widehat{FH}[/tex] divided by 2.

[tex]m\widehat{F'KJ}[/tex] = 360° - [tex]m\widehat{FH}[/tex] - [tex]m\widehat{HJ}[/tex]

[tex]\widehat{FH}[/tex] = [tex]\widehat{JH}[/tex]

[tex]\widehat{FH}[/tex] ≅ [tex]\widehat{JH}[/tex]

The lengths of the chord intercepted by congruent arcs are congruent.

Therefore; [tex]\widehat{JH}[/tex] ≅  [tex]\widehat{FH}[/tex]

Which indicates;

[tex]m\widehat{JH}[/tex] = 106° = [tex]m\widehat{FH}[/tex]

[tex]m\widehat{F'KJ}[/tex] = 360° - 106° - 106° = 148°

m∠G = ([tex]m\widehat{F'KJ}[/tex] - [tex]m\widehat{FH}[/tex]) ÷ 2

m∠G = (148° - 106°) ÷ 2 = 21°

[tex]m\widehat{F'KJ}[/tex] = 148°

m∠FHJ = 148° ÷ 2 = 74° (Angle at the center is twice angle formed at the circumference)

∠FHJ = ∠HFG + ∠G (exterior angle to triangle ΔFGH)

∠HFG = ∠FHJ - ∠G

Therefore; m∠HFG = 74° - 21° = 53°

m∠HFG = 53°

m∠FHG = 180° - 74° = 106° (linear pair angles property)

The correct option is option C.

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Let's calculate the distance between F and G:

F=(-4,-2)

G=(2,-2)

The distance between M and P is half the distance between F and G, so:

The coordinates of P are:

P=(2,-8)

and

M=(x,-8)

So:

Since M is in the 3rd quadrant:

M= (-5,-8)

----------------------------------------------

Let:

(x1,y1)=(-2,1)

(x2,y2)=(-5,4)

The angle sum property of a triangle the and in isosceles triangle base angles are equal theorem are used.

In the given triangle, the measure of two angles are 67° and 35°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

7a) Using angle sum property of triangle, we get

Now, 67°+35°+x=180°

⇒ 102°+x=180°

⇒ x=180°-102°

⇒ x=78°

7b)

67°+78°+y=180°

⇒ 145°+y=180°

⇒ y=180°-145°

⇒ y=35°

8a) In isosceles triangle base angles are equal.

Here, p=q

50°+p+q=180°

⇒ 50°+p+p=180°

⇒ 2p=130°

⇒ p=65°

So, p=q=65°

8a) Here, c+115°=180°

⇒ c=180°-115°

⇒ c=65°

So, b=c=65°

Now, a+b+c=180°

⇒ a+65°+65°=180°

⇒ a+130°=180°

⇒ a=50°

Hence, the angle sum property of a triangle the and in isosceles triangle base angles are equal theorem are used.

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To order the values ​​from least to greatest, we must take into account some important rules, for example.

1.a whole number is greater than a decimal number

2. The greater the decimal number that has more in its integer part.

3.The number placed furthest to the right of the number line is greater. For example +2 is greater than -1. -2 is greater than -3

Now taking into account these rules, we are going to order the numbers given in the exercise from lowest to highest;

-35

-4.3

1.21

2.7

III ;which is equal to 3 integers

4.6

The equation for the distance between the friends after t hours is 47.17t.

Let one point be (x, y) and another point be (h, k). Then the distance between the points will be

D² = (x - h)² + (y - k)²

Two companions drive off this way and from a similar spot. One travels North at 40 miles each hour, while different travels East at 25 miles each hour.

The equation for the distance between the friends after t hours is given as,

Let the x-axis as east and the y-axis as north. Then the coordinate after t hours will be (25t, 0) and (0, 40t). Then the distance between them is given as,

D² = (25t - 0)² + (0 - 40t)²

D² = 625t² + 1600t²

D² = 2,225t²

D = 47.17 t

The equation for the distance between the friends after t hours is 47.17t.

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ANSWER

w = 6.71 or -6.71

EXPLANATION

The correct option C; 4x + y = 21 is the equation combines with the x + 2y = 21 equation to form a system of equations with the solution x = 3 and y = 9.

x + 2y = 21    eq .....(i)

The solutions are x = 3 and y = 9.

Put the values of x and y in equation (i),

3 + 2 × 9 = 21

3 + 18 = 21

21 = 21

Now, evaluate every option by substituting the values.

A. 4x + 6y = 64

Put the values of x and y in equation,

4 × 3 + 6 × 9 ≠ 64

48 ≠ 64

In correct option.

B. 2x + y = 36

Put the values of x and y in equation,

2 × 3 + 9 ≠ 36

15 ≠ 36

Incorrect option

C. 4x + y = 21

Put the values of x and y in  equation,

4 × 3 + 9 = 21

12 + 9 = 21

21 = 21

Correct option.

Thus, equation combines with the x + 2y = 21 equation to form a system of equations with the solution x = 3 and y = 9 is  4x + y = 21.

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We can start by plotting the triangle JAG and the line y = 2 to see how we can solve it:

We can see the line y = 2 (red line) over which we have to reflect the point J, A and G.

To do that we have to look at the distance of each point to the line.

This distance will be the distance at which the image point will be located, opposite to the the original point.

As y = 2 is an horizontal line, the distance is vertical and the x-coordinate of the original points and the images will remain equal. Only the y-coordinate will change.

We can sketch the procedure as:

Then, for example, poing G is 1 unit below y = 2, so its image G' will be one unit over the line y = 2, locating at (2,3).

Point J is 2 units above y = 2, so J' will be 2 units below y = 2.

Point A is 3 units above y = 2, so A' will be 3 untis below y = 2

We can plot the remaining points as:

The red triangle is the original triangle and the blue triangle is the image.

Answer:

The coordinates are J'=(1,0), A'=(3,-1) and G'=(2,3).

Since the weight varies directly, we have that

where k is the constant of proportinality.

In order to find k, we can divide both sides by 26.64 and get

which gives

Once we know the constant of proportionallity, we can write

where x denotes the unknown weight on the Moon. Since k is 5.8825, we get

Then, by dividing both sides by 5.8825, we obtain

Therefore, we have

Finally, by rounding to the nearest tenth, the answer is: 36.3 lb

The correct option B. It is compressed horizontally by a factor of 2 and translated up 3 units.

For the given question;

The image function is defined as ;  y = ㏒(2x) + 3

The parent function is; y = ㏒(x).

Thus, the image function  y = ㏒(2x) + 3 is obtained by the process as,compressed horizontally by a factor of 2 and translated up 3 units.

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The complete question is-

How is the graph of y = ㏒(2x) + 3 related to the graph of y = ㏒(x).

Options are-

A. It is stretched horizontally by a factor of 2 and translated up 3 units.

B. It is compressed horizontally by a factor of 2 and translated up 3 units.

C. It is stretched vertically by a factor of 2 and translated up 3 units.

D. It is compressed vertically by a factor of 2 and translated up 3 units.

Answer:

5.5, 5¼, 5 1/5 and 5.1.

Explanation:

To list the height from greatest to least, we convert each of them to a decimal.

Therefore, the weights are: 5.1, 5.2, 5.5 and 5.25

Arranging them from greatest to least gives:

5.5, 5.25, 5.2 and 5.1 which is equivalent to: 5.5, 5¼, 5 1/5 and 5.1.

The expression is given as,

Rearranging the like terms,

Like terms : Terms that have same power of variable.

Simplifying further,

Thus the result of the given expression is,

Answer:

-8 + 10x^2 - 6x

Step-by-step explanation:

(doesn’t have to be in this order)

1. Combine numbers with the x^2

-3 + 10x^2 - 4x - 5 - 2x

2. Combine regular numbers

-8 + 10x^2 - 4x - 2x

3. Combine numbers with the plain x

-8 + 10x^2 - 6x

Here, we want to find the circumfrence and area of the circle

To find either of this, we need the value of the radius of the circle

The radius of a circle is the distance btetween the center of the circle and the circumfrence of the circle. In this question, this distance is 20 ft

Mathematically, we can calculate the area with the formula;

To calculate the circumfrence of the circle, we use the formula below;

If the larger number is x, and the smaller one is y, then what we have is;

Therefore, the numbers are 7 and 1

Answer:

Inequality Form: -5<x<2

Interval Notation: (-5,2)