In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles.

Based on the given information, answer the questions below. Round each answer to the nearest tenth.

Part A: How tall is the pole? Show your work.

Part B: How far from the base of the pole does Wire 2 attach to the ground? Show your work.

Part C: How long is Wire 1? Show your work.

Answer:

que tienes que realizar no se entiende tu pregunta lo siento

Answer: 2a+5

5a-2-3a+7

First gather together the like terms

5a-3a  and  -2+7

then solve

5-3=2   and -2+7=5

answer = 2a+5

Answer:

See below

Step-by-step explanation:

The equations are in form   y = mx + b  where m = slope

  if the lines are parallel then the slopes are equal :

3/K  = H/2      Done.

The Pythagorean Theorem indicates the following relationship between the squares and triangles.

Part A

Part E

Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.

Part A

The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached

The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²

Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.

Part E

The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n

It was shown that c² = n²

Therefore;

c = n

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Answer:

x = 16

Step-by-step explanation:

1: Put the numbers into an equation.

(1672.50 - 1068.50) / 37.75x

2: Solve the equation in parentheses.

(604) / 37.75x

3: Divide.

16 = x

Only 16 players can be brought to the tournament

Every game of skee ball game requires 2 tokens and every game of pin ball game require 4 tokens.

Given that,

Cindy and Irma visited an arcade where the games accepted tokens. Irma used 58 tokens in total while playing 9 games of skee ball and 10 games of pinball. Cindy used up 26 tokens playing 5 games of skee ball and 4 games of pinball concurrently.

We have to find how many tokens are needed for each game. How many tokens are required for each skee ball game.

Let us take the skee balls as x and the pin ball as y.

We get,

9x+10y=58---> equation (1)

5x+4y=26---> equation (2)

Multiply equation (1) with 5 and equation (2) with 9.

5(9x+10y=58)⇒45x+50y=290

9(5x+4y=26)⇒45x+36y=234

                     ------------------------          (subtracting those equation)

                       0+14y=56

14y=56

y=56/14

y=4

Substitute y=4 in equation(2)

5x+4y=26

5x+4(4)=26

5x+16=26

5x=26-16

5x=10

x=10/5

x=2

Therefore, Every game of skee ball game requires 2 tokens and every game of pin ball game require 4 tokens.

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The value of R when A equal 5 is 3.6 and the value of A when R equal 9 is 2 as R is varies inversely to A.

Proportional relationships are relationships between two variables where their ratios are equivalent.

If R is inversely proportional to A.

R ∝ 1/A, then

R = k/A

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

R = k/A

Plug in R = 12 and A = 1.5 and solve for k

k = R × A

k = 12 × 1.5

k = 18

a) The value of R when A = 5 will be;

R = k/A

R = 18 / 5

R = 3.6

b) The value of A when R = 9

R = k/A
R × A = k

A = k/R

A = 18 / 9

A = 2

Therefore, the value of A when R equal 9 is 2.

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The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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According to the triangle inequality, the length of a triangle's third side must be greater than the sum of any two other triangle lengths, so the length of the steel piece will likely be 4 or 5 inches.

Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b≥ c. The basic tenet of the theorem is that a straight line connects any two points.

Here,

If they are an integer number of inches long and less than six, the following lengths are possible: 4 ,5

According to the triangle inequality, any two other triangle lengths must be greater than the third side of a triangle's length:4+4 = 8 > 6

4+6 = 10 > 4

5+5 = 10 > 6

6+5 = 11 > 5

According to "The Triangle Inequality," which states that the length of a triangle's third side must be greater than the sum of any two other triangle lengths, the piece of steel's potential length will be 4 or 5 inches.

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The graph of (y = 4x), which depicts the relationship between the quantity of tickets sold (x) and the sum of the proceeds from the sales (y), can be drawn by first formulating the linear equation and then using the transformation.

Which is the function's graph?

We have a piecewise function right here:

If x > 6, f(x) = 0.5*x - 2.

If x > 6, f(x) = -x - 1

Given:

Each ticket for the school play is $4.

There have been 'x' tickets sold in total.

The tickets generated 'y' in total revenue.

The graph showing the relationship between the quantity of tickets sold (x) and the sum of the ticket sales (y) can be drawn using the procedures below:

Form the linear equation in two variables as a first step.

y = 4x

The total revenue from the tickets is shown in the equation above.

Draw the graph of (y = x) in step two.

Step 3: In the graph of (y = x), multiply the x-axis by 4 units. The graph that is produced is (y = 4x).

You may find the graph for (y = 4x) below.

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Answer:

Bracelets: 7 Necklaces: 9

Step-by-step explanation:

b+n=16

6n+24n=258

b=-n+16

6(-n+16)+24n=258

-6n+96+24n=258

18n=162

n=9

6n+24(9)=258

6n+216=258

6n=42

n=7

B stands for bracelets

N stands for necklaces

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

Let the length (cm) be l , width (cm) be w , area be A ([tex]cm^{2}[/tex]) and time (s) be t .

Given : dl / dt = 6 cm/s and dw / dt = 8 cm/s

Area of rectangle = l * w

Differentiating wrt. t ,

dA / dt = ( l ) ( dw / dt ) + ( dl / dt ) ( w )

Therefore , dA / dt = 8l + 6w

Hence , when l = 12 cm and w = 10 cm

dA / dt = ( 8 * 12 ) + ( 6 * 10 )

dA / dt = 156 [tex]cm^{2}[/tex]/s .

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

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The distance from one corner of the field to the opposite corner, using the Pythagorean Theorem, is of:

125 meters.

The Pythagorean Theorem is a geometry axiom relating the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the equation presented as follows:

[tex]h^2 = l_1^2 + l_2^2[/tex]

From the situation described in this problem, we have that:

Hence the distance from one corner of the field to the opposite corner is obtained as follows:

d² = 68² + 105²

d = sqrt(68² + 105²)

d = 125 meters.

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The answer to the given quadratic equation is y =  ( x + 4 )²

A(x + m)2 + n is the formula for completing the square, where m is any real number and n is a constant factor.

The following straightforward formula can be used to finish the square instead of the intricate step-by-step procedure. Find the following in order to complete the square in the phrase ax2 + bx + c:

N = c - (b2/4a) and m = b/2a

Enter these numbers where they belong: ax2 + bx + c = a(x + m)2 + n. These equations are geometrically derived.

Given : A quadratic equation y = 7x² + 56x + 117

this can also written as y = x² + 8 x + 17

y = x² + 4² - 4² + 17

y =  ( x + 4 )²

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Answer:

not a solution

Step-by-step explanation:

we can just fill it in on both equations

-4(4)+3(1)=2

-16+3=2

-13=2

It doesn’t work for this equation so it’s not a solution

Hopes this helps please mark brainliest

Answer:

No

Step-by-step explanation:

For (4, 1 ) to be a solution then both equations must be true

substitute x = 4 and y = 1 into both equations

- 4(4) + 3(1) = - 16 + 3 = - 13 ≠ 2

3(4) - 9(1) = 12 - 9 = 3

Since both equations are not true then (4, 1 ) is not a solution of the system.

Answer: 13,8 litres

Step-by-step explanation:

£1.45 ------------ 1 L

 £20 ------------- ?

?= [tex]\frac{20 *1}{1.45} = 13,79310345 L[/tex] = 13,8 L

The pounds of flour the bakery has at the end of the month is 92.725 lb

The negative numbers denote when flour was used while the positive numbers denote when flour was added. The negative numbers would be subtracted while the positive numbers would be added.

For ease of computation, the mixed numbers would be converted to decimals.

-58 1/2 = -58.5

75 3/10 = 75.3

-67 7/8 = -67.875

Pounds of flour the bakery has at the end of the month: 215.4 - 58.5 - 70.6 + 75.3 - 67.875 = 92.725 lb

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Equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

Given:

x - intercept = 4

y - intercept = 5

At x intercept y = 0 and at y intercept x = 0

(4,0) and (0,5)

slope = 5-0/0-4

= 5/-4

m = -5/4

substitute (4,0) and m value,

y = mx+c

0 = -5/4*4 +c

0 = -5 + c

c = 5

y = mx + c

y = -5/4(x) + 5.

Therefore equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

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The measure of angle EAC IS 50°

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.

∠BAE = x + 30, ∠EAC = 3x - 10

If AE is a line that bisects BAC,

then ∠BAE = ∠EAC

which becomes,

x + 30 = 3x - 10

collecting like terms,

x - 3x = -10 - 30

-2x = -40

x = -40/-2

x = 20°

But m ∠EAC = 3x - 10

substituting x = 20°

we have ∠EAC = 3(20) - 10

                          = 60 - 10

    ∠EAC       = 50°

In conclusion, the value of  ∠EAC  = 50°

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The graph of the given functions is (see in attachments).

From the question, we have

g(x) = 0.44√3.2x−4.1

Graph:

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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The car travels 30 miles in 45 minutes with the speed 40 miles/hour with the constant speed.

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. The distance traveled by a moving object in a specific amount of time is its speed. How quickly something is moving is determined by its speed. The distance traveled by an object in a given amount of time divided by the time gives the object's average speed.

Here,

45 minutes/60 minutes= .75 hours (this gives you the amount of time in hours)

time x speed = distance

.75 hours time x 40 mph speed = 30 miles distance

With a constant speed of 40 miles per hour, the car covers 30 miles in 45 minutes.

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The number of real roots found are-

1. (x-4)(x+3)^2(x-1)^3=0 ; 6 real roots.

2. X^2(x^3-1)=0 ; 3 real roots.

3. X(x+3)(x-6)^2=0 ; 4 real roots.

4. 3x(x^3-1)^2=0 ; 3 real roots.

5. (x^3-8)(x^4+1)=0​ ; 1 real roots.

Consider the given cases-

1. (x-4)(x+3)^2(x-1)^3=0,

Put each equals zero.

x – 4 = 0 or (x + 3)^2 = 0 or (x – 1)^3 = 0,

Thus,

x = 4

x = –3 twice

x = 1 thrice

All are real numbers, thus given polynomial has 6 real roots.

2. x^2(x^3-1)=0

Put each equals zero.

x² = 0

x³ – 1 = x³ – 1³ = (x – 1)(x² + x + 1) = 0

The quadratic expressions has 2 imaginary roots.

Use the discriminant formula to find-

D = b² – 4ac = 1² – 4(1)(1) = 1 – 4 = –3 < 0.

Thus, roots that are not real.

So, the real roots of this polynomial : 0(twice) and 1.

Hence, thus given polynomial has 3 real roots.

3. x(x+3)(x-6)^2=0

Put each equals zero.

x = 0

x = 3

x = 6 twice

Hence, thus given polynomial has 4 real roots.

4. 3x(x^3-1)^2=0

Put each equals zero.

3x = 0 and  x = 0

(x^3 – 1)² = [(x – 1)(x² + x + 1)]² = (x – 1)²(x² + x + 1)² = 0,

Here, only two roots are real

The quadratic expression do have unreal roots, thus 1 twice are the real roots.

Hence, thus given polynomial has 3 real roots..

5. (x^3-8)(x^4+1)=0

Put each equals zero.

x³ – 8 = x³ – 2³ = (x – 2)(x² + 2x + 4) = 0

There is only one real root i.e, 2, the quadratic expression do have imaginary roots

Check using the discriminant formula

D = b² – 4ac = 2² – 4(1)(4) = 4 – 16 = – 12 < 0.

x⁴ + 1 = 0 has imaginary roots.

Hence, thus given polynomial has 1 real roots..

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The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.

Given that, last week, Lora used 840 minutes. This week, Lora used 504 screen time minutes on the phone.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Now,

Difference=840-504

= 336

Percentage decrease = Difference in value/Original value ×100

= 336/840 ×100

= 0.4 ×100

= 40%

The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.

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Applying the transformation rule (x - 2.y + 4) and using the scale factor k = 3 for dilation gives

preimage      translation image     Dilation image

A (1.-2)             A' (-1, 2)                   A'' (-3, 6)  

B (4,-1)             B' (2, 3)                    B'' (6, 9)

C (5.-3)            C' (3, 1)                     C'' (9, 3)

Transformation is a term used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

Applying the transformation rule (x - 2.y + 4 ) gives

A (1.-2) = (1 - 2, -2 + 4) = (-1, 2)

B (4,-1) = (4 - 2, -1 + 4) = (2, 3)

C (5.-3) = (5 - 2, -3 + 4) = (3, 1)

preimage        image

A (1.-2)             A' (-1, 2)

B (4,-1)             B' (2, 3)

C (5.-3)            C' (3, 1)

Dilation involves making the image bigger or smaller. In this case K > 1 hence the image is bigger

Using the scale factor k = 3 for dilation rule (kx, ky) gives

A' (-1, 2) = (-1 * 3, 2 * 3) = (-3, 6)

B' (2, 3) = (2 * 3, 3 * 3) = (6, 9)

C' (3, 1) = (3 * 3, 1 * 3) = ( 9, 3)

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Answer:

-64

Step-by-step explanation:

Start by moving everything to the left side making the equation equal 0. Then combine like terms.

If the equation 2(x-7) = 36, then the value of x is 13 and 1

The equation is

[tex](x-7)^2[/tex] = 36

The equation is defined as the statement the connect the two expression with an equal sign.

We know the square of 6 is 36

[tex]6^2[/tex] = 36

Substitute the value in the equation

[tex](x-7)^2=6^2[/tex]

Apply square root in the both side of the equation

[tex]\sqrt{(x-7)^2} = \sqrt{6^2}[/tex]

Then the equation will become

x - 7 = ± 6

If the value is +6

x - 7 = 6

Add both side of the equation by 7

x - 7 +7 = 6+7

x = 13

If the value is -6

x - 7 = -6

Add both side of the equation by 7

x - 7 + 7 = -6 + 7

x = 1

Hence, If the equation 2(x-7) = 36, then the value of x is 13 and 1

The complete question is:

Given [tex](x-7)^2=36[/tex], find the value of x.

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Answer:

5 and 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

(a)

y = 5x - 3 ← is in slope- intercept form

with gradient m = 5

(b)

3y - 12x + 7 = 0 ( add 12x to both sides )

3y + 7 = 12x ( subtract 7 from both sides )

3y = 12x - 7 ( divide through by 3 )

y = 4x - [tex]\frac{7}{3}[/tex] ← in slope- intercept form

with gradient m = 4

Time taken by bus to travel from Las Vegas to salt lake city is 6.41 hours.

Here it is given that bus travel from La to Lv in 4 hours and the distance between them is 265 miles.

We have to find the time taken to travel from Las Vegas to salt lake city whose distance between them is 425 miles.

Formula to find the speed is:

Speed = Distance / Time

Distance = 265 miles

Time = 4 hours

Speed = 265/4

= 66.25 miles/ hour

From this, we can find the time taken to travel from Las Vegas to salt lake city.

Distance = 425 miles

Speed = 66.25 miles/ hours

Speed = Distance/time

Time = Distance / Speed

= 425/ 66.25

= 6.41 hours

Therefore the time taken is 6.41 hours.

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