A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a short vertical support.
What is the length x of a diagonal support, to the nearest tenth of a foot?

x≈_____ feet

Using the corresponding angle theorem, the value of y is 36 degree.

In the given question, b||c.

We have to find the value of y.

Given: b||c

Find: Value of y

Let x be the value of side angle of (2y+34) degree.

So, using the corresponding angle theorem

x = 74 degree

As we know that the sum of straight line is 180 degree.

So 2y+34+x = 180

Now putting the value of x

2y+34+74=180

After simplifying

2y+108=180

Subtract 108 on both side, we get

2y=72

Divide by 2 on both side, we get

y=36

Hence, the value of y is 36 degree.

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The option 1 "Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT." is correct.

In the given question, the triangles below are similar.

So, we have to state the reason and write the similarity statement.

ΔQRS≈

(a) Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT.

(b) Similar to due SAS and a scale factor of 0.29. Triangle QRS is similar to triangle TUV.

(c) Similar due to AA. Triangle QRS is similar to triangle VUT.

(d) Similar due to SSS and a scale factor of $0.29$. Triangle QRS is similar to triangle VUT.

As we know that, the ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.

Since the both triangle area similar so using the SSS theorem;

Triangle QRS congruence to triangle VUT.

QR/VU = RS/UT = SQ/TV

So QR/VU = 56/16; RS/UT = 70/20; SQ/TV = 98/28

QR/VU = RS/UT = SQ/TV = 3.5

Hence, ΔQRS≈ΔVUT using the SSS theorem with the scale factor of 3.5. So the option 1 "Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT." is correct.

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Answer:

[tex]1\frac{8}{9}[/tex]

Step-by-step explanation:

[tex]\sf 8-6\frac{1}{9}[/tex]

First, make 6 1/9 an improper fraction.

[tex]\sf8-\frac{55}{9}[/tex]

And now to solve the fractions you have to make the denominators the same.

For that, multiply both the numerator and denominator of 8 by 9.

Let us solve it now.

[tex]\sf8-\frac{55}{9}\\\\\sf\frac{8*9}{1*9} -\frac{55}{9}\\\\\sf\frac{72}{9} -\frac{55}{9}\\\\\frac{72-55}{9} \\\\\frac{17}{9}[/tex]

And now let us write the answer as a mixed number.

[tex]1\frac{8}{9}[/tex]

Answer: x

Step-by-step explanation:

-3x-7+4x+7

than because the 7's cancel each other out it would become

-3x+4x which would be equal to x

Answer:69.69

Step-by-step explanation:

FIrst add the sides then subtract the top and then mutilpy it by 2

Answer:

The surface area of the box is 52 square meters. To calculate the surface area of a rectangular box, we need to find the area of each face and then add them together. In this case, the box has six faces, each with a different length and width. The top, bottom, and side faces are all rectangular, while the front and back faces are also rectangular but have a different size.

To find the surface area of the box, we can start by finding the area of the top and bottom faces. The top and bottom faces are both 2 meters by 4 meters, so the area of each face is 2 * 4 = 8 square meters. Therefore, the total area of the top and bottom faces is 8 * 2 = 16 square meters.

Next, we can find the area of the front and back faces. The front and back faces are both 3 meters by 2 meters, so the area of each face is 3 * 2 = 6 square meters. Therefore, the total area of the front and back faces is 6 * 2 = 12 square meters.

Finally, we can find the area of the side faces. The side faces are both 3 meters by 2 meters, so the area of each face is 3 * 2 = 6 square meters. Therefore, the total area of the side faces is 6 * 2 = 12 square meters.

To find the total surface area of the box, we need to add the areas of the top, bottom, front, back, and side faces together.

Step-by-step explanation:

Answer: 52 square meters

Step-by-step explanation:

at first just off of the top of my head i thought it would be 26.

Answer:

1. (1/2)x + 6

2. (1/2)x - 4

3. y = (2/1)x + 2

4. y = 5x - 1

5. y = (1/5)x + 3

Step-by-step explanation:

y = mx + b

Parallel lines have the same "mx"

1. y = (-1/2)x - 2

Parallel line:

y = (-1/2)x + 6

2. y = (1/2) + 4

Parallel line:

y = (1/2)x - 4

3. y = 2x - 4

Parallel line:

y = (2/1)x + 2

4. y = 5x + 2

Parallel line:

y = 5x - 1

5. y = (1/5)x + 10

Parallel line:

y = (1/5)x + 3

I hope this helps!

The equation of the conic represents a circle with an area of 36π square units.

In this problem we find the equation of the conic in general form, on which we need to determine what kind of conic it represents. This can be done by finding the standard form of the equation by means of algebra properties, using a strategy known as completing the square. The quadratic equation in general form is described by the quadratic equations of the form:

A · x² + B · y² + C · x + D · y + E · x · y + F = 0

Now we proceed to find the standard form of the equation. First, write the equation in standard form:

x² + y² - 3 · x + 6 · y = 7 · x + 2

x² + y² - 10 · x + 6 · y - 2 = 0

Second, complete the square:

(x² - 10 · x + 25) + (y² + 6 · y + 9) = 2 + 25 + 9

(x - 5)² + (y + 3)² = 36

The standard form of the quadratic equation indicates the equation of a circle with a diameter of 12 units and a center at (h, k) = (5, - 3). The area of the circle is calculated below:

A = 0.25π · D²

Where D is the diameter of the circle, in units.

A = 0.25π · 12²

A = 36π

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The solution is Option A.

The mean of the actual weights of the samples is 1.002

What is Mean?

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the observations be represented as M

Now , the value of mean M is calculated as

The number of samples be = 10

The weight of the samples can be given from set A

The value of set A is

Set A = { 1.01 , 1.03 , 0.98 , 0.99 , 1.01 , 1.02 , 0.98 , 1.05 , 0.97 , 0.98 }

The sum of the values of weights of set A is S

Sum S = 1.01 + 1.03 + 0.98 + 0.99 + 1.01 + 1.02 + 0.98 + 1.05 + 0.97 + 0.98

Sum of weights S = 10.02

Now , the mean of the weights is given by

Mean = Sum of Values / Number of Values

Mean = Sum of weights / Number of samples

Substituting the values in the equation , we get

Mean = 10.02 / 10

Mean M = 1.002

Therefore , the value of M is 1.002

Hence , The mean of the actual weights of the samples is 1.002

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For 10.75 years I'll receive an amount of $1,193 for an annuity of $12,083.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

A principle of $12,083 with 6.1% interest rate becomes $(12,083×1.061)

= $12,820.063.

∴ The no. of years the annuity provides you with payments of $1,193 is

= (12,820.063/1193).

= 10.75 years Or 10 years 9 months.

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A triangle cannot be formed with side lengths 3, 9, 17 because A. No, because 3 + 9 < 17

In geometry, a triangle is a polygon with three sides, three edges, and three vertices. The main characteristic of a triangle is that the sum of its internal angles is 180 degrees.

This is referred to as the triangle's angle sum property. It should be noted that any two sides of a triangle must have a sum of lengths greater than the third side.

In this instance, the result of multiplying 3 by 9 equals 12, which is less than 17. Therefore, choice A is the right one.

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Answer:

18 days

Step-by-step explanation:

1) Write an Equation:

50t + 100 = 1000

Where

100 is the set cost to sign up for the car service

t is time in days

2) Solve the Equation for t

50t + 100 = 1000

50t + 100 - 100 = 1000 - 100

50t = 900

50t / 50 = 900 / 50

t = 18

Answer:

D

Step-by-step explanation:

as a negative exponent always means 1/..., D is the correct answer.

9^-4 = 1/(9^4)

that is the precise definition of a negative exponent.

Answer:

-3x + y = -39

Step-by-step explanation:

If it is perpendicular to y=-1/3x+2, then the slope is positive 3. If it passes through (9, -12), then we can set up our equation:

y+12 / x-9 = 3. Simplifying, we have:

y=3x-39, which in standard form is:

-3x+y= -39

Hope this helps!

Answer:

d. h = 11.3 ft

Step-by-step explanation:

volume of cone = [tex]\frac{1}{3}[/tex]r²[tex]\pi[/tex]h

r = 4 feet

Put in your values:

[tex]\frac{1}{3}[/tex](4)²(3.14)h = 189 ft³

16(3.14)h = 567

50.24h = 567

h = [tex]\frac{567}{50.27}[/tex] = 11.3

The height of the cone is h = 11.3 feet

In geometry,  a cone is a three-dimensional shape formed by joining a set of line segments from a common point called apex to all the points of the base which is a circle.

Height of the cone is distance from apex to the center of the circular base.

Volume of a cone is defined as the total capacity of the cone and the formula for the same is given by,

V = [tex]\frac{1\\}{3}[/tex]πr²h

Here, V = 189 ft³, r = 4 ft, π = 3.14

Substituting these values in formula for the volume,

189 = [tex]\frac{1}{3}[/tex] × 3.14 × 4² × h

189 = [tex]\frac{50.24}{3}[/tex]h

h = 189 × 3 / 50.24

h = 11.285 ≈ 11.3

Hence the height of the cone with radius 4 ft and volume 189 ft³ to the nearest tenth of a foot is 11.3 ft.

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Earning of Jim, Bill and Tom are $x, $3x, and $(x + 5) respectively.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let Jim earned $x in one weekend.

Bill earned 3 times as much as Jim which is $3x.

Tom earned $5 more than Jim which is $(x + 5).

Sum of their all earnings will be,

= $(x + 3x + x + 5).

= $(5x + 5).

So, Jim is the least earner and Bill is the most earner.

The main concept of these types of questions is to form the expression interpreting from the given statements.

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The angles in the parallel lines are as follows;

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, let's find the angles m∠1 and m∠2.

Hence,

138 + m∠1 = 180(angles on a straight line)

The sum of angles on a straight line is 180 degrees.

m∠1 = 180 - 138

m∠1 = 42 degrees

Therefore,

m∠1 =  m∠2 (alternate exterior angles)

Alternate exterior angles are the pair of angles that are formed on th outer side of the parallel lines but on the opposite side of the transversal.

Alternate exterior angles are congruent.

Therefore,

m∠1 =  m∠2 = 42 degrees.

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The value of the given composite function f(g(x)) at x = -1 is that f(g(-1)) will be 6.2.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given function f(x) and g(x) are linear functions.

Take (-6,6) and (-1,5)

The equation will be as follows,

f(x) - 6 = (5 - 6)/(-1 + 6)(x + 6)

f(x) - 6 = -x/5 - 6/5

f(x) = -x/5 - 6/5 + 6

f(x) = -x/5 + (- 6 + 30)/5

f(x) = -x/5 + 24/5

Take (-6,-12) and (-1,-7)

g(x) + 12 = (-7 + 12)/(-1 + 6)(x + 6)

g(x) + 12 = x + 6

g(x) = x - 6

Now, f(g(x)) = -(x - 6)/5 + 24/5

f(g(-1)) = -(-1 - 6)/5 + 24/5

f(g(-1)) = 7/5 + 24/5 = 6.2

Hence "At x = -1, the value of the composite function f(g(x)) is that f(g(-1)) will be equal to 6.2.".

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Answer:

-120

Step-by-step explanation:

f(x) = 2-27+1

f(x) = 2-27+1

f(x) = -24

g(x) = 2²+1

g(x) = 4+1

g(x) = 5

f(x) g(x) = f(x) * g(x) = -24 * 5 = -120

Answer:

Step-by-step explanation:

180 = x + 50 +50

180 = x + 100

x + 100 = 180

x = 80

80 is the value of x.

The number that must be added to complete the square in the expression is 0.9².

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x² + 1.8x

The complete square is given as,

(a + b)² = a² + 2ab + b²

Now,

x² + 2 x 0.9(x) + 0.9²

(x + 0.9)²

Thus,

0.9² completes the square in the expression.

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The amount invested in the account that pays 1.5% interest is $584,285.71.

The amount invested in the account that pays 8.5% interest is $155,714.29.

The system of equations that represent the information in the question is:

x + y = 740,000 equation 1

0.015x + 0.085y = 22,000 equation 2

Where:

In order to determine the values, the elimination method would be used.

Multiply equation 1 by 0.015

0.015x + 0.015y = 11,100 equation 3

Subtract equation 3 from equation 2

0.070y = 10,900

Divide both sides of the equation by 0.070

y = 10,900 / 0.07

y = 155,714.29

Subtract 155,714.29  from $740,000

x = 740,000 - 155,714.29

x = 584,285.71

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Answer: True.

Step-by-step explanation:

        First, a right angle will always be equal to 90 degrees.

        Next, bisecting an angle means cutting it into two parts.

        Since the resulting two angles will always be less than 90 degrees, they will always be acute angles. The answer to this question is true.

Every three candy bars cost a dollar.

Divide 25 by three.  

$8.33

Using division, we know that the total number of students that wil plant 1280 plants are 256 in grade 5.

Division's opposite is multiplication.

If 3 groups of 4 total up to 12, then 4 are in each group when 12 is divided into 3 equal groups.

The fundamental goal of division is to produce equal groups or to ascertain how many individuals are in each category following a fair distribution.

So, we know that each student plant 5 trees.

In all, total 1280 plants were planted.

Then, calculate the number of studensts that planted 1280 plants as follows:

1280/5

256

Therefore, using division, we know that the total number of students that wil plant 1280 plants are 256 in grade 5.

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The slope intercept form is y= ( -3/2 ) x + 7/2

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

(x1,y1)= (3. -1) and (x2,y2)= (5, -4)

slope intercept form:

y=mx+b , m=slope, b = constant

m= (y2-y1) /( x2-x1) = (-4-(-1)) / ( 5-3) =  -3/2

line equation:

y-y1=m(x-x1)

Substitute the values

y-(-1)=( -3/2 ) (x-3)

y+1=( -3/2 ) x + 9/2

y= ( -3/2 ) x + 9/2 - 1

y= ( -3/2 ) x + 7/2

Thus, the slope intercept form is y= ( -3/2 ) x + 7/2

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The statement, "If m∠X ≅ m∠Y and m∠Y ≅ m∠Z, then m∠X ≅ m∠Z" demonstrates: D. the transitive property.

In geometry, the transitive property of congruency states that when two angles, sides, or triangles are congruent to a third angle, side, or triangle, then all three angles, sides, or triangles will be congruent to each other.

Illustrating the transitive property, if a = b, and b = c, therefore, a = b = c. We can then state that a = c.

Therefore, given that If m∠X ≅ m∠Y and m∠Y ≅ m∠Z, then m∠X ≅ m∠Z, we have:

Two angles, X and Z, which are both congruent to a third angle, Y.

Therefore, based on the transitive property, we can state that all three angles are congruent to each other, which leads us to conclude that:

m∠X ≅ m∠Z.

Thus, the statement given demonstrates the: D. transitive property.

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Answer:

5x + 15

Step-by-step explanation:

5(x + 3) ← multiply each term in the parenthesis by 5

= 5x + 15

"5x+15" is an expression equivalent to "5(x+3)".

If we expand this factorization, the resulting expression is equivalent to the original expression. This is how you expand it:

[tex]5(x+3)[/tex]

Check the attached image.

[tex](5)(x)+(5)(3)=\\ \\5x+15[/tex]

3. Conclude.

5x+15 is an expression equivalent to 5(x+3).