In ΔFGH, the measure of ∠H=90°, the measure of ∠G=85°, and GH = 4.5 feet. Find the length of FG to the nearest tenth of a foot.

See attachment for the graph of g(x) = 1/2x^2

The equation of the function is:

g(x) = 1/2x^2

The above function is a quadratic function that has only one term

Next, we plot  the graph using a graphing tool

See attachment for the graph of g(x)

Read more about quadratic functions at:

https://brainly.com/question/1214333

#SPJ1

The correct equation for the triangle is,

⇒ DF ≅ FD

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

By the figure, the coordinate of triangles are,

D = (- 5, 1)

E = (- 2, 3)

F = (- 3, - 2)

Hence, By using distance formula;

DE = √ (- 5 + 2)² + (1 - 3)²

     = √9 + 4

     = √13

EF = √ (- 2 + 3)² + (3 + 2)²

     = √1 + 25

     = √26

FD = √ (- 5 + 3)² + (1 + 2)²

     = √4 + 9

     = √13

Thus, We have;

⇒ DF ≅ FD

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer:

C. 1/8y¹²

Step-by-step explanation:

Simplify:

Correct choice is C

Solution of given expression (2y⁴)⁻³ is 1/8y¹². So, the correct option is option C.

Given expression: (2y⁴)⁻³

To simplify this expression

( 2 y⁴ )⁻³ = 1/( 2 y⁴ )³

= 1/2³ y ⁴*³

= 1/ ( 2 * 2 * 2 y¹² )

= 1/8 y¹².

Therefore, the expression (2y⁴)⁻³ is equal to 1/8 y¹².

Learn more about expression here;

https://brainly.com/question/27944537

#SPJ6

Answer:

60%

Step-by-step explanation:

Answer:

One possible dividend is 1,237

Step-by-step explanation:

One possible dividend will be 1,237

This is because of we multiply 247 by 5, we get 1,235 and we can add 2 so we can have remainder 2

The difference between the next factor of 5 and the last one which has 247 as the multiple of 5 is 5

So adding 1,2,3 and 4 to the product will give a number that is not up to the next multiple of 5 and thus we can have our dividend with the remainder

Answer:

0.06

Step-by-step explanation:

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle either is in the hexagon or in the circle

Area of rectangle = 26.2 * 13 =  340.6 sq inch

Area of Hexagon  = 3√3(side)²/2 = 3√3 (1.8)²/2 = 8.42 sq inch

Area of circle = π(radius)² = 3.14 * (2)² = 12.56 sq inch

Area of hexagon + area of circle = 12.56 + 8.42 = 20.98 sq inch

Probability of selecting point inside the hexagon or in the circle  = 20.98/340.6

= 0.06

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

5 groups ===> 1

1 group ====> 5

Step 02:

We must apply the algebraic rules to find the solution.

5 groups * 1 = 1 group * 5

5 * 1 = 1 * 5

5 = 5

The answer is:

Brent is correct

There are 11.66 moles of copper in a 9.00 cm x 9.00 cm x 9.00 cm cube.

To determine the number of moles of copper in a cube, we need to know the volume of the cube and the density of copper.

The volume of the cube can be found using the formula for the volume of a cube:

V = l x w x h

where l, w, and h are the length, width, and height of the cube, respectively. In this case, l = w = h = 9.00 cm, so:

V = 9.00 cm x 9.00 cm x 9.00 cm = 729 cm³

Next, we need to find the density of copper. According to the periodic table, the density of copper is 8.96 g/cm³.

Finally, we can use the density and volume to determine the number of moles of copper in the cube. We can do this by multiplying the density by the volume and then dividing by the molar mass of copper:

moles = (density x volume) / molar mass

moles = (8.96 g/cm³ x 729 cm³) / 63.55 g/mol

moles = 11.66 mol

So, there are 11.66 moles of copper in a 9.00 cm x 9.00 cm x 9.00 cm cube.

To learn more about the Volume, visit:

brainly.com/question/1578538

#SPJ4

For x = 7 will make the third side equal, so the triangles will be congruent by SSS.

What is the midpoint of the line?

In geometry, the midpoint is the middle of a line segment. It is equidistant from both endpoints and serves as the segment and endpoint centroid.

Given that M is a midpoint.

By definition of midpoint AM=MD.

It is given AB=CD in figure.

Two of the sides are equal .to prove the triangles to be congruent by SSS the third side must be equal

That is BM=CM,

Or  4x-1=3x+6

4x - 3x - 1 = 3x - 3x + 6

Simplifying, we get

x = 7.

Hence, x = 7 will make the third side equal, so the triangles will be congruent by SSS.

To learn more about the midpoint of the segment, visit:

https://brainly.com/question/896396

#SPJ4

Answer:

C-7

Step-by-step explanation:

took the assignment

Based on the definitions of vertical angles and linear pair, the values of the angle measures are:

m<1 = 117°

m<4 = 63°

Two angles that can be formed when a transversal crosses two parallel lines are:

Given the image above, we know that:

Measure of angle 2 = 63°

Therefore:

m<1 = 180 - m<2 [linear pair]

m<1 = 180 - 63

m<1 = 117°

m<4 = m<2 [vertical angles]

m<4 = 63°

Learn more about vertical angles on:

https://brainly.com/question/14362353

#SPJ1

Answer:

( 32/y ) - 6

Step-by-step explanation:

okay so quotient means the result obtained by dividing one quantity by another and the problem that follows that is 32 and a number, y

this is meaning that 32 and y and going to be dividing (32/y)

less than means subtraction and the number that's surrounding that is 6.

this means that 6 is going to be subtracted from (32/y)

hopefully this helped! good luck bud <3

Reason: Given

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

Reason: Perpendicular lines form right angles.

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

Reason: All right angles are congruent.

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

Reason: Given

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

Reason: Given

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

Reason: HL

Using statistics helps us make decisions based on empirical evidence, which is obtained through data analysis and inference.

Statistics provides us with a set of tools and methods to collect, analyze, and interpret data. By applying statistical techniques, we can make decisions based on evidence derived from empirical observations and measurements.

Statistics allows us to summarize and describe data, identify patterns and relationships, and draw conclusions from samples or populations. It helps us quantify uncertainty and assess the strength of evidence supporting different claims or hypotheses.

Decision-making based on statistics involves making inferences about a larger population based on the information available from a sample. By using probability theory and statistical models, we can estimate population parameters, test hypotheses, and make predictions about future events or outcomes.

Statistics provides a systematic and rigorous framework for evaluating evidence and reducing bias in decision-making. It allows us to objectively assess the reliability and validity of information, making decisions that are informed by data-driven analysis rather than intuition or anecdotal evidence.

In summary, statistics helps us make decisions based on evidence obtained through data analysis, enabling us to draw reliable conclusions, quantify uncertainty, and make informed choices in various fields such as business, medicine, social sciences, and more.

Learn more about parameters here:

https://brainly.com/question/29911057

#SPJ11

Therefore, the value of the integral ∫2^6 (5f(x))^2 dx is 900.

If the average value of the function f on the interval 2 ≤ x ≤ 6 is 3, we can express it mathematically as:

(1/(6 - 2)) ∫2^6 f(x) dx = 3

Simplifying this equation, we have:

(1/4) ∫2^6 f(x) dx = 3

Now, let's calculate the value of the integral ∫2^6 (5f(x))^2 dx:

∫2^6 (5f(x))^2 dx = 25 ∫2^6 (f(x))^2 dx

Since the average value of f on the interval 2 ≤ x ≤ 6 is 3, we can substitute it into the equation:

25 ∫2^6 (f(x))^2 dx = 25 * (4/1) * 3^2

Simplifying further, we get:

25 * (4/1) * 3^2 = 25 * 4 * 9 = 900

To know more about integral,

https://brainly.com/question/27428583

#SPJ11

Step-by-step explanation:

a number plus 10

x + 10

the product of 5 and a number

5x

2 times a number

2x

a number r subtracted by 10

r - 10

twice a number and 14

2x + 14

the sum of triple a number and 5

3x + 5

the quotient of n and 8

n/8

7 less than a number

x - 7

8 more than a number z

z + 8

a number n divided by 2

n/2

Answer:

x+10

5x

2x

r-10

2x+14

3x+5

n/8

x-7

z+8

n/2

Step-by-step explanation:

In principal, replace "a number" by x.

Answer:

5/8 inch longer

Step-by-step explanation:

Given:

Slope is undefined.

To find:

Which graph has an undefined slope?

Solution:

We know that, slope is change in y-values with respect to x-values.

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

The slope is undefined if the denominator is 0.

\(x_2-x_1=0\)

\(x_2=x_1\)

It means, the x-values are same. It is possible only for a vertical line.

Therefore, the slope of vertical lines are undefined or we can say that graph of a vertical line has an undefined slope. It is of the form \(x=a\), where, a is a constant and it can be any real number.

The values of m and n are 2.5 and 6, respectively

The size of the computer hard disk is given as:

\(a = 7.5 \times 10^7\)

The size after adding the extra memory stick is given as:

\(b = 7.75 \times 10^7\)

The size (s) of the memory stick is calculated by subtracting the size of the computer hard disk before and after adding the memory stick.

This is represented as:

\(s =b -a\)

So, we have:

\(s =7.75 \times 10^7 -7.5 \times 10^7\)

Factor out 10^7

\(s =(7.75 -7.5 )\times 10^7\)

Subtract 7.5 from 7.75

\(s =0.25\times 10^7\)

Rewrite as:

\(s =2.5\times 10^6\)

From the question, we have:

\(s =m\times 10^n\)

So, the equation becomes

\(m\times 10^n = 2.5\times 10^6\)

By comparison:

\(m =2.5\)

\(n = 6\)

Hence, the values of m and n are 2.5 and 6, respectively

Read more about scientific notation at:

https://brainly.com/question/5565320

Answer:

x=5

Step-by-step explanation:

slope = -8 - 5 / 5 - 5

-13/0 = 0 (undefined)

y intercept = no y intercept

x intercept = 5

338 students went on the field trip.

Given:

Four-ninth of the total participants rode a large bus, and the rest rode a smaller bus.

156 people rode the larger bus.

Let x be the total participants.

4/9 x = 156

multiply by 9 on both sides

4*9/9 x = 156*9

4x = 156*9

4x = 1404

divide by 4 on both sides

4x/4 = 1404/4

x = 1404/4

x = 351.

number of students = total participants - adult chaperones.

= 351 -13

= 338 students

Therefore 338 students went on the field trip.

Learn more about the students and field trip here:

https://brainly.com/question/22445131

#SPJ1

Answer:

4.72222222222

Step-by-step explanation:

I just calculate

can I have brainliest

Answer:

Step-by-step explanation:

1.First find the left songs after delete:

65-20= 45 kept

2.Now find deleted: 20 deleted

3.Ratio to kept to deleted= 45:20

4.Simplify: 9:4

The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

For more such information on: significant figures

https://brainly.com/question/30169

#SPJ8

Answer:

\(x = 45\)

Step-by-step explanation:

collect like terms

\(4x + 180 = 360\)

move the constant

\(4x = 360 - 180\)

calculate

\(4x = 180\)

divide by 4

X = 45

Answer:

Answer: The length of string from kite to the ground is 111.5 feetStep-by-step explanation:Given ... of the ground, and its string is pulled tout. The angle of elevation of the kite is 43. Find the length of the string. Round your answer to the ... The height from the ground at which kite is flying = BC = h = 76 feet.

Step-by-step explanation:

Using the elimination method, the solution to the system of equations is as follows:

x = 19 / 13  and y = - 74 / 13

System of equations can be solved using different methods such as the elimination method, substitution method, and graphical method.

Let's use the elimination method to solve the system of equations as follows:

The elimination method is the process of eliminating one of the variables in the system of equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Therefore,

4x - 7y = 10

3x + 2y = -7

multiply equation(ii) by 3.5

4x - 7y = 10

10.5x - 7y = 24.5

subtract equation(i) from equation(ii)

6.5x = 14.5

x = 14.5 / 6.5

x =  145 / 65

x = 19 / 13

Let's find y

3(19 / 13) + 2y = -7

57 / 13 + 2y = -7

2y = - 7 - 57 / 13

2y = -91 - 57  / 13

2y = - 148 / 13

cross multiply

26y = - 148

y = - 148 / 26

y = -  74 / 13

learn more on system of equation here: brainly.com/question/28453461

#SPJ1

Given a right angle triangle ABC with altitude BD drawn to hypotenuse AC, It AD = 1 and BD = 2, the length of AC is 5 units.

In a right triangle ABC, if the altitude BD is drawn to the hypotenuse AC, we can use the concept of similar triangles to find the length of AC.

Since triangle ABD and triangle ABC are similar, we can set up the following proportion:

AC/AB = AB/AD

Substituting the given values, we have:

AC/AB = AB/1

We are given that BD = 2, and since BD is the altitude, it divides the hypotenuse AC into two segments: AD and DC.

By the Pythagorean Theorem, we know that \(AD^2 + BD^2 = AB^2\). Substituting the given values, we have:

\(1^2 + 2^2 = AB^2\)

\(1 + 4 = AB^2\)

\(5 = AB^2\)

Taking the square root of both sides, we get:

√5 = AB

Substituting this value back into the proportion, we have:

AC/√5 = √5/1

Cross-multiplying, we get:

AC = (√5)^2

AC = 5

Therefore, the length of AC is 5 units.

For more details regarding triangle, visit:

https://brainly.com/question/2773823

#SPJ1