pls find the angle HAF in the diagram ​

Pls Find The Angle HAF In The Diagram

Answers

Answer 1

Answer:

  ∠HAF ≈ 64.90°

Step-by-step explanation:

You want the angle HAF, a base angle in the isosceles triangle formed by the face diagonals of the cuboid with dimensions 6 cm, 6 cm, and 8 cm.

Diagonal lengths

The lengths of the diagonals can be found using the Pythagorean theorem:

  HA² = HD² + DA²

  HA² = 6² +6² = 2·6²

  HA = 6√2 . . . cm

  FA² = FB² +BA²

  FA² = 6² +8² = 36 +64 = 100

  FA = 10 . . . cm

Diagonal FH is the diagonal of a rectangle with the same dimensions as the rectangle whose diagonal is FA:

  FH = FA = 10 . . . cm

Law of Cosines

The angle A can be found using the law of cosines:

  FH² = FA² +HA² -2·FA·HA·cos(A)

  A = arccos((FA² +HA² -FH²)/(2FA·HA))

  A = arccos((100 +72 -100)/(2·10·6√2)) = arccos(72/(120√2))

  A = arccos(0.3√2) ≈ 64.90°

Angle HAF is about 64.90°.


Related Questions

[NEED HELP ASAP] How do I find the surface area of the shape in the picture?

Answers

When calculating the surface area of a 3D shape, it is important to remember to include the area of all the components that make up the shape.

How do I find the surface area of the shape in the picture?The surface area of the shape in the picture is approximately 300.4 cm².To calculate this, use the formula for the surface area of a triangular prism, which is SA = 2(bhl) + 2(bh + la).In this case, b = a = 4 cm, h = 12 cm, and l = s = 4.6 cm, so the calculation is SA = 2(4 x 12 x 4.6) + 2(4 x 4.6 + 4 x 12) = 300.4 cm².To calculate the surface area of the shape in the picture, you need to first calculate the area of the rectangle, triangle and circle.The rectangular portion has a height of 12 cm and a length of 4 cm, so the area is 48 cm^2.The triangle has a height of 12 cm and a base of 4 cm, so the area is 24 cm^2. The circle has a radius of 4.6 cm, so the area is 66.48 cm^2. Therefore, the total surface area of the shape is 138.48 cm^2. To calculate the surface area, you need to add the area of each of the components.For example, the area of the rectangle is 48 cm^2, the area of the triangle is 24 cm^2, and the area of the circle is 66.48 cm^2.The total surface area of the shape is then the sum of all these components, which is 138.48 cm^2.In this example, the rectangular portion, triangle and circle each had to be calculated separately in order to find the overall surface area.

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hich are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct representations of the inequality are

-6x + 15 < 10 - 5x

A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Solving inequality and determining the correct representations

From the question, we are to determine the correct representations of the inequality

From the given information,

The given inequality is

-3(2x - 5) < 5(2 - x)

To determine the correct representations, we would proceed to solve the inequality

Solving the inequality

-3(2x - 5) < 5(2 - x)

-6x + 15 < 10 - 5x

This is one of the representations of the inequality

Then,

Collect like terms

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

Multiply through by -1

x > 5

If the solution is represented on a number line, we would have a number line from negative 3 to 3 with an increments of 1 and an open circle at 5 and a bold line starts at 5 and is pointing to the right.

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PLEASE HELP FRACTION S EASY!! A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses pounds of gravel. For each pound of gravel, he uses pound of cement. He is making enough concrete that he needs to use 3 pounds of sand.


How many pounds of cement does he use?

Answers

The pound of cement used based on the information will be C. 2 pounds.

How to illustrate the fraction?

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.

The pound of cement used will be:

Gravel = 1 2/3 × 3

= 5 pounds

Cement used will be:

= 2/5 × 5.

= 2 pounds.

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F(x)=2 sin (1/2x)+1
What is the midline of the function

Answers

Answer:

Step-by-step explanation:

Its A

Help me solve solution to the system of equations.

Answers

Answer:

[tex](\frac{5}{3} ;\frac{4}{3} ).[/tex]

Step-by-step explanation:

[tex]\left \{ {{x+y=3} \atop {\frac{y+2}{2} =x}} \right. \ = > \ \left \{ {{x+y=3} \atop {y+2=2x}} \right. \ = > \ \left \{ {{x+y=3} \atop {2x-y=2}} \right. \ = > \ \left \{ {{x=\frac{5}{3} } \atop {y=\frac{4}{3} }} \right.[/tex]

The ratio 81:108 in the simplest form

Answers

The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.

If a jacket is marked up 75% to be $350 and a month later is 20% off and then two weeks later is 30% off how much money did the company gain or lose


PLEEEEASE HELP!!!!!

Answers

280 AND 245 RS  the company GAIN,20% OFF it is 280 rs and 30% off it is 245 rs

How to calculate discount price in rupees?For example, you may want to calculate the sale price of a shirt that regularly costs Rs 1,000. If the shirt is 20% off, you must convert 20% to a decimal (20/100 = 0.2). You have Rs 1,000 * 0.2 = Rs 200. You then subtract the discount from the original price as Rs 1,000 – Rs 200 = Rs 800.Discount is the difference between the marked price (list price) and the selling price of an article. Therefore, the formula used to calculate discount is: Discount = List price - selling price.For example, $100 invested today in a savings scheme that offers a 10% interest rate will grow to $110. In other words, $110, which is the future value (FV), when discounted by the rate of 10% is worth $100 (present value) as of today

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The physician orders 150 mg/5 kg. The patient’s weight is 75 kg. How many grams of medication has the physician ordered?

Answers

Answer: 2.25 grams

Step-by-step explanation:

In this problem, we are given the ratio of grams to weight. Since we are trying to find how many grams to give to a person with a specific weight, we can use proportions to solve.

[tex]\frac{150mg}{5kg} =\frac{x}{75kg}[/tex]               [cross multiply]

[tex]11250=5x[/tex]                  [divide both sides by 5]

[tex]x=2250mg[/tex]

We are almost done with the problem. The problem is asking for grams, not mg, so we can use unit conversions to change that.

[tex]\frac{1000mg}{1g}=\frac{2250mg}{y}[/tex]          [cross multiply]

[tex]1000y=2250[/tex]               [divide both sides by 1000]

[tex]y=2.25[/tex]

Therefore, we need to give 2.25 grams.

Given points A (1, 5) and B (-7, -5), which of the following coordinates is the midpoint of AB? (-3, 0) (-4, 0) (-2, 0) (4, 0) (2, 0)

Answers

Using formula of midpoint of a line, the coordinate of the midpoint is (-3, 0)

What is Midpoint of Line

The midpoint of a line is a point that is equidistant from both endpoints of the line. It can be found by taking the average of the x-coordinates of the two endpoints, and then taking the average of the y-coordinates of the two endpoints. For example, if the two endpoints of a line are (x₁, y₁) and (x₂, y₂), then the midpoint of the line is:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

The formula of midpoint of a line is given as;

M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2

Substituting the values into the formula;

M(x, y) = (-7 + 1) / 2, (-5 + 5) / 2

M(x , y) = -6/2, 0/2

M(x, y) = -3, 0

The coordinate of midpoint is (-3, 0)


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Please help me, I need help asap !! I can’t figure it out

Answers

23/35

when you make them have a common denominator you get 30/35 wants to get down to 7/35


when you subtract them you get 23/35, meaning you have to take off 23/35 inches of the pipe in order to get it to 1/5

Judi is making a rope ladder. She uses 1/2 yard of for each step. How many yards of rope can she make for step?

Answers

The number of yards of rope she can make for the step is 3 yards

How to determine the number of yards of rope she can make for the step?

From the question, we have the following parameters that can be used in our computation:

Yards of rope per step = 1/2 yards per step

Total number of steps = 6 steps

The number of yards of rope she can make for the step can then be calculated using the following equation

The number of yards of rope = Total number of steps * Yards of rope per step

Substitute the known values in the above equation, so, we have the following representation

The number of yards of rope = 1/2 * 6

Evaluate

The number of yards of rope = 3

Hence, the number of yards of rope is 3

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Complete question

Judi is making a rope ladder. she uses 1/2 yard of rope for each step. how many steps can she make with 6 yards of rope?

what's the y intercept of y=-2x+ -20​

Answers

Answer: y=20-2x

Step-by-step explanation:

solve number 13 please

Answers

The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105 .

What is expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

An algebraic expression is made up of a number of variables, constants, and mathematical operations. We are aware that variables have a wide range of values and no set value. They can be multiplied, divided, added, subtracted, and other mathematical operations since they are numbers. as in 3x Plus 4.

Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :

G = 6t^4+ 3t³ – 2t² + 5t + 60

I = 3t^4 - 3t³ + 5t² - 5t + 45

where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.

A new model {A} for the total number of new green tea and fruit juice sales can be written as -

{A} = {G} + {I}

{A} = 6t^4+ 3t³ – 2t² + 5t + 60 + 3t^4 - 3t³ + 5t² - 5t + 45

{A} = 9t^4 + 3t² + 105

Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105

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2 alien spaceships are traveling toward each other from space stations that are 7100 km apart at speed of 110000 km

Answers

It would take 116.18 seconds for the space stations that are 7100 km apart at speed of 110000 km to meet

How to solve an equation?

An equation is an expression that shows the relationship between two or more numbers.

The speed of an object is the ratio of the total distance travelled to the total time taken. It is given by:

Speed = distance / time

Distance = Speed * time

The spaceships are moving at 110000 km/h

The distance covered by each in x hours is:

Distance = 110000 * x = 110000x

Since they are 7100 km apart, hence:

110000x + 110000x = 7100

220000x = 7100

x = 0.03227 hours = 116.18 seconds

It would take 116.18 seconds for the spaceships to meet.

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Which symbol makes the number sentence true?

-2.5O 10/4
A. <
B. >
C. =

Answers

Answer: I'm sorry if it's wrong I'm pretty sure it's ≥ if not I'm sorry

Step-by-step explanation:


Find the distance between the points.
(−3,− 8), (6, – 8)
The distance is

Answers

To calculate the distance between two points:

We apply the following formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

(x₁,y₁) = -3, -8(x₂,y₂) = 6, -8

We substitute data and solve:

[tex]\bf{d=\sqrt{(6-(-3))^2+(-8-8(-8))^2 } }\\ \\ \bf{ d=\sqrt{9^2+0^2}=\sqrt{81+0} }\\ \\ \bf{d=\sqrt{81}=9 }[/tex]

The distance between the points (−3,− 8), (6, – 8) is 9.

3a+2b
Help me please
I can’t do it

Answers

Answer:

Question is not clear

Step-by-step explanation:

The sum of two angles is 85, one angle is five more than the measure of the other angle. Write the equation that represents this scenario and find the measure of each angle. Be sure to show your
work.

Answers

Therefore , the solution of the given problem of angles comes out to be equation :  x+ y =85°.

'

An angle is what?

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the tone's flanks, that meet at a midpoint known as such angle's vertex. Two rays may combine to form an angle there in plane where they are positioned. When two planes collide, an angular is also generated. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays of lines that share a termination. The origin of the English term "angle" is the Latin phrase "angulus," which meaning "horn." The vertex is the point in which the two vectors, also known as that of the faces of the angle, converge.

Here,

Given :

Let two angles be x and y  is

=> x+ y =85°

So, the equation is represented as  x+ y =85°.

Therefore , the solution of the given problem of angle comes out to be equation :  x+ y =85°.

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17. Among 2.6, 2.006, 2.66 and 2.08, the largest number is (a) 2.006 (b) 2.08 (c) 2.6​

Answers

Answer:

2.66

Step-by-step explanation:

Answer:

2.66

Step-by-step explanation:

look at first at tenths for the biggest no .if there is a tie proceed to hundredths for biggest no and so on

4.75% as a fraction in simplest form

Answers

Answer:  19/400

Step-by-step explanation:

4.75% = 4.75/100 (in fractions)

          = 475/10000 (multiply by 100 for both the numerator and denominator)

           = 19 / 400 (divide by 25 for both the numerator and denominator)

How do I know it is 25 for the last step?

Obtain the highest common factor of 475 and 10000. The highest common factor of these two numbers is 25.

Jahnay is following this recipe to make cakes. Jahnay uses 780 g of butter. How many cakes is Jahnay making? Recipe: Makes 1 Cake 120 g sugar 130 g butter 260 g flour 3 eggs

Answers

Jahnay is making 6.5 cakes from the given ingredients.

What is division?

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Recipe: Makes 1 Cake =  120 g sugar + 130 g butter + 260 g flour + 3 eggs.

Jahnay is following this recipe to make cakes.

Jahnay uses 780 g of butter.

To find the number of cakes:

Use division operation,

780 ÷ 120,

= 780/120

= 78/12

= 6.5

Therefore, Jahnay makes 6.5 cakes.

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Which sentence is incorrect?
A. -3 > -8
B. -4 > -7
C. -2/5=0.4
D. -5/2=0.4

Answers

Answer:

D

Step-by-step explanation:

Toni runs around her school's baseball diamond. Each side is 27 m long. Note: A baseball diamond is square. How far does Toni run? m​

Answers

Answer:

If we assume she runs around it once and since they tell us its a square: 27x4=108

Step-by-step explanation:

5. Find the value of side x and y. Leave answers in simplest radical form a applicable.

Answers

Therefore , as a result, x = 53 and y = 10 are the answers to the trigonometry problem that was presented.

What is trigonometry?

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every ahead and move form may indeed be resolved to a set of triangles. Amazingly intricate connections exist between geometry and other areas of mathematics, particularly arithmetic, real or abstract, infinite series, arithmetic, and infinite series.

Here,

Sin 30 = Opposing Side/High

1/2 = 5 / y

y = 5 / (1/2)

y = 10

Cos 30 = Adjustment Side/ Hyp

√3/2 = x/y

√3/2 = x/10

x = 10√3 / 2

x = 5√3

In light of this, the given fractional problem's answer is

x = 5√3 and y = 10.

Therefore , as a result, x = 53 and y = 10 are the answers to the trigonometry problem that was presented.

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Please help. Assignment is due today. I am terrible with math, I don't understand this. Thanks in advance.

Answers

Answer:

a. A' (-3, -1) B' (3, 2) C' (6, 0); b. A' (-1, -3) B' (1, 6) C' (2, 0); c. A' (-2, -3) B' (2, 6) C' (2, 0)

Step-by-step explanation:

Solutions for graph a, b and c are attached.

a. (x, y) to (3x, y)

A' (-3, -1) B' (3, 2) C' (6, 0)

b. (x, y) to (x, 3y)

A' (-1, -3) B' (1, 6) C' (2, 0)

c. (x, y) to (2x, 3y)

A' (-2, -3) B' (2, 6) C' (2, 0)

REMEMBER: Connect the lines to make the triangles for each graph BEFORE submitting.

the phone company charges $33 for having a smartphone plus $9.95 a month for 2gb. IF mark has only $146.43 to spend on a phone, how many months can he have the phone? inequalities

Answers

The number of months Mark can have the phone is given by the equation

A = 11.4 months

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of months be represented as = A

Now , the equation is

Now , the total amount with Mark = $ 146.43

The initial amount for the smartphone = $ 33

The amount per month for 2GB is = $ 9.95

So , the amount for A months = $ 9.95 ( A )

So , the equation will be

Initial amount for the smartphone + the amount for A months = total amount with Mark

Substituting the values in the equation , we get

33 + 9.95 ( A ) = 146.43   be equation (1)

On simplifying the equation , we get

Subtracting 33 on both sides of the equation , we get

9.95 ( A ) = 113.43

Divide by 9.95 on both sides of the equation , we get

A = 11.4 months

Therefore , the value of A is 11.4 months

Hence , the number of months is 11.4 months

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I need help asap , this is geometry. I need it solve in the simplest radical form.

Answers

let the third side be b then use the pythagoras theorem

Can somebody help me? I need help please

Answers

By using concept of angle relationship, we get x equal to 27°.

What are angle relationships defined as?

We compare the position, measurement, and congruence of two or more angles when we talk about angle relationships. For instance, two pairs of vertical angles are created when two lines or line segments intersect.

∠BAF+∠EAF=180°

∠EAF=180° - 138°

∠EAF=42°

Since, ∠EAF and ∠BAC are vertically opposite angle,

Hence,

∠EAF =  ∠BAC =42°

Again,

∠EAD+∠DAC+BAC=180°

4x+30°+42°=180°

4x=180°-72°

4x=108°

x=27

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ABC~A'B'C'. Their scale factor is 7:9. If the perimeter of smaller ABC is 42, then the
perimeter of A'B'C' is.

Pls hurry!!

Answers

Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

Find the equivalent measures. Express as a decimal
(a) 250 cm =

Answers

The answer is 2.50. This, 250% in deciaml form is 2.50, in improper fraction form is 52 and as a mixed number it is 2 12. 2 1 2.

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