Triangle FGH is an equilateral triangle with sides measuring 34 StartRoot 3 EndRoot units.

Triangle F G H is shown. A perpendicular bisector goes from point G to point R on side H F. The length of G H is 34 StartRoot 3 EndRoot, the length of G F is 34 StartRoot 3 EndRoot, and the length of H F is 34 StartRoot 3 EndRoot.

What is the height of the triangle?

17 units
34 units
51 units
68 units

The value of sin x in Q II is 0.86 .

This the field in Maths which deals with a right angled triangle and the other angles in the triangle.

It is given that cot = -0.59

cot x = cos x / sin x

Using online trigonometric calculator

sin x in Q II is 0.86 .

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Answer: $3.5

Step-by-step explanation:

If a product cost $1.50 and you paid $5, the change will be equal to

$5 - $1.50 = $3.5 for change

Answer: C. 7.5%

Solve as decimal

0.5*0.15=0.075

Move two decimal points over

0.075 -> 7.5

Change back to percent

7.5%

Answer:

a. 42 g

b. 2.8 g

Step-by-step explanation:

a. Since the entire thing weighs 56g and gold is 75% of the mass you simply find 75% of the mass. This is done by converting the 75% into decimal form by dividing it by 100 to get 0.75 and then multiply it by the 56 g to get (0.75 * 56 g) = 42 g

b. same thing here as the previous answer. 5%/100 = 0.05. (0.05 * 56 g) = 2.8 g

Yes, they can be added and simplified further. 2√3 + 5√3 = 7√3 .

Take √3 as common factor:

2√3 + 5√3

(2 + 5)√3

7√3

The two irrational numbers sums to form another irrational number 7√3 . In decimals that is 12.12435...

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Yes, The terms assigned above are alike so they can be added easily by simple algebric method where root number can be treated as a variable.

[tex]\qquad \sf  \dashrightarrow \: 2 \sqrt{3} + 5 \sqrt{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2 + 5) \sqrt{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 7 \sqrt{3} [/tex]

The 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

As part of a community-service project, a local club has decided to paint 864 walls across town. The club has 36 volunteers.

Total number of volunteers = 36

Number of walls = 864

The number of walls each volunteer paint can be expressed as a fraction:

= 864/36

= 24

Thus, the 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.

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(a) 10% of x = 9

x = 9 ⋅ (100/10)

x = 90 kg

(b) 12% of x = 12/100 of 90

Weight she lost = 10.8

Her new weight = 90 - 10.8

= 79.2kg

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:Angle \:\: of \:\: elevation= 30° [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Let the angle of elevation be " x "

[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{9 \sqrt{3} }{18} [/tex]

[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{ \sqrt{3} }{2} [/tex]

[tex]\qquad \tt \rightarrow \: x = \cos {}^{ - 1} \bigg( \cfrac{ \sqrt{3} }{2} \bigg ) [/tex]

[tex]\qquad \tt \rightarrow \: x = 30 \degree \: \: or \: \: \cfrac{ \pi}{6} \: \: rad[/tex]

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Answer:

The angle is 60 degree.

Step-by-step explanation:

First of all, we will find the height if the tree by using Pythagorean theorm.

Let, height of tree be x.

18^2=(9(3^1/2))^2+x^2

324=243+x^2

x^2=324-243

x^2=81

x=9

Now, let the angle be y.

tan y= x/base

tan y=9/9×(3^1/2)

tan y=1.73

y=cot 1.73

y= 60

p → q  represents the original conditional statement and the contrapositive of the original conditional statement. Then the correct options are A and E.

The missing options are given below.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

Doubling the dimensions of a rectangle increases the area by a factor of 4.

If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4.

Then the true statement will be

Then the correct options are A and E.

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Answer:

Each point (or pair) in a proportional relationship must share the same difference is the false statement.

Answer:

x = 10

Step-by-step explanation:

5(2x - 12) + 21 = 2x + 41 ← distribute parenthesis and simplify left side

10x - 60 + 21 = 2x + 41

10x - 39 = 2x + 41 ( subtract 2x from both sides )

8x - 39 = 41 ( add 39 to both sides )

8x = 80 ( divide both sides by 8 )

x = 10

The volume of the rectangular prism can be express in standard polynomial as follows:

x³ + 12x² + 35x

volume of a rectangular prism = lwh

where

Therefore,

let

height = x

width = x + 5

length = x + 5 + 2 = x + 7

Therefore,

volume = x(x + 5)(x + 7)

volume = x(x² + 7x + 5x + 35)

volume = x(x² + 12x + 35)

volume = x³ + 12x² + 35x

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Answer:

Your classmate says that there is not enough information to determine whether the two triangles below are congruent. Is your classmate correct?

yes it is

The two triangles are congruent triangles by RHS theorem of congruent triangles

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔMLJ

Let the second triangle be represented as ΔLJK

Now , the measure of ∠MLJ = 90°

The measure of ∠LJK = 90°

The measure of side MJ = measure of side LK

So , the two sides of the triangles are similar and they have a common hypotenuse

Therefore , the triangles are congruent by right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Hence , the triangles are congruent

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If the subset y is the empty set, then the statement is false. That is the counterexample.

We know that for an invertible function, we always have that:

[tex]f(x) = y\\f^{-1}(y) = x[/tex]

Now, the range of f(x) is the set b. This means that the domain of the inverse is the set b. Such that:

f^{-1} is defined on b→a

Now we want to work on a subset y ⊆ b.

And here comes the problem.

The empty set {∅} is a subset of ay other set. So, if y is the empty set, there are no elements where we can evaluate the inverse function. From that counterexample, we conclude that the statement is false.

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Answer:

x=1/5

Step-by-step explanation:

You have to isolate x. First, add the one to the sider to give you 5x=1. In order to get the x by itself, you have to divide the 5 into both sides. In the end, this gives you x=1/5.

Answer:

Step-by-step explanation:

The molar heat of fusion for substance X , given the data is 775.6 cal/mol

Mole = mass / molar mass

Mole = (326 / 58.45) moles

Q = n × ΔHf

4325.8 = (326 / 58.45) × ΔHf

4325.8 = (326 × ΔHf ) / 58.45

Cross multiply

326 × ΔHf = 4325.8 × 58.45

Divide both sides by 326

ΔHf = (4325.8 × 58.45) / 326

ΔHf = 775.6 cal/mol

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:m\overbrace{DB}= 90 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + m \overbrace{TB} = 180 \degree[/tex]

[ linear pair ]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + 90 \degree = 180 \degree[/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 180 \degree - 90 \degree[/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 90 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

330.6

Step-by-step explanation:

You have to enter 290 for x.

T(290) = 290 + 0.14(290)

T(290) = 290 + 40.6

T(290) = 330.6

Answer:

22.5 hours

Step-by-step explanation:

One cubic foot of water contains 7.48 gallons, so 40 cubic feet of water would equal 7.48 × 40, or 299.2 gallons. So the pumping rate is 299.2 gallons per minute. Multiplying 299.2 by 60, we have

299.2 × 60, or 17952 gallons per hour. Finally, divide 403,920 by 17,952 to find the number of hours to remove all the water: 403,920 ÷ 17,952 = 22.5 hours

The probability of selecting a jack, replacing the card, and then selecting a king is 1/169

In a standard deck of cards, we have:

Total = 52

Jack = 4

King = 4

The probability of each is:

P(Jack) = 4/52

P(King) = 4/52

So, we have:

P = 4/52 * 4/52

Simplify

P = 1/13 * 1/13

Evaluate

P = 1/169

Hence, the probability is 1/169

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Answer:

[tex] \frac{18}{12} = \frac{24}{x - 2} [/tex]

Step-by-step explanation:

see photo for detailed analysis

Answer:

1) -
2) +

3) -
4) +

Step-by-step explanation:

сумма внутренних углов треугольника не должна превышать 180 градусов

Answer:

a).1000/400*100

= (1000*100)/400

= 100000/400 = 250

b).600

Step-by-step explanation:

a). Percentage solution with steps:

Step 1: We make the assumption that 400 is 100 % since it is our output value.

Step 2: We next represent the value we seek with x.

Step 3: From step 1, it follows that 100 % = 400.

Step 4: In the same vein, x % = 1000 .

Step 5: This gives us a pair of simple equations:

100 % = 400(1).

x % = 1000(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

100 % / x % = 400/1000

Step 7: Taking the inverse (or reciprocal) of both sides yields

x/100 = 1000/400

x = 250 %

Therefore, 1000 is 250 % of 400.

b) $1000-$400= 600

= $400+$600=$1000

The slant height of the given cone will be 12.06 inches.

The measurement from the base to the peak along the "center" of a lateral face of an object, such as a cone, is its slant height.

Given that:-

The slant height will be calculated as:-

Surface area = π r l

151.58 = π x 4 x l

l = 151.58 / ( π x 4 )

l = 12.06 inches.

Therefore slant height of the given cone will be 12.06 inches.

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Answer:

4,300

Step-by-step explanation:

total cost of the shipment of tile cost =$64,500

each tile cost =$15

how many pieces will now be the total cost of shipment tile divided by the cost of each tile

which will be

64500/15

=4,300 tiles are there

i am glad I helped

By finding the probability, we can expect that 2 out of the 30 students will win the prize.

First, we should get the probability of winning this game.

Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.

Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:

p = 1/6

The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:

q = 1/5

The joint probability is then:

P = 2*(1/6)*(1/5) = 1/15.

Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.

Then the expected number of students that will win is equal to the probability times the total number of students:

(1/15)*30 = 2

So out of the 30 students, we can expect that 2 will win.

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The length and width of this rectangle are 15 cm respectively

The perimeter is given as:

Perimeter, P = 60

The greatest area is calculated as:

Greatest = (P/4)^2

Substitute 60 for P

Greatest = (60/4)^2

Evaluate the quotient

Greatest = 15^2

Evaluate the exponent

Greatest = 225 square centimeters

Hence, the greatest area is 225 square centimeters

We understand that the area is the greatest.

In such a scenario;

Length = Width

This means that:

Area =Length^2 =Width^2

So, we have:

Length^2 =Width^2 = 225

Take the square root

Length =Width = 15

Hence, the length and width of this rectangle are 15 cm respectively

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