Given:
AC
≅
BD
and ∠CAB≅∠DBA.

Prove: △ABC≅△BAD.

If the hypotenuse of an isosceles right-angled triangle is 3√2 cm, then each of the side of the triangle is 3 cm.

Given that,

Hypotenuse of the right angled triangle = 3√2 cm

Since the triangle is isosceles, the other two sides or the legs of the triangle will have equal length.

Let x be the length of each leg.

Using Pythagoras theorem,

x² + x² = (3√2)²

2x² = 18

x² = 9

x = 3

Hence the length of each side is 3 cm.

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Answer: 60 in.

Chain of Thought Reasoning:

Step 1: P = 2L + 2W

Step 2: 18 = 2L + 2(4)

Step 3: 18 = 8 + 2L

Step 4: 10 = 2L

Step 5: 5 = L

Step 6: Convert feet to inches: 1 foot = 12 inches

Step 7: 5 feet = 5 * 12 inches

Step 8: 5 feet = 60 inches

Therefore, the length of the rectangular yard is 60 inches.

Answer:

26.74 degrees!

Step-by-step explanation:

The formula you can plug the numbers into is:

angle = L / r

Angle = the central angle

L = the length of the arc

r = radius of the circle

Answer:

b ≈ 54.94

Step-by-step explanation:

using the Sine rule in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

where a is the side opposite ∠ A, b is opposite ∠ B , c is opposite ∠ C

we require to calculate ∠ B

∠ B = 180° - (42 + 41.5)° = 180° - 83.5° = 96.5°

to find b using the pair of ratios

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{a}{sinA}[/tex] ( substitute values )

[tex]\frac{b}{sin96.5}[/tex] = [tex]\frac{37}{sin42}[/tex] ( cross- multiply )

b × sin42° = 37 × sin96.5° ( divide both sides by sin42° )

b = [tex]\frac{37sin96.5}{sin42}[/tex] ≈ 54.94 ( to 2 decimal places )

Answer:

c = 45 and e = 30

Step-by-step explanation:

Since we know that A = 45, B = 90, we can calculate C knowing that the total angle of a triangle is 180, so you do 180-45-90 = 45

Finding the angle C helps us find F by subtracting 45 from 180, since a straight line is 180 degrees, which is 135.

We know that E = 15, and what was said earlier about how the toal angle is 180 in a triangle, we can subtract 15 and 135 from 180, which is 30.

Hope that answers your question

Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;

1. 2144.57 m³

2. 696.6 m³

3. 20569.1m³

4. 2637ft³

5. 56.5km³

6. 6381.79 in³

The volume of a sphere is given as 4/3πr³

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

1. The volume of the sphere is;

v = 4/3 * 3.14 * 8³ = 2144.57m³

2. The volume of the sphere is;

v = 4/3 * 3.14 * (11/2)³ = 696.6m³

3. The volume of the sphere is;

v = 4/3 * 3.14 * 17³ = 20569.1m³

4. The volume of the hemisphere is;

v = 2/3 * 3.14 * 10.8³ = 2637ft³

5. The volume of the hemisphere is;

v = 2/3 * 3.14 * 3³ = 56.5km³

6. The volume of the hemisphere is;

v = 2/3 * 3.14 * (29/2)³ = 6381.79in³

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1/4 or 0.25 is the probability that the coin shows heads and the die shows an odd number.

To find the probability that the coin shows heads and the die shows an odd number, we need to consider the possible outcomes for each event and calculate the probability of their intersection.

For the coin toss, there are two possible outcomes: heads (H) or tails (T). Each outcome has an equal chance of occurring, so the probability of the coin showing heads is 1/2.

For the die roll, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. Out of these outcomes, three numbers (1, 3, and 5) are odd. Again, each outcome has an equal chance of occurring, so the probability of rolling an odd number is 3/6 or 1/2.

To find the probability of both events occurring, we multiply the individual probabilities:

Probability of coin showing heads = 1/2

Probability of die showing an odd number = 1/2

Probability of both events occurring = (1/2) * (1/2) = 1/4

Therefore, the probability that the coin shows heads and the die shows an odd number is 1/4 or 0.25.

This means that out of all possible outcomes from tossing a coin and rolling a die, there is a 1 in 4 chance that the coin shows heads and the die shows an odd number. It's important to note that this calculation assumes fair and unbiased coin and die, where the probabilities of each outcome are equally likely.

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Graph is attach below for this question and the equation of this graph is

A(x) = 400(1.25)ˣ +0

We have,

In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" indicates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

Given that the boat's value increasing at a rate of 25% per year.

So after each year the value becomes = 1 + 25% = 1 + 0.25 = 1.25 of the previous year.

So the equation becomes: A(x) = 400(1.25)ˣ +0

Since, b = 1.25 > 1, so A(x) is a increasing function. And for every value of x, A(x) < 0.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

Amount = Principal ( 1 + i) ^n     i = decimal interest per month = .08/12

                                                    n = 16 months

     amount = $ 300 ( 1+ .08/12)^16 = $  333.65

1. In terms of x and y, the height of the tree is  and

2. The height of the tree is 6.71 meters

Since, From the question, we are to determine the height of the tree in terms of x and y

Hence, By Using SOH CAH TOA, we can write that

tan t° = h / y

h = y × tan t°

Also, We get;

tan s° = h / x

h = x × tan s°

2. If m ∠t = 38° and y = 3 meters,

Then, the height of the tree;

h = 3 × tan 38°

h = 3 × 0.78 meters

h = 2.34 meters

Hence, the height of the tree is 2.34 meters.

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Bishnu selling price paid Rs 1,42,048 for the motorcycle.

To find out how much Bishnu paid for the motorcycle, we need to calculate the selling price after the 8% loss.

Let's start with the purchase price: Shiva bought the second-hand motorcycle for Rs 1,53,200.

Then, Shiva spent Rs 1,200 to repair it. So, the total cost for Shiva becomes:

Total cost = Purchase price + Repair cost

= Rs 1,53,200 + Rs 1,200

= Rs 1,54,400

Now, to calculate the selling price after an 8% loss, we need to subtract 8% of the total cost from the total cost:

Loss = 8% of Total cost

= 8/100 * Rs 1,54,400

= Rs 12,352

Selling price = Total cost - Loss

= Rs 1,54,400 - Rs 12,352

= Rs 1,42,048

Therefore, Bishnu selling price paid Rs 1,42,048 for the motorcycle.

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The real dimensions of the object are 144 inches by 216 inches.

Given that, 6:1 scale with dimensions of 24 inches by 36 inches.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

In a 6:1 scale, the real dimensions of an object would be 6 times the scaled dimensions. Therefore, the real dimensions of the object given in the question would be 24 inches x 6 = 144 inches by 36 inches x 6 = 216 inches. So, the real dimensions of the object are 144 inches by 216 inches.

Therefore, the real dimensions of the object are 144 inches by 216 inches.

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The equation of the graph is (b) y = (x + 4)(x + 2)(x - 1)

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

The graph

The graph is a polynomial graph with the following zeros and multiplicities

The equation is then represented as

y = (x - zero) to the exponent of the multiplicities

So, we have

y = (x + 4)(x + 2)(x - 1)

Hence, the equation of the graph is (b) y = (x + 4)(x + 2)(x - 1)

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Based on the given information, we cannot determine if the triangle is acute, right, or obtuse (A, B, C). However, we can conclude that the triangle is scalene (F).

To determine the terms that apply to triangle ABC with vertices A(0, 5), B(1, -3), and C(-3, 3), we can analyze the properties of the triangle based on its side lengths and angles.

Side Lengths:

AB: Distance between points A(0, 5) and B(1, -3)

BC: Distance between points B(1, -3) and C(-3, 3)

AC: Distance between points A(0, 5) and C(-3, 3)

Using the distance formula, we can calculate the side lengths:

AB = [tex]\sqrt{ (1 - 0)^2 + (-3 - 5)^2)} = \sqrt{(1^2 + (-8)^2} = \sqrt{65}[/tex]

BC = [tex]\sqrt{((-3 - 1)^2 + (3 - (-3))^2} = \sqrt{((-4)^2 + 6^2)} = \sqrt{52}[/tex]

AC = [tex]\sqrt{((-3 - 0)^2 + (3 - 5)^2)} = \sqrt{(-3)^2 + (-2)^2)} = \sqrt{13}[/tex]

We can conclude that the triangle is not equilateral (D) since all sides have different lengths. We can also conclude that the triangle is not isosceles (E) since no two sides have the same length. Therefore, the triangle is classified as scalene (F).

In summary, based on the given information, we cannot determine if the triangle is acute, right, or obtuse (A, B, C). However, we can conclude that the triangle is scalene (F).

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The direction that the quadratic function f(x) is to be translated is to the left and the units is 4.

Here given two functions, f(x) and g(x).

General form of the quadratic function is,

ax² + bx + c.

It is clear that, f(x) is simply the square of the x values.

f(x) = x²

Since g(x) is the translation of the function f(x) and the value of g(x) = 0, when x = -4,

g(x) = (x + 4)²

That is,

g(x) = f(x + 4).

So f(x) is shifted left by 4 units.

Hence f(x) is shifted left by 4 units.

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Answer:

Step-by-step explanation:

15 % of x  =  3

[tex]\frac{3x}{20} = 3\\ x = 20[/tex]

Answer:

Step-by-step explanation:

3 : 15 × 100 =

0.2 × 100 =

20

3 : 15 = x : 100

x = 3 × 100 : 15

x = 20

Brian is correct, because the graph shows the circle with a center (-3, 2) and a radius of 2.

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Brian says the graph shows the circle with a center (-3, 2) and a radius of 2.

And, Mia says the graph shows all possible centers for a circle that passes through (-3, -2) with a radius of 2.

Now, By given graph we can see that,

Center of circle = (- 3, 2)

And, Radius of circle = - 1 + 3 = 2

Hence, Brian is correct, because the graph shows the circle with a center (-3, 2) and a radius of 2.

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Axiom of Infinity states that there is at least one set that contains an infinite number of elements.

A basic tenet of set theory, the Axiom of Infinity affirms the existence of an endless set. In plainer language, it proves that at least one set has elements with an infinite number.

This axiom is crucial because it enables rigorous and consistent mathematical reasoning about and interaction with infinite collections. It offers a fundamental premise for many infinity-related mathematical notions and structures, including infinite sequences, series, and cardinality.

The Axiom of Infinity ensures that mathematics is not restricted to only finite quantities and allows for the exploration of the rich and intriguing realm of infinite structures by declaring the existence of an endless set.

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Answer: £16.25

Step-by-step explanation:

In order to find the answer we will use a method called unitary method, it is very simple and you must know it as it's repeatedly given in Year 7 and 8 here's the explanation

Cost of 3kg= £7.50

Cost of 1 kg = £7.50÷3

=2.5

Cost of 6.5kg = 2.5×6.5 = £16.25

By the Side-Angle-Side (SAS) congruence criterion, triangle ABC is congruent to triangle BAD.

To prove that triangle ABC is congruent to triangle BAD based on the given information, we can apply the Side-Angle-Side (SAS) congruence criterion.

AC is congruent to BD (Side)

angle CAB is congruent to angle DBA (Angle)

To prove triangle ABC congruent to triangle BAD using the SAS congruence criterion, we need to show that they share two congruent sides and a congruent angle between them.  

Side AB is common to both triangles.

Side AC is congruent to BD (given).

angle CAB is congruent to angle DBA (given).

By satisfying the SAS congruence criterion, we can conclude that triangle ABC is congruent to triangle BAD.

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In this case, we have side AB in common, and side AC is congruent to BD, along with angle CAB being congruent to angle DBA.

Therefore, all the conditions of the SAS criterion are satisfied.

Hence, we can conclude that triangle ABC is congruent to triangle BAD based on the given information.

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The length of side m is, 5.1 inches.

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

Given that;

In ΔMNO,

⇒ o = 8 inches, m ∠M = 28° and m ∠O = 48°.

Now, Let the length of side m = x

So, By sine rule, we get;

[tex]\rightarrow \sf \dfrac{sin \ M}{m} = \dfrac{Sin \ O}{o}[/tex]

Substitute all the values, we get;

[tex]\sf \rightarrow \dfrac{sin \ 28^\circ}{x} = \dfrac{sin \ 48^\circ}{8}[/tex]

[tex]\sf \rightarrow \dfrac{0.47}{x} = \dfrac{0.74}{8}[/tex]

[tex]\sf \rightarrow x=\dfrac{ 0.47 \times 8}{0.74}[/tex]

[tex]\sf x = 5.08\thickapprox 5.1 \ inches[/tex]

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Answer:

Step-by-step explanation:

The output of the exponential function when x = 5 is given as follows:

f(5) = 96.

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

Hence the function is given as follows:

[tex]f(x) = 3(2)^x[/tex]

The numeric value at x = 5 is given as follows:

[tex]f(5) = 3(5)^x = 96[/tex]

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The Area of Rhombus QRST is 78.32 in².

We know the formula of Area of Rhombus

= 1/2 x product of diagonals

We have, QS = 8.8 and RT = 17.8

So, Area of Rhombus QRST

= 1/2 x QS x RT

= 1/2 x 8.8 x 17.8

= 78.32 in²

Thus, the Area of Rhombus QRST is 78.32 in².

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The distance traveled by the supplies is given as follows:

27 feet.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

The distance is the hypotenuse of the right triangle, while the height of 23 feet is opposite to the angle of 60º.

Applying the sine ratio, we have that:

sin(60º) = 23/x

x = 23/sine of 60 degrees

x = 27 feet.

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Answer:

y = (1/2)log₂ (x - 7) - 5

$316,160.00

Interest is the amount of money earned on an initial investment.

Simple Interest

Since the question does not talk about being compounded, we can assume the company is earning simple interest. Simple interest is the amount of money earned on the principal. The principal is the initial investment. Additionally, interest is earned at a specific rate; in this case, the rate is 5.2% each year.

Interest Formula

The formula to find the amount of interest earned is I = Prt. In this formula, I is the amount of interest earned, P is the principal, r is the rate as a decimal, and t is the time in years. To find the interest earned, all we need to do is plug in the information we know.

The account will earn $316,160 of interest.

We can also determine the total of the account by using the formula A = P (1 + rt). If we solve this formula, we can figure out that the account total is $1,076,160.