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Answer:

[tex]\rightarrow \fbox {Yes} \leftarrow[/tex]

Step-by-step explanation:

ΔABC is a right triangle as it possesses a right angle (90°).

Triangle ABC is a right angled triangle since it holds Pythagoras theorem.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

For a right angled, triangle, there is a theorem called Pythagoras Theorem which relates the three sides of the triangle.

Pythagoras theorem states that,

Hypotenuse² = Base² + Altitude²

Here AC is the hypotenuse, BC is the base and AB is the altitude.

Base² + Altitude² = (BC)² + (AB)²

                             = 5² + 12²

                             = 25 + 144

                             = 169

                             = 13²

                             = AC²

                             = Hypotenuse²

Pythagoras theorem holds for the given triangle.

Hence the given triangle ABC is a right angled triangle.

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The question was incomplete. Below you will find the missing graph image.

The range contain all the real numbers greater than or equal to –3 .

Range of function : The set of outputs of a function is called range of that function. Range of a function is also called co-domain of the function.

Example : If f(x) = x² is the function with domain as all real numbers, then the range of that function is the set of all non-negative real numbers.

We have to find the range of the function on the graph.

We can see by the graph minimum value of y of function is -3 and the graph continues to extend upward in the positive direction.

So, the range contain all the real numbers greater than or equal to –3 .

Therefore, the range contain all the real numbers greater than or equal to –3 .

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The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is [tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]

The expression given is [tex]9^{1/3}=\sqrt[3]{9}[/tex].

The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is as follows:

Therefore, using indices law,

[tex]a^{x/y} =\sqrt[y]{a^{x} }[/tex]

Hence,

[tex]9^{1/3}=\sqrt[3]{9}[/tex]

Therefore, the equation that shows it is correct is as follows;

[tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]

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Answer:

Triangles:

- Equilateral: Has three equal sides

- Isosceles: Has two equal sides

- Right angled: One angle of a right angle triangle measures 90 degrees

- Scalene: All sides are different lengths

Quadrilaterals:

- Square: Has four right angles and four equal sides

- Rectangle: Has four right angles and opposite sides are equal

- Rhombus: A parallelogram with four equal sides

- Parallelogram: Opposite sides are equal and parallel

- Trapezium: At least one set of sides are parallel

- Kite: Two pairs of adjacent sides are the same length

Answer:

18

Step-by-step explanation:

x = number    

45  +  1/2 x   =   3x  

45 = 2.5 x

x = 45/2.5 = 18

Answer:

18

Step-by-step explanation:

Hello!

"Half a number" can be represented by 0.5x and "triple the number" can be represented by 3x.

This just becomes a one variable equation: 45 + 0.5x = 3x

Solve:

The missing number is 18.

Answer:

[tex]1875m^{3}[/tex]

Step-by-step explanation:

To find [tex]\frac{3}{4}[/tex] of the volume, we first must know the total volume.

The formula to find volume:

[tex]volume = length * width * depth[/tex]

We know the length is 25m, we know the width is 20m and we know the depth is 5m.

So, we can substitute them into the equation:

[tex]volume=25*20*5=2500m^{3}[/tex]

Now we know the total volume, we can find out the volume when it is [tex]\frac{3}{4}[/tex] full:

[tex]\frac{3}{4} * 2500 = 1875m^3[/tex]

Therefore, our final answer is [tex]1875m^{3}[/tex].

The product of the two functions is:

[tex](f \times g)(x) = 10x[/tex]

So the correct option is A.

Remember that the square root has the property.

[tex]\sqrt{a}*\sqrt{b} = \sqrt{a*b}[/tex]

Here we have:

[tex]f(x) = \sqrt{2x} \\\\g(x) = \sqrt{50x}[/tex]

Then the product is:

[tex](f \times g)(x) = 10x = f(x)*g(x) = \sqrt{2x}*\sqrt{50x} = \sqrt{(2x)*(50x)} \\\\(f \times g)(x) = 10x = \sqrt{100x^2} = \sqrt{100}*\sqrt{x^2} = 10*x[/tex]

the correct option is A.

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The area of the kite ABCD will be 60 square millimeters.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

In the Kite ABCD, AB = 5√2mm = 7.07 mm, AP= 5mm, PD = 7mm

Then the area of the kite ABCD will be

Area = 2(area of triangle APB and area of triangle APD)

The side length of PB will be

AB² = AP² + PB²

PB² = AB² – AP²

PB² = 7.07² – 5²

PB² = 50 – 25

PB² = 25

 PB = 5 mm

Then the area will be

Area = 2[(1/2 × 7 × 5) + (1/2 × 5 × 5)]

Area = 60 square mm

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Answer: [tex]59^{\circ}[/tex]

Step-by-step explanation:

In triangle ABC, we know that [tex]\angle ABC=130^{\circ}-\theta[/tex]. So, by the inscribed angle theorem, minor arc AC is equal to [tex]260^{\circ}-2\theta[/tex].

Thus, major arc AC is equal to [tex]100^{\circ}+2\theta[/tex].

Using the fact that the angle formed by the two tangents is 38 degrees,

[tex]\frac{(100^{\circ}+2\theta)-(260^{\circ}-2\theta)}{2}=38^{\circ}\\\\100^{\circ}+2\theta-260^{\circ}+2\theta=76^{\circ}\\\\4\theta-160^{\circ}=76^{\circ}\\\\4\theta=236^{\circ}\\\\\theta=\boxed{59^{\circ}}[/tex]

The decision when the z value is within the rejection region is that we'll have to reject the null hypothesis.

It should be noted that the rejection region is also known as the critical region. It is the set of values where the null hypothesis is rejected.

When the observed test statistic is in the rejection region, we'll have to reject the null hypothesis and then accept rte alternative hypothesis.

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1) line segment MJ≅ Line segment MP

2) ∡OJP≅∡OML

3) line segment OM≅line segment MP

The below mentioned statements are true according to the figure , Option A, B and D is the correct answer.

A line that intersects the curve at a single point at 90 degree is called a tangent.

In the given figure it can be seen that the

Therefore , Option A , B and D is the correct answer

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The single transformation that will cause the same effect as that of these two transformation is  the reflection of shape in the x-axis .

(x,y) -----------> (x,−y)

The change done to a shape on a coordinate plane by reflection ,translation and rotation is a called Transformation .

It is given that a shape is rotated to its origin

Then its image is reflected in the y axis.

The single transformation that would have the same result as the two transformations is (x,y) to (x,−y)

reflection of shape in x-axis .

The x stays the same, but the y changes sign.)

The change caused by Rotation by 180° about the origin,

(x,y) ------->  (−x,−y)

The change caused when reflected in the y-axis,

(x,y) --------> (−x,y)

Therefore the single transformation that will cause the same effect as that of these two transformation is  the reflection of shape in the x-axis .

(x,y) -----------> (x,−y)

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[tex]\huge\color{red} {\boxed{\tt{A}}} \color{blue} {\boxed{\tt{N}}} \color{hotpink}{\boxed{\tt{S}}} \color{blueviolet}{\boxed{\tt{W}}} \color{fuchsia}{\boxed{\tt{E}}}\color{lavender}{\boxed{\tt{R}}}[/tex]

[tex] \red{ \star} \pmb{Diameter \: of \: the \: sphere = 7 m}[/tex]

[tex] \red{ \star} \pmb{Radius =\frac{7}{2} = 3.5 m}[/tex]

[tex] \pink{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

[tex] \sf{Area \: available \: to \: motorcyclist \: for \: riding = Area \: of \: sphere}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 4πr^2}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 4*\frac{22}{7}*3.5*3.5}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 154}[/tex]

The area available to the motorcyclist for riding is 154 m²

Diameter of the sphere = 7m

[tex]{Radius =\frac{7}{2} = 3.5 m}[/tex]

Area available to motorcyclist for riding = Area of sphere

[tex]{= 4πr^2} \\ \\ {= 4*\frac{22}{7}*3.5*3.5} \\ \\ {= 154}.[/tex]

The area available to the motorcyclist for riding is 154 m²

The reflection is written as:

[tex]g(x) = -3*(1.5)^x[/tex]

And the graph can be seen below.

Here we have the function:

[tex]f(x) = 3*(1.5)^x[/tex]

A reflection across the x-axis is given by:

[tex]g(x) = -f(x).[/tex]

Then, replacing the function f(x) by the actual equation:

[tex]g(x) = -3*(1.5)^x[/tex]

The graph of the function g(x) can be seen below:

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The correct answer is option B which is y > 3x + 2.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The given statement says that On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2)

The plot of the inequality is given in the graph attached with the answer the inequality will be y > 3x +2 which passes through the points (-3,-7 ) and ( 0, 2 ).

Therefore the correct answer is option B which is y > 3x + 2.

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the pronunciation of this question is wrong make it right first then I will answer

Step-by-step explanation:

please send this question again because I I think you want to write it fast and by mistake you are wright wrong

Answer:

54°

Step-by-step explanation:

Since the 5 vertex angles are congruent, each vertex angle = 360/5 = 72°

The sum of the angles of each triangle is 180-72 = 108°

The base angles of each triangle are equal to each other so each base angle = 108/2 = 54°

Answer:

The amount of time he spent on the bicycle using substitution method is 4.5 hours .

Step-by-step explanation:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

A linear equation is defined as an equation that is written in the form of Ax+By=C. It is the combination of two variables and a constant value present in them.

The first step in the substitution method is to find the value of any one of the variables from one equation in terms of the other variable.

Let the total time taken  to complete the race by bicycle be x

Let the total time taken  to complete the race by walking be y

We know,

Speed=Distance/Time

4y+30x=145

x+y=7

Using the substitution method ,

x=7-y

4y+30(7-y)=145

4y+210-30y=145

210-145=26y

y=65/26

y=2.5

So, the amount of time he spent on bicycle is x

x=7-y

x=7-2.5

x=4.5 hours

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Answer:

the first one

Step-by-step explanation:

0.0206×0.188<0.0769/0.000023

Answer:

For 60 gallons of fuel, the airplane would weigh 2430 gallons.

Step-by-step explanation:

Concept: Use the values and conditions to make a linear equation of a straight line. Let the y-axis be fuel and x-axis be airplane weight. The given points are (2210, 20) and (2397, 54). Use these points to make an equation of line.

[tex]\frac{y-20}{x-2210} =\frac{54-20}{2397-2210} \\\frac{y-20}{x-2210} = \frac{34}{187}[/tex]

Let this be the equation of straight line.

We have to find the airplane weight at 60 gallons of fuel. This means y = 60 and we have to find the x.

[tex]\frac{60-20}{x-2210} =\frac{34}{187} \\x-2210=\frac{(187)(40)}{34} \\x-2210=220\\x=2430[/tex]

So, the airplane weight is 2430 gallons.

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The length of KI is 10 cms.

The skill of measuring the lengths of objects and understanding the units of length is very crucial as it helps us to interact with our environment in a more organized manner.

Here, ΔRJS ≈ Δ IJK

then JR / JI = SR/KI

         1/2   =5 /ki

         kI = 5 X 2

        kI = 10 units.

Thus, The length of KI is 10 cms.

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Answer:

choosing 1 red marble

choosing 1 white marble, replacing it, and choosing another white marble

choosing 1 white marble

Step-by-step explanation:

red marble has a 30 percent chance

1 white marble and then replacing and another white marble is 25% chance

1 white marble is 50% chance

Based on the information provided, the equation of this new circle is equal to: B. (x - h)² + (y - k)² = r²

Mathematically, the equation of a circle can be derived by using Pythagorean theorem;

x² + y² = r²

Where:

After translating h units along the x-axis and k units along y-axis on a coordinate plane, the equation of this new circle is given by:

(x - h)² + (y - k)² = r²

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Answer: B) (x – h)2 + (y – k)2 = r2

Step-by-step explanation:

Answer:

1=76°

2=76°

3=36°

Step-by-step explanation:

To find 1, add the other angles in the triangle and subtract by 180.

85+19=104

180-104=76.

1 is equal to 2 so 2=76

To find 3, add 76 and 68, then subtract by 180.

76+68=144

180+144=36

3=36

Hope this helps!

If not, I am sorry.

Answer:

m∠1 = 76°

m∠2 = 76°

m∠3 = 36°

Step-by-step explanation:

The interior angles in a triangle sum to 180°

⇒ m∠1 + 85° + 19° = 180°

⇒ m∠1 + 104° = 180°

⇒ m∠1 + 104° - 104° = 180° - 104°

⇒ m∠1 = 76°

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

⇒ m∠2 = m∠1

⇒ m∠2 = 76°

The interior angles in a triangle sum to 180°

⇒ m∠2 + m∠3 + 68° = 180°

⇒ 76° + m∠3 + 68° = 180°

⇒ m∠3 + 144° = 180°

⇒ m∠3 + 144° - 144°= 180° - 144°

⇒ m∠3 = 36°

Answer:

Exact Area of shaded region = 141.39cm²

Step-by-step explanation:

Quadrant of a circle - Quadrant refers to the four quarters in the coordinate plane system. Each of the four sections is called a quadrant. When it comes to circle, the quarter of a circle is called a quadrant, which is a sector of 90°.

area of circle  =πr²

area of quadrant of a circle = πr²/4

where r is the radius of the circle.

In the given figure there are 2 types of quadrants of circle are present

one with radius AB (bigger )

another with radius AB/2 (smaller)

Now area of quadrant having radius = AB

⇒ π(AB) ²/4

here AB is the side of square

so AB = 12cm

substituting this in the area of quadrant formula

area of bigger quadrant = π(12²)/4

                               area₁ = 144×π/4

                                area₁ = 144×3.142/4

                                area₁ = 113.112cm²

now area of smaller quadrant = π(AB/2) ²/4

                                    area ₂   = π(6) ²/4

                                    area ₂   = 36π/4

                                    area ₂   = 9×π

                                     area ₂  = 28.278cm²

Now it is clear from the given figure,

area of shaded region is =    area₁ -   area₂ +2×area₂

                                         =     113.112cm² -  28.278cm² + 2× 28.278cm²

                                         =     113.112cm² +  28.278cm²

                                         =      141.39cm²   (answer)

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Answer:

B = 42°

Step-by-step explanation:

All of the internal angles of a triangle  sum to 180°

x + 2x + 54 = 180

3x = 180 - 54

x = 42 °            which is angle B

First we must solve the bottom situations.

___________________________________________ (2A and 2B)

First expression (2A): 2v+8.3+2v-6.1

⇒  Collect like terms

(2v + 2v)  + (8.3 - 6.1)

⇒ Simplify

4b + 2.2

Second expression (2B): 3v+14.4-v

⇒ Collect like terms

(3v - v) + 14.4

⇒ Simplify

2v + 14.4

They are not equivalent because when simplified they both have different coefficients and constants each of different values.

_____________________________________________ (4A and 4B)

First expression (4A): 10 + 3 (1/3x + 2)

⇒ Simplify 1/3x to x/3.

10 + 3(x/3 + 2)

⇒  Expand by distributing terms.

10 + x + 6

⇒ Collect like terms.

x + (10 + 6)

⇒ Simplify.

x + 16

Second expression: x + 16

This expression can not be simplified any further. This is because it is a simplified version of another expression.

These expressions are equivalent because expression 4B is the simplified version of expression 4A.

______________________________________

Level: 7th Grade

Unit: Distributing and Combing Like Terms