Khan academy question

Answer:

hi

Step-by-step explanation:

Answer:B.

Step-by-step explanation:

Answer: C

Step-by-step explanation:

In the quadrant IV, it is only a cos θ that is positive.

Given that tan θ = –8∕15

Where tan θ = opposite ÷ adjacent

Where opposite = 8 and adjacent = 15

We can find the hypothenus by using pythagorean theorem

Hypothenus = sqrt(15^2 + 8^2)

Hypothenus = sqrt(289)

Hypothenus = 17.

Sin θ = opposite ÷ hypothenus

Sin θ = 8/17

Since Sin θ is also negative in the fourth quadrant, therefore

Sin θ = - 8/17

Option C is correct.

Answer:

Option B

Step-by-step explanation:

The absolute value of a number is how far a number is from zero. We can use ' | | ' to represent the absolute volume of a number.  The distance, or absolute value, of -8 is 8.

We can represent this by writing:

|-8| = 8

Option B should be the correct answer.

Answer:

B

Step-by-step explanation:

The absolute value of a number means the distance from 0.

For example, |-2| is 2 units from 0.

|-8| = 8

-8 is 8 units from 0.

Answer:

Surface area of triangular prism is:

Surface area = 2376ft

Step-by-step explanation:

A triangular prism is the one which has 3 rectangular sides and 2 triangular sides. To find the surface area of a triangular prism, we have to find the surface area of 3 rectangular side and 2 triangular sides and add them up

Surface Area (rectangle) = Length · Width

Surface Area (triangle) = (1/2)(Base)(Height)

Rectangular side 1:

Length = 40 ft

Width = 24 ft

Surface Area = 40 · 24

Surface Area = 960ft

Rectangular side 2:

Length = 40 ft

Width = 15 ft

Surface Area = 40 · 15

Surface Area = 600ft

Rectangular side 3:

Length = 40 ft

Width = 15 ft

Surface Area = 40 · 15

Surface Area = 600ft

Triangular side 1:

Base = 24 ft

height = 9 ft

Surface Area = (1/2)(24)(9)

Surface Area = 108ft

Triangular side 2:

Base = 24 ft

height = 9 ft

Surface Area = (1/2)(24)(9)

Surface Area = 108ft

SURFACE AREA OF TRIANGULAR PRISM:

Add all surface areas found above

Surface area = 960 + 600 + 600 + 108 + 108

Surface area = 2376ft

Answer:

Answer:

(B) Surface area of triangular prism is:

Surface area = 2376ft

Step-by-step explanation:

A triangular prism is the one which has 3 rectangular sides and 2 triangular sides. To find the surface area of a triangular prism, we have to find the surface area of 3 rectangular side and 2 triangular sides and add them up

Surface Area (rectangle) = Length · Width

Surface Area (triangle) = (1/2)(Base)(Height)

10 L of a 25% acid solution contains 0.25 * (10 L) = 2.5 L of acid.

Adding x L of pure water dilutes the solution to a concentration of 10%, such that

(2.5 L)/(10 L + x L) = 0.10

Solve for x :

2.5 = 0.10 * (10 + x)

2.5 = 1 + 0.10x

1.5 = 0.10x

15 = x

so 15 L of pure water are needed.

Answer:

Step-by-step explanation:

Perimeter of the rectangle = 332m

Perimeter of a rectangle = 2(L+b)

Breadth = 75m

= 2 ( L + 75) = 332

2L + 150 = 332

2L = 332-150

L = 182/2

L= 91m

Answer:

average speed of sprinter will be 10.42m/s

Step-by-step explanation:

distance covered=s=100m

time taken=t=9.67m/s

average speed=[tex]\frac{distance covered}{time taken}[/tex]

average speed=[tex]\frac{100m}{9.67s}[/tex]

average speed=10.42m/s

Answer: its 3

Step-by-step explanation:

Answer:   2

Step-by-step explanation: Because their are 2 squares

Answer:

[tex]Fraction = \frac{3}{14}[/tex]

Step-by-step explanation:

Given:

[tex]Total\ Length = 5\frac{5}{6}[/tex]

[tex]Straight\ Section = 1\frac{1}{4}[/tex]

Required:

Fraction of the circuit that is straight section

To solve this, we simply divide the length of the straight section by the total length of the circuit;

This is done as follows;

[tex]Fraction = 1\frac{1}{4} / 5\frac{5}{6}[/tex]

Convert both fractions to improper fractions

[tex]Fraction = \frac{5}{4} / \frac{35}{6}[/tex]

Change division sign (/) to multiplication (*)

[tex]Fraction = \frac{5}{4} * \frac{6}{35}[/tex]

Combine to form a single fraction

[tex]Fraction = \frac{5*6}{4*35}[/tex]

[tex]Fraction = \frac{30}{140}[/tex]

Divide numerator and denominator by 10

[tex]Fraction = \frac{3}{14}[/tex]

Hence, the fraction of the straight section is; [tex]Fraction = \frac{3}{14}[/tex]

It is important to consider salary and benefits because you should consider how much money you need to buy necessities and a few things you want, but you should also look into whether the benefits can wave some of the necessity costs, such as health insurance, etc.

Answer:

c

Step-by-step explanation:

In the given line the relationship between angle w and z is Measure of angle w + measure of angle z = 180 degrees.

This is the type of angle that when measured, two of the angles would sum up to 180 degrees.

The supplementary angle is the sum of angle w + angle z = 180 degrees. Hence c is correct.

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Answer:

3f(x)  

3x^2  

12  

-x+6

0

Step-by-step explanation:

Fashoo

Answer:

10 meters

Step-by-step explanation:because they are square and they would have to be 5 meters long and she dose not want any left over so...

Answer:

Answer:

3 < c < 13

Step-by-step explanation:

A triangle is known to have 3 sides: Side a, Side b and Side c.

For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).

To solve the above question, we would be using the Triangle Inequality Theorem.

The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.

Side a + Side b > Side c

Side a + Side c > Side b

Side b + Side c > Side a

For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,

side (a) = 5

side (b) = 8

Let's represent the third side as c

To solve for the above question,we would be having the following Inequality.

= b - a < c < b + a

= 8 - 5 < c < 8 + 5

= 3 < c < 13

Answer: B $2.22

Step-by-step explanation:

2 controllers will cost

= 2 x 18.50 = 37

6% tax = 37 x 0.06 = 2.22

Answer:

B

Step-by-step explanation:

i took the test

Answer:

Question 1:

The smallest 5-digit no. is 10,000

The product of its prime factors is:

=> 10,000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

Question 2:

The prime factors of 1729 are:

=> 1729 = 7 × 13 × 19

The relation between their 2 consecutive prime factor is that when they both are subtracted, they give the result 6

Such as :

=> 13-7 = 6

=> 19-13 = 6

Hope this helps!

Don't hesitate asking anything regarding this question!

Answer:

1. The smallest 5-digit number is: 10000

10000= 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

2. 1729= 7 × 13 × 19

7= 6+1

13= 6*2+1

19= 6*3+1

Answer:

None. (or B)

Step-by-step explanation:

A)  AC≅ZY

B) AZ≅

C) ∠A ≅ ∠C

D) ∠B ≅ ∠X

Options C and D are not true and Options A is wrong and B is incomplete but using process of elimination, the answer is probably B.

The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Given that, Δ ABC has been translated right to create triangle Δ XYZ

We know that in translation transformation, in translation, only the position of the object changes, its size remains the same.

That means Δ ABC ≅ Δ XYZ Therefore, we get,

Congruent parts are;

Angles:-

∠ A ≅ ∠ X,

∠ B ≅ ∠ Y and

∠ C ≅ ∠ Z

Side:-

AB ≅ XY,

BC ≅ YZ and

AC ≅ XZ

Hence, The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

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Answer:

(-9/2 , -10)

Step-by-step explanation:

2x-3y=21

-6x+2y=7

Multiply the first equation by 3

3(2x-3y)=21*3

6x - 9y = 63

Add this to the second equation to eliminate x

6x - 9y = 63

-6x+2y=7

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

0x -7y = 70

Divide by -7

-7y/-7 = 70/-7

y = -10

Now find x

2x- 3y = 21

2x -3(-10) = 21

2x +30 =21

subtract 30 from each side

2x = 21-30

2x= -9

Divide by 2

x = -9/2

(-9/2 , -10)

Now lets solve it by elemination method !

[tex]:\implies\sf 2x-3y=21--------(1)\\ \\ \\ :\implies\sf -6x+2y=7-------(2)\\ \\ \\ \sf Eleminate\ (x) \\ \\ \\ \it Multiply\ first \ equation \ with \ 3\ \ \ and \ 2nd \ \ with \ 1 \\ \\ \\ :\implies\sf (2x-3y=21)\times 3 \\ \\ \\ :\implies\sf (-6x+2y=7)\times 1\\ \\ \\ :\implies\sf 6x-9y=63------(3) \\ \\ \\ :\implies\sf -6x+2y=7-----(4)\\ \\ \\ \it\ \ Add \ equation\ 3\ \ and \ 4\\ \\ \\ :\implies\sf 6x-9y=63+ (-6x+2y= 7)\\ \\ \\ :\implies\sf (6x-6x)+(-9y+2y) = 63+7\\ \\ \\ :\implies\sf 0-7y=70\\ \\ \\ :\implies\sf y= \cancel{\dfrac{70}{-7}}= - 10\\ \\ \\ :\implies\sf y= -10 [/tex]

★ Now find the value of x

let's substitute the value of y in equation 4

[tex]:\implies\sf -6x+2y=7\ \ \ \ \ \ (y= -10)\\ \\ \\ :\implies\sf -6x+2\times (-10)=7\\ \\ \\ :\implies\sf -6x-20= 7\\ \\ \\ :\implies\sf -6x = 7+20 \\ \\ \\ :\implies\sf x= \cancel{\dfrac{27}{-6}}= \dfrac{-9}{2}[/tex]

[tex]\underline{\textit{ \ \ So, \ the \ value \ of \ x\ and \ y }}[/tex]

[tex]\bigstar{\boxed{\sf x= \dfrac{-9}{2}}}[/tex]

[tex]\bigstar{\boxed{\sf\ y= (-10)}}[/tex]

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Distribute

1/2 x + 3 = 18

Subtract 3 from each side

1/2x +3-3 = 18-3

1/2x = 15

Multiply each side by 2

1/2x*2 = 15*2

x = 30

Answer:

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

Step-by-step explanation:

Given

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

Required

Solve

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

In trigonometry;

[tex]1 - cos^2x = sin^2x[/tex]

So, make substitution

[tex](1-cos^2 x ).(1+tan^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(1+tan^2 x)[/tex]

Also; in trigonometry:

[tex]1 + tan^2x = sec^2x[/tex]

Make another substitution

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex]

Recall that [tex]secx = \frac{1}{cosx}[/tex]

So;

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(\frac{1}{cos^2 x})[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = \frac{sin^2 x }{cos^2 x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = (\frac{sin x }{cosx})^2[/tex]

In trigonometry;

[tex]tan x = \frac{sin x}{cos x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

The expression cannot be further simplified

Answer:

This function is True

Step-by-step explanation:

Since there is one value of  y  for every value of  x .

Answer:

y = (-2/125)(x - 50)² + 40

Step-by-step explanation:

The total length of the bridge is 100 meters.

Maximum height always occurs at midpoint of x.

So for x=50 meters , y = 40 meters.

As the vertex is given at the maximum height,  Vertex can be defined at the point (50,40)

We know that the general equation for vertical parabola is:

y = a(x - h)² + k

Where (h,k) = Vertex = (50,40)

Substitute in the equation:

y = a(x - 50)² + 40 ⇒ Equation (i)

We know 2 more points on the parabola. We know that when x=0 , y=0 and we also know that when x=100m, y=0 meters.

Substitute any point in the above equation

Substituting (100,0) in the equation

0 = a(100 - 50)² +40

Solve the equation for a:

a = - 2/125

Substitute a in Equation (i)

y = (-2/125)(x - 50)² + 40

Answer:

132 dollars, I think

Step-by-step explanation:

15*2=30

66*2=132

Answer:

D

Step-by-step explanation:since 15 cases is $66 multiply 66 by 2 to get $132

Answer:

Step-by-step explanation:Jo's Mobile Plan:

Fixed monthly charge = £16

Monthly 150 free minutes, post that 13p (or £0.13) per minute,

Monthly 150 free texts, post that 15p (or £0.15) per text

Jo's mobile phone usage details:

170 minutes of calls

182 texts

Total Charges for Jo = Fixed Monthly Charge + Charges for Calls + Charges for Texts

⇒ Total Charges for Jo = 16 + (170-150) × 0.13 + (182-150) × 0.15

⇒ Total Charges for Jo = 16 + (20) × 0.13 + (32) × 0.15

⇒ Total Charges for Jo = 16 + 2.6 + 4.8

⇒ Total Charges for Jo = 23.4

Hence, Jo should be charged £23.4 for the month.

Answer:

A:

(4x+5)(3x+10)=

(12x^2) + (40x) + (15x) + (50)

12x^2 + 55x + 50

B: 2nd degree trinomial.

C:  it is demonstrated in part A because when we added it, the variable do not change and neither do the  exponents.  

Step-by-step explanation:

do not copy. used this on my test.

Answer:

2

Step-by-step explanation:

3x + 2 =y y=8

3x + 2=8

3x=6

x=2

Answer:

x = 2

Step-by-step explanation:

3x + 2 = 8

3x = 6

x = 2

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Step-by-step explanation:

[70,30] = 210 miles per hour

d=76.157t is the expression for two vehicles, a car and a truck which were distance apart d (in miles) at the end of t hours.

Two vehicles, a car and a truck, leave an intersection at the same time. The car heads east at an average speed of 70 miles per hour, while the truck heads south at an average speed of 30 miles per hour. we need to find expression for their distance apart d at the end of t hours

Distance=Speed*Time

distance= speed * time.

*70t be the car traveling EAST at 60 miles per hour after t hours

*30t be the distance of the truck traveling SOUTH at 20 miles per hour after t hours.

*Use the Pythagorean Theorem to find the distance d.

The Pythagoras theorem states that sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

d^2=(70t)^2+(30t)^2

d^2=4900t^2+900t^2

d^2=5800t^2

d=76.157t

Therefore d=76.157t is the required expression for their distance apart d (in miles) at the end of t hours.

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Answer:

See below

Step-by-step explanation:

You have to find the number in the middle of all of the heights and multiply them by the all of the frequency. When you have those answers, add them together and divide the answer by 40. That is why, our answer in part (a) is an estimate.

The mean is the average value of an observation, the mean of the grouped data is 129.3 cm

The mean value can be calculated using the relation :

ΣF = (7 + 8 + 13 + 9 + 3) = 40

Σfx = (7 × 122) + (8 × 126) + (13 × 130) + (9 × 134) + (3 × 138) = 5172

Mean = ΣFx /ΣF

Mean = 5172 / 40 = 129.3 cm

B.)

The mean value obtained is an estimate because, calculation used the midpoint value existing within a certain range, and not the exact height value of individual student.

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Answer:

If you use a graphing calculator, at x= 0   (t =0)  the graph starts at 60 mb   and then climbs 4 mb per sec   (slope = 4 mb/sec)  from there until Agent Hunt gets caught and executed for espionage.

Hope this helps!