Two cyclists left simultaneously from cities A and B heading towards each other at constant rates and met in 5 hours. The rate of the cyclist from A was 3 mph less than the rate of the other cyclist. If the cyclist from B had started moving 30 minutes later than the other cyclist, then the two cyclists would have met 31.8 miles away from A. What is the distance between A and B, in miles?

Answer:

A

Step-by-step explanation:

The arc length formula is:

Arc Length = [tex]\frac{\theta}{360}*2\pi r[/tex]

Where

[tex]\theta[/tex] is the angle measure of the arc, and

2πr is the circumference

Putting 84 in place of circumference and 14 in place of arc length, we can solve for [tex]\theta[/tex]:

Arc Length = [tex]\frac{\theta}{360}*2\pi r[/tex]

14 = [tex]\frac{\theta}{360}*(84)[/tex]

14 = [tex]\frac{84\theta}{360}[/tex]

[tex]14*360=84\theta\\5040=84\theta\\\theta=\frac{5040}{84}=60[/tex]

answer choice A is right.

I believe it’s b or c... Hope this helps!

Answer:

1. We already have the measure of the hypotenuse and one out of two acute angle, therefore:

sin53° = x/45 => x = sin53° · 45 ≈35.94

2. We already have one out of two legs of the triangle and one acute angle so we know that:

tan27° = 48/x => x = 48/tan27° ≈ 94.21

The value of x in the first right angle triangle is 27.08.

The value of x in the second right angle triangle is 24.46.

In order to determine the value of x in the first triangle, cos would be used.

Cos 53 = opposite / hypotenuse

Cos 53 = x / 45

0.7071 = x /45

x = 45 x 0.6018

x = 27.08

In order to determine the value of x in the second triangle, tan would be used.

Tan 27 = opposite / adjacent

Tan 27 = x / 48

x = 0.5095 x 48  

x = 24.46

Answer: 2

Step-by-step explanation:

If 8 hours are spent the week, and there is only 1/4 used to play piano then you have to know how much 1/4 is of 8.

To get 1/4 of 8 you need to multiply 8 by 1/4.

The answer is 2.

Answer:

B

Step-by-step explanation:

Two times the quantity of a number minus 12.

Represent the number with the variable y.

The quantity of a number minus 12 is then: (y-12).

Two times this quantity is 2(y-12).

So the answer is 2(y-12), which is B.

ANSWER

A. 150 units^2

EXPLANATION

The surface area of a cube is calculated using the formula:

[tex]SA=6 {l}^{2} [/tex]

where

[tex]l = 5[/tex]

We substitute the length to obtain:

[tex]SA=6 {l}^{2} [/tex]

[tex]SA=6 \times {5}^{2} [/tex]

[tex]SA=150 \: {units}^{2} [/tex]

Answer:

5,000 meters * 1 kilometer / 1,000 meters = 5 kilometers answer is B

Step-by-step explanation:

Answer:

the answer is 5k

Step-by-step explanation:

For angles between 180° and 360°, only cosine (cos) and cosecant (csc) may yield a positive value. This is because these angles fall in the third and fourth quadrants of the unit circle where only certain functions yield positive results.

In the trigonometric functions, the sign of the function's result can vary depending on the size of the angle. For angles between 180° and 360°, only cosine (cos) and cosecant (csc), which is the reciprocal of sine, may have positive values.

In mathematics circle, these angles are in the third and fourth quadrants. In the third quadrant (180° ≤ θ < 270°), only the function tangent (tan) and its reciprocal cotangent (cot) can be positive. While in the fourth quadrant (270° ≤ θ < 360°), the functions cosine (cos) and its reciprocal secant (sec) can be positive.

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Answer:

6

Step-by-step explanation:

The Geometric Mean Theorem states that the altitude (in this case, j) is equal to radical(g*f).

Therefore, j=√(g*f), j=√(3*12), j=6

Answer:

[tex]\boxed{6}[/tex]

Step-by-step explanation:

The Geometric Mean Theorem states that the altitude to the hypotenuse of a right triangle is the geometric mean of the two segments it creates.

Thus, in your triangle,

j = √(fg)

If f = 12 and g = 3,

j = √(12 × 3) = √ 36 = 6

[tex]\boxed{j = 6}[/tex]

ANSWER

D. [tex]a_n= - 7( \frac{1}{3} )^{n - 1}[/tex]

EXPLANATION

The given explicit formula is

[tex]a_1= - 7[/tex]

and

[tex]a_n=\frac{1}{3} a_{n-1}[/tex]

This implies that,

[tex]r = \frac{1}{3} [/tex]

The explicit formula is given by:

[tex]a_n=a_{1}( \frac{1}{3} )^{n - 1} [/tex]

We substitute the known values to get;

[tex]a_n= - 7( \frac{1}{3} )^{n - 1}[/tex]

Answer:

D

Step-by-step explanation: A P E X

YX is corresponding with ED

Hope it helps.

Please mark me brainliest

So I could be completely wrong, or I could be completely right, but quadrilaterals interior angles equal 360 degrees.

So, if you ad up 98, 72, and 65 you end up with 235 degrees.

In order to find the fourth angle, you would just subtract 235 from 360 and get 125 degrees.

BUT, maybe see if someone else answers too, because I am not 100% sure.

Answer:

A

Step-by-step explanation:

Answer:

5 by 4 face = 20 * 2 = 40

5 by 7 face = 35 * 2 = 70

4 by 7 face = 28 * 2 = 56

Total surface area = 166 square meters

Answer is "b"

Step-by-step explanation:

Answer:

your answer will be A

Four litres of pure water should be mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.

To find the litres of pure water mixed:

Given:

Pure water is mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.

Amount of pure water mixed =?

Now,

As given in the question, we have

18 litres of 12% saline solution

= 18 × (12/100)

= 2.16 litres

To make a saline solution containing 3% salt

Hence, four litres should be mixed to obtain a saline solution having 3% salt.

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=================================================

Explanation:

The base is 10 and the height is 6. So b = 10 and h = 6.

We don't use the 7 at all.

Let's use those b and h values into the formula below

A = b*h/2

A = 10*6/2

A = 60/2

A = 30

Answer:

30 square units

Step-by-step explanation:

Always remember that the equation for the area of a triangle is 1/2 times base times height. With an obtuse triangle, you must always ignore the slant. So, half of the base, which is 10, is equal to 5 and 5 times 6 is 30. Also, remember you can multiply in whichever order and the answer will always be the same because of the commutative property.

Answer:

126 cm²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← diagonals

The diagonals of a rhombus are perpendicular bisectors of each other, thus

d₁ = 7 + 7 = 14 and d₂ = 9 + 9 = 18, hence

A = 0.5 × 14 × 18 = 126 cm²

The area of the rhombus is equal to 126 cm². The correct option is B.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rhombus in a two-dimensional plane is called the area of the rhombus.

The area (A) of a rhombus is calculated as

A =  × d₁ × d₂ ← diagonals

The diagonals of a rhombus are perpendicular bisectors of each other,

d₁ = 7 + 7 = 14

d₂ = 9 + 9 = 18, hence

The area of the rhombus will be calculated as,

A =  0.5 × d₁ × d₂

A = 0.5 × 14 × 18

A = 126 cm²

Therefore, the area of the rhombus is equal to 126 cm². The correct option is B.

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The sequence that shows geometric progression are options A), B), C), and E) and this can be determined by finding the geometric ratio.

Check all the options in order to determine which sequence is the geometric sequence.

A) 10, 7.5, 5.625, 4.21875,...

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{7.5}{10}[/tex]

r = 0.75

Ratio between second and third term:

[tex]\rm r =\dfrac{5.625}{7.5}[/tex]

r = 0.75

So, yes this sequence is in geometric progression.

B) 160, 40, 10, 2.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{40}{160}[/tex]

r = 0.25

Ratio between second and third term:

[tex]\rm r =\dfrac{10}{40}[/tex]

r = 0.25

So, yes this sequence is in geometric progression.

C) 20, 70, 245, 857.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{70}{20}[/tex]

r = 3.5

Ratio between third and fourth term:

[tex]\rm r =\dfrac{857.5}{245}[/tex]

r = 3.5

So, yes this sequence is in geometric progression.

D) 13, 16.5, 20, 23.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{16.5}{13}[/tex]

r = 1.27

Ratio between third and fourth term:

[tex]\rm r =\dfrac{23.5}{20}[/tex]

r = 1.175

So, no this sequence is not in geometric progression.

E) 5, 5.5, 6.05, 6.655, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{5.5}{5}[/tex]

r = 1.1

Ratio between third and fourth term:

[tex]\rm r =\dfrac{6.655}{6.05}[/tex]

r = 1.1

So, yes this sequence is in geometric progression.

F) 16, 17.1, 18.2, 19.3, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{17.1}{16}[/tex]

r = 1.07

Ratio between third and fourth term:

[tex]\rm r =\dfrac{19.3}{18.2}[/tex]

r = 1.06

So, no this sequence is not in geometric progression.

For more information, refer to the link given below:

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Answer:

1, 2, 3, 5

Step-by-step explanation:

The geometric transformation shown in the figure is reflection.

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

here, we have,

Given is a set of lines in the music note.

Three line are drawn separating from a line.

In the first part, when we find the mirror image of the first part, we will get the second part.

Mirror images are found in the transformation of reflection.

So, here, we can say that reflection is the transformation here.

Hence the kind of geometric transformation shown in the line of music is reflection.

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Answer:

Hence correct chcie is C.

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]

Step-by-step explanation:

Given function is [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex]

Now it says that function is shifted 4 units to the left and 4 units up.

We need to find about which of the given choice is correct for the given transformation.

When f(x) is shifted "h" units left then we write f(x+h)

So [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex] will change to

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex]

When f(x) is shifted "h" units up then we write f(x)+h

So [tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex] will change to

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]

Answer:

C

Step-by-step explanation:

For a function f(x) = [tex]x^{\frac{1}{3}}[/tex], we have:

Keeping these translation rules in mind, we can clearly say that 4 units shifted left and 4 units up has the equation  [tex]f(x)=(x+4)^{\frac{1}{3}}+4[/tex]

correct answer is C

Answer:

The surface area of the rectangular prism is 700 units² ⇒ answer A

Step-by-step explanation:

* Lets revise how to find the surface are of the rectangular prism

- The rectangular prism has 6 rectangular faces

- Each two opposite faces are equal

- It has 4 side faces and 2 bases

* We can find the surface area of it by adding the area of

 the 6 faces

- In the problem

# The dimensions of the bases are 12 units and 14 units

# The dimensions of the side faces are 12 units and 7 units,

   14 units and 7 units

* Now lets find the area of each 2 equal faces

- In the bases

∵ Area of the rectangle = length × width

∴ The area of one base =  12 × 14 = 168 units²

∴ The area of the two bases = 2 × 168 = 336 units² ⇒ (1)

- In the two opposite faces with dimensions 12 units and 7 units

∵ The area of one face = 12 × 7 = 84 units²

∴ The area of the two faces = 2 × 84 = 168 unit² ⇒ (2)

- In the two opposite faces with dimensions 14 units and 7 units

∵ The area of one face = 14 × 7 = 98 units²

∴ The area of the two faces = 2 × 98 = 196 unit² ⇒ (3)

* To find the surface area of the prism add (1) , (2) , (3)

∴ The surface area of the prism = 336 + 168 + 196 = 700 units²

* The surface area of the rectangular prism is 700 units²

Answer:

x=0  and x=5

Step-by-step explanation:

x^2 – 5x = 0

Factor out an x

x(x-5) = 0

Using the zero product property

x=0 and x-5 =0

Solving

x=0 x-5+5 = 0+5

x=0  and x=5

In the village of 3500 people, 63 individuals are both left-handed and have blonde hair.

To find out how many people in the village are both left-handed and have blonde hair, we first need to calculate the number of left-handed people, and then find 15% of that number to determine those who are also blonde.

Therefore, 63 people in the village are both left-handed and blonde-haired.

Answer:

Domain = (-∞,∞)

Range: [0,∞)

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)=|2x|-sin(x)

From the graph we can see that

- the domain is equal to all real numbers.

- The range goes from [0,∞)

The correct answer is option d, but bear in mind that the range includes zero as well, so it would be Range: [0,∞)

Answer:

Answer is D!!!

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Let's rewrite this a bit.

[tex]-11-(-7-9)=-11+7+9[/tex]

This is because there is a -1 before the expression inside the parentheses, so every sign is reversed.

Now we can add.

[tex]-11+7+9=5[/tex]

Answer:

2√21

Step-by-step explanation:

Diagonal =√(L²+W²+H²)

Diagonal =√(8²+4²+2²)=√(64+16+4)=√84=2√21

**Cracks knuckles** let's do this.

Area of triangle = 31.25 yd^2

10 x 6.25 = 62.5

62.5 / 2 = 31.25

Area of rectangle A = 50 yd^2

10 (length) x 5 (7.5 - 2.5) (width) = 50

Area of rectangle B = 48.75 yd^2

7.5 x 6.5 = 48.75

Total area of composite = 130 yd^2

31.25 + 50 + 48.75 = 130

Answer: Option A

[tex]P(A|B) = \frac{40}{49}[/tex]

Step-by-step explanation:

In a probabilistic experiment, when two events A and B are dependent on each other, then the probability of occurrence A since B occurs is:

[tex]P(A|B) = \frac{P(A\ and\ B)}{P(B)}[/tex]

Then if [tex]P(A\ and\ B) = \frac{5}{7}[/tex] and [tex]P(B) = \frac{7}{8}[/tex] then:

[tex]P(A|B) = \frac{\frac{5}{7}}{\frac{7}{8}}\\\\P(A|B) = \frac{40}{49}[/tex]

Answer:

Correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].

Step-by-step explanation:

Given that [tex]P(A\cap B)=\frac{5}{7}[/tex], [tex]P(B)=\frac{7}{8}[/tex].

Now using those values , we need to find the value of [tex]P(A|B)[/tex].

So apply the formula of conditional probability:

[tex]P(A\cap B)=P(B) \times P(A|B)[/tex]

Plug the given values into above formula,  we get:

[tex]\frac{5}{7}=\frac{7}{8} \times P(A|B)[/tex]

[tex]\frac{7}{8} \times P(A|B)=\frac{5}{7}[/tex]

[tex]P(A|B)=\frac{\frac{5}{7}}{\frac{7}{8}}[/tex]

[tex]P(A|B)=\frac{5}{7}\cdot\frac{8}{7}[/tex]

[tex]P(A|B)=\frac{40}{49}[/tex]

Hence correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].

Answer:

both

Step-by-step explanation:

Depending on how u look at it, one is comprised of 2d figures and the other is of 3d, but the 2d shapes combine to make the faces of any 3d shape, so its basically the same.