Randy starts biking at a rate of 6 miles per hour toward a store that is 20 miles away. Cali leaves the store when Randy starts biking. Cali bikes toward Randy along the same route at 2 miles per hour. How many hours will pass before they meet on the road?


PLEASE HELP

let the number be x and y

x + y = 30 -----(1)

x = y + 15 -----(2)

y + y + 15 = 30

2y = 15

y = 7.5

x = 7.5 + 15 = 22.5

x= 22.5 , y = 7.5

Answer:

y= -3x -3

Step-by-step explanation:

Answer: 8.123 is a decimal

Step-by-step explanation:

A decimal is a whole number and a fractional part

there is a decimal point

The simplification of the vector complex number is: -2 - 14i

We are given the expression to simplify which is:

-2 + 14(i¹⁵)

Now, when it comes to complex numbers we know the following that:

i² = -1

i³ = -i

i⁴ = 1

Applying the above to the given expression is

i¹⁵ = i⁴ × i⁴ × i⁴ × i³

i¹⁵ = -i

Therefore we can easily write the following:

-2 + 14(i¹⁵) = -2 - 14i

Thus, the expression which is equivalent to the given expression is; -2 -14i

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Answer:

Consider the form x 2 + b x + c . Find a pair of integers whose product is c and whose sum is b . In this case, whose product is 77 and whose sum is 18 . 7 , 11 Write the factored form using these integers. ( x + 7 ) ( x + 11 ).

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^2 - 18x + 77

(x - 11)(x - 7)

The Relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

The relationship between the points D(6, 9) and A(8, 12) can be described in terms of dilations. In mathematics, a dilation is a transformation that changes the size of an object while keeping its shape intact. It involves scaling the object by a certain factor, either enlarging or reducing it.

To understand the relationship between D and A, we can calculate the dilation factor. The dilation factor, denoted by 'k', is the ratio of the corresponding side lengths or distances between the pre-image (original object) and the image (transformed object).

The dilation factor between D(6, 9) and A(8, 12):

First, we need to find the change in x-coordinates and y-coordinates:

Δx = 8 - 6 = 2

Δy = 12 - 9 = 3

Next, we calculate the dilation factor:

k = Δy / Δx = 3 / 2 = 1.5

The dilation factor of 1.5 indicates that the image point A is 1.5 times as far from the origin (point D) compared to the pre-image. This means that A is located at a greater distance from the origin than D, both horizontally and vertically.

Moreover, since the dilation factor is positive, the dilation is an enlargement. This means that A is enlarged with respect to D. The ratio of the corresponding side lengths will also be 1.5.

the relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

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2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

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Answer:

x = 5

Step-by-step explanation:

using the sine or cosine ratio in the right triangle and the exact value

sin30° = \(\frac{1}{2}\) , then

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{10}\) = \(\frac{1}{2}\) ( cross- multiply )

2x = 10 ( divide both sides by 2 )

x = 5

The digits in millions period of the number is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

Given the number is 21,468,127,471.

The digits in which are given in the large numbers are in groups of three places. The groups are called periods. Commas are usually used to separate the periods.

The groups of numbers are 3 digit group and which is starting from the right to left.

As we all know that we read the group of periods as ones, tens, hundreds, thousand, ten thousand, hundred thousand, million, ten million, hundred million, billion etc.

From  the above, we find that the given number 21,468,127,471 contains digit 1 is in the ones place, 7 is in the tens place, 4 is in the hundredth place, 7 is in the thousand place, 2 is in the ten thousand place, 1 is in the hundred thousand place, 8 is in the million place, 6 is in the ten million place, 4 is in the hundred million place , 1 is the billion place and 2 is in the ten bilion.

Hence, the digits in millions period of the given number 21,468,127,471 is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

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Answer: Check attached picture

Step-by-step explanation:

hello!! :D

answer:  The GCF is 3x^2yz.

Hope this helps! Have a wonderful day! :D

The evaluated line integral in the (x, y) plane from (0,0) to (1,4) for the given options is as follows: (a) For C: y = 4x³, I = ∫[0 to 1] (2.42 + 3 + 3²) dx + ∫[0 to 4] (4.2 - y) dy, (b) For C: y = 4x, I = ∫[0 to 1] (2.42 + 3 + 3²) dx + ∫[0 to 4] (4.2 - y) dy.

(a) In option (a), we have the curve C defined as y = 4x³. We calculate the line integral I by evaluating two integrals: the first integral is with respect to x from 0 to 1, and the second integral is with respect to y from 0 to 4.

(a) For C: y = 4x³, I = ∫[0 to 1] (2.42 + 3 + 3²) dx + ∫[0 to 4] (4.2 - y) dy

= (2.42 + 3 + 3²) ∫[0 to 1] dx + ∫[0 to 4] (4.2 - 4x³) dy

= (2.42 + 3 + 3²) [x] from 0 to 1 + (4.2y - x³y) from 0 to 4

= (2.42 + 3 + 3²)(1 - 0) + (4.2(4) - 1³(4)) - (4.2(0) - 1³(0))

= (2.42 + 3 + 3²)(1) + (4.2(4) - 64)

= (2.42 + 3 + 9)(1) + (16.8 - 64)

= (14.42)(1) - 47.2

= 14.42 - 47.2

= -32.78

b) In option (b), we have the curve C defined as y = 4x. Similar to option (a), we evaluate two integrals: the first integral is with respect to x from 0 to 1, and the second integral is with respect to y from 0 to 4. The integrands for the x-component and y-component are the same as in option (a).

To find the specific numerical values of the line integrals, the integrals need to be solved using the given limits.

For C: y = 4x, I = ∫[0 to 1] (2.42 + 3 + 3²) dx + ∫[0 to 4] (4.2 - y) dy

= (2.42 + 3 + 3²) ∫[0 to 1] dx + ∫[0 to 4] (4.2 - 4x) dy

= (2.42 + 3 + 3²) [x] from 0 to 1 + (4.2y - xy) from 0 to 4

= (2.42 + 3 + 3²)(1 - 0) + (4.2(4) - (1)(4)) - (4.2(0) - (1)(0))

= (2.42 + 3 + 9)(1) + (16.8 - 4)

= (14.42)(1) + 12.8

= 14.42 + 12.8

= 27.22.

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Answer:

I think that they are genuinely very nice and humble people. From my knowledge, I think that they really like spicy food and including a variety of spices while cooking.

Step-by-step explanation:

The value of the expression 5(3r - 10) means the product of 5 and the difference of three times r minus 10. If r= 4, the value of the expression is 10.

Mathematical expression is mathematical statement which involves variables, numerical values, mathematical operations, and exponent.

Given the expression in words "the product of 5 and the difference of three times r minus 10"

Three times of 'r' is = 3r

Difference between three times of r and 10 = 3r - 10

The product of 5 and difference between three times of r and 10 = 5(3r - 10)

So the expression is given by, f(r) = 5(3r - 10)

Also the given value of the variable is, r = 4.

Substituting the value in the expression we get,

f(4) = 5(3*4 - 10) = 5*(12 - 10) = 5*2 = 10

Hence the value of the expression when r = 4 is 10.

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if the train line is 130 kilometers long, it took 0.9 hour  time  before the two trains meet

A freight train on the bluepoint-vindale line departs bluepoint, traveling at a speed of 42 kilometers per hour.

at the same time, a second train leaves vindale, bound for bluepoint, and is moving at speed of  97 kilometers per hour.

if the train line is 130 kilometers long, distance is 130km

how much time will pass before the two trains meet?

Time = Distance /speed

Let the encounter take time x

the sum of the distance between two trains when they meet is 130 km

42x +97 x=130

139x =130

  x= 0.9 hour

Hence it took 0.9 hour before the two trains meet.

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Answer:

B

Step-by-step explanation:

The explanation is attached below.

\(\implies {\blue {\boxed {\boxed {\purple {\sf {(2).\: \: \frac{ - 27}{3}\:and\: (5).\: - 9 }}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\( \frac{27}{ - 3} \)

2. \( \: \frac{ - 27}{3} \) ✔

5. \( - 9\) ✔

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Mystique35♨}}}}}∘\)

Answer:

Rounded to the nearest whole number is 1

Step-by-step explanation:

when you divide 6 by 5 you get 1.2. Since 2 is not five or greater you round down.

The calculated population of the village 2 years before is 10000

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

Inital population, a = 10816

Rate of increase, r = 4%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 + r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 10816 * (1 + 4%)ˣ

So, we have

f(x) = 10816 * (1.04)ˣ

The value of x 2 years before is -2

So, we have

f(-2) = 10816 * (1.04)⁻²

Evaluate

f(-2) = 10000

Hence, the population of the village 2 years before is 10000

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Answer:

C) y=-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-(-1))/(0-4)

m=(-1+1)/-4

m=0/-4

m=0

y-y1=m(x-x1)

y-(-1)=0(x-4)

y+1=0

y=0-1

y=-1

Rounded to the nearest tenth, the angle between the two vectors is approximately 1.8. To find the dot product between two vectors, we multiply their corresponding components and sum the results.

To find the dot product between two vectors, we multiply their corresponding components and sum the results. Let's denote the two vectors as v and w. Given that the components of v are 1 and -5, and the components of w are -5 and 0, the dot product can be calculated as follows:
v · w = (1 * -5) + (-5 * 0) = -5 + 0 = -5
Now, let's find the angle between the two vectors. The dot product can be used to find the angle using the formula:
cos(theta) = (v · w) / (||v|| * ||w||)
Where ||v|| and ||w|| represent the magnitudes (lengths) of the vectors. In this case, both vectors have a magnitude of \(\sqrt(26)\).
Substituting the values into the formula:
cos(theta) = -5 / \((\sqrt(26) * \sqrt(26))\) = -5 / 26
To find the angle theta, we can use the inverse cosine function:
theta = acos(-5 / 26)
Evaluating the expression gives:
theta ≈ 1.810
Rounded to the nearest tenth, the angle between the two vectors is approximately 1.8.

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We want to find the measure of x given that we know that m and n are congruent.

The measure of x is 116°.

Two angles are congruent if they have the same measure.

Then we have ∠n = ∠m

We also know that the sum of all interior angles of a triangle is equal to 180°, then if we look at the smaller triangle we have that:

114° + ∠n + ∠m = 180°

∠n + ∠m = 180° - 114° = 66°

Knowing that these measures are equal we can write:

2*∠m = 66°

∠m = 66°/2 = 33°

Now that we know the measure of m, we can do the same thing for the larger triangle:

∠x + ∠m + 31° = 180°

∠x + 33° + 31° = 180°

∠x = 180° - 64° = 116°

The measure of x is 116°.

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Applying the exterior angle theorem and the sum of triangles, the value of x in the figure is: \(\mathbf{x = 64^{\circ}}\)

Recall:

Sum of triangles = 180 degrees

Exterior angle = sum of two interior opposite angles

Since we know that angles m and n are congruent, therefore:

\(m = \frac{1}{2} (180 - m \angle RTU)\)

\(m = \frac{1}{2} (180 - 114)\\\\\mathbf{m = 33^{\circ}}\)

Find x (exterior angle of triangle SUV):

\(x = 31 + m\) (exterior angle of a triangle theorem)

\(x = 31 + 33\\\\\mathbf{x = 64^{\circ}}\)

Therefore, applying the exterior angle theorem and the sum of triangles, the value of x in the figure is: \(\mathbf{x = 64^{\circ}}\)

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Answer:

93

Step-by-step explanation:

v=66×62/44=93

hope it helps

Hey there!

“66 / v = 44 / 62”

~ FIRST you have to CROSS MULTIPLY

66 • 62 = 44 • v

66 • 62 = 4,092

44 • v = 44v

➡️ 4,092 = 44v

~ SECOND TURN/FLIP your EQUATION

44v = 4,092

~ THIRD DIVIDE both SIDES by 44

44v / 44 = 4,092 / 44

CANCEL out: 44 / 44 because that gives you 1

KEEP: 4,092 / 44 because that gives you the v-value

FOURTH: SOLVING

4,092 / 44 = v ; v = 4,092 / 44

Solve the equation that’s in STEP FOUR and you have your v-value

Answer:

v = 93 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

D) 20.5.

Step-by-step explanation:

To find the angle of rotation, we can use the formula:

Angle of rotation = Arc length / Radius

First, we need to calculate the radius of the ferris wheel. The diameter is given as 224 feet, so the radius is half of that:

Radius = 224 feet / 2 = 112 feet

Now, we can calculate the angle of rotation:

Angle of rotation = 40 feet / 112 feet

Angle of rotation ≈ 0.3571 radians

To convert this to degrees, we multiply by 180/π:

Angle of rotation ≈ 0.3571 * (180/π) ≈ 20.4646 degrees

Rounding to the nearest tenth of a degree, the angle of rotation is approximately 20.5 degrees.

Therefore, the correct answer is option D) 20.5.

For the data  12, 14, 21, 19, 25, 29, 26, 21, 15, and 18.

the mean is 20

the standard deviation is 3.7

the interquartile is 10

For the data  12, 14, 21, 19, 25, 29, 26, 21, 15, and 18. the mean is calculated as follows

= sum of data / number of data

sum = 200

number of data = 10

mean (x bar)  = 200 / 10

= 20

standard deviation

standard deviation is the square root of  the ratio of sum of squares to number of samples

sum of squares = (x - x bar)²

= (12 - 20)² + (14 - 20)² + (21 - 20)² + ......+(21 - 20)² + (15 - 20)² + (18 - 20)²

= 274

standard deviation = √(274 / 20) = 3.7

Interquartile range = upper quartile - lower quartile

raw data = 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18

arranged data =  12, 14, 15, 18, 19, 21, 21, 25, 26, 29,

upper quartile = 25

lower quartile = 15

Interquartile range = 25 - 15 = 10

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Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Answer:Thus, a product that normally costs $72 with a 30 percent discount will cost you $50.40, and you saved $21.60. You can also calculate how much you save by .

So therefore answer:50.40  please brainIlist

Step-by-step explanation:

Answer:

\( \frac{ \sqrt[3]{x} }{9} \)

Quotient means the answer after dividing two numbers.

Therefore, the radius of the outer edge of the rainbow is 23.3196 feet.

Given that the inner edge of the purple strip is 4 feet from the center (distance r), and the angle is a = 42.1 degrees. To find the radius of the outer edge of the rainbow (the distance R), we can use the following formula.

The formula for the sector of a circle is:

A = 1/2 r²θ

Where A is the area of the sector. r is the radius of the sector.θ is the angle of the sector in radians.

Converting the angle from degrees to radians, we get:

θ = 42.1° × (π/180)θ = 0.7356 radians

Also, we know the area of the rainbow A = 100.298So, we get:100.298 = 1/2 R²(0.7356)

Simplifying the above expression, we get:

R² = (2 × 100.298)/0.7356R² = 544.4977

Taking the square root of both sides, we get:

R = 23.3196 feet

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