two cars travel down the highway at the same speed. if the first car travels 10 kilometers per hour faster than its current speed and the second car travels 10 kilometers per hour slower than its current speed than the first car would travel in two hours the same distance the second car would travel in thee hours. what is the original speed of the cars?

Answer:

Step-by-step explanation:

[tex]\frac{x}{5} +1=\frac{1}{15}[/tex]

[tex]\frac{x}{5} = \frac{1}{15} -1[/tex]

[tex]\frac{x}{5} = \frac{1-15}{15}[/tex]

[tex]\frac{x}{5} = \frac{-14}{15}[/tex]

multiply both sides by 5

[tex]5*\frac{x}{5} = \frac{-14}{15} *5[/tex]

[tex]x=-\frac{14}{3}[/tex]

Answer:

0.245

Step-by-step explanation:

Divide both the numerator and denominator by 2.

49/200 will be 24.5/100

If you divide a number by 100, you move the decimal place 2 digits to the left. 24.5/100 will become 0.245

The 4th, 5th, 6th,and 7th terms of the sequence an = n²/{n+1} are 16/5, 25/6, 36/7, and 49/8 respectively.

According to the given question.

We have,

A formual for finding the gereral term of the sequence i.e.

an = n²/{n+1}.

Since, we have to find the 4th, 5th, 6th, and 7th term of the sequence.

Therefore,

4th term of the sequence is given by

[tex]a_{4}[/tex]  = (4)^2/{4 + 1) = 16/5

5th term of the sequence is given by

[tex]a_{5}[/tex]  = (5)^2/{5 + 1}  = 25/6

6th term of the sequence is given by

[tex]a_{6}[/tex]  = 6^2/{6 + 1} = 36/7

7th term of the sequence is given by

[tex]a_{7}[/tex] = 7^2/{7 + 1} = 49/8

Hence, the 4th, 5th, 6th,and 7th terms of the sequence an = n²/{n+1} are 16/5, 25/6, 36/7, and 49/8 respectively.

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Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.

Given the data in the question;

A bisector divides a line or angle into two equal halves.

Hence

Segment JM = Segment MK

7x + 5 = 8x

Solve for x

8x - 7x = 5

x = 5

Now, numerical value of segment JM will be;

Segment JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40

Segment JK = (7x + 5) + 8x = 7(5) + 5 + 8(5) = 80

Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.

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Answer:

Step-by-step explanation:

-y = -4x +6

y = 4x -6

Any line with a slope of 4 and y-int other than -6 is parallel to y = 4x-6

When written as a radical, the index of a expression x²/³ is 2.

To rewrite the expression x²/³ as a radical expression, we must first understand what such a radical expression is.

A radical expression is a form expression:  ⁿ√x.

As,  ⁿ√x = x¹/ⁿ

Thus the given expression x²/³ can be written in the above form as;

x²/³ = (³√x)²

Now, the obtained result (³√x)² is written in the radical form where (³√x) is a radical.

As, the expression (³√x) is raised to the 2 power, the index of the expression when the expression is written as x²/³ have a radical is 2.

As a result, the index of the expression x²/³ when rewritten as a radical is 2.

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The complete question is-

What is the index when the expression x^2/3

is rewritten as a radical expression?

Answer 825

Step-by-step explanation:

275/2=137.5

137.5x6=825

The portion of wooden strip that is left from the original strip is 1/4

Samantha is using a wooden strip that measures 7/8 yard

Samantha cuts off a piece of the wood that is 3/4 long

The fraction that represents the proportion of the original strip that is left can be calculated as follows

7/8 - 3/4

The LCM of both fractions is 8

7 - 6/8

= 2/8

convert to the lowest term

1/4

Hence the proportion of the original wooden strip that remains is 1/4

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Answer:

470,006,962

hope this helped :)

Answer:

407,006,962

you can check it on the internet ;)

The simplified answer to 5.3. √2 will be 7.495.

It should be noted that we are to find the simplified answer to 5.3. √2 .

This means that we have to multiply them. This will be:

= 5.3 × ✓2

= 5.3 × 1.1414

= 7.495

Note that the options given aren't complete.

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The quadratic equation which has solutions x = 8 and x = -1 is [tex]\bold{x^2-7x-8}[/tex] = 0.

An equation of degree 2 is called a quadratic equation. That is, the highest power of x in the equation will be two. It has at most two solutions.

Given the solutions are x = 8 and x = -1.

If x = a is a solution, then (x-a) is a factor for the equation.

So here, x-8 and x+1 are factors of the required quadratic equation.

Thus, the quadratic equation will be, (x-8)(x+1) = [tex]\bold{x^2-7x-8}[/tex] = 0.

We can check if x = 8 and x = -1 are the solutions. Put x = 8 in [tex]\bold{x^2-7x-8}[/tex]

Then, 8 x 8 - 7 x 8 - 8 = 0 and -1 x -1 - 7 x -1 - 8 = 0.

So [tex]\bold{x^2-7x-8}[/tex] = 0 is the quadratic equation with solutions x = 8 and x = -1.

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There are 190 more birds than expected at the refuge.

The information provided in the question indicates that there are 3 percent more birds than there were previously. The sanctuary houses 175 birds, which may be pictured as follows:

There are 175 birds in all.

According to the inquiry, it is rising by 3%.

Number of birds = (175)(3%) = 5.25 at this point.

As a result, given the data, the anticipated enhanced data is as follows:

Added birds is 175 + 5 + 5 + 5 = 190.

190 more birds are therefore expected in the refuge.

The final computed numbers should be divided by the total value and then multiplied by 100 to obtain the percentage.

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Answer:

[tex]\textsf{1.} \quad 5x+3-\dfrac{3}{x-4}[/tex]

[tex]\textsf{2.} \quad 2x^2-4x+3[/tex]

[tex]\textsf{3.} \quad x^3+3x^2-2x+4+\dfrac{25}{2x-5}[/tex]

Step-by-step explanation:

Long Division Method of dividing polynomials

Divide the first term of the dividend by the first term of the divisor and put that in the answer.

Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.

Repeat until no more division is possible.

Write the solution as the quotient plus the remainder divided by the divisor.

[tex]\large \begin{array}{r}5x+3\phantom{)}\\x-4{\overline{\smash{\big)}\,5x^2-17x-15\phantom{)}}}\\{-~\phantom{(}\underline{(5x^2-20x)\phantom{-b)..}}\\3x-15\phantom{)}\\-~\phantom{()}\underline{(3x-12)\phantom{}}\\-3\phantom{)}\\\end{array}[/tex]

Solution

[tex](5x^2-17x-15) \div (x-4)=\dfrac{5x^2-17x-15}{x-4}=5x+3-\dfrac{3}{x-4}[/tex]

[tex]\large \begin{array}{r}2x^2-4x+3\phantom{)}\\3x-2{\overline{\smash{\big)}\,6x^3-16x^2+17x-6\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-4x^2)\phantom{-bbbbbbbb.)}}\\-12x^2+17x-6\phantom{)}\\-~\phantom{()}\underline{(-12x^2+8x)\phantom{))))).}}\\9x-6\phantom{)}\\-~\phantom{()}\underline{(9x-6)\phantom{}}\\0\phantom{)}\end{array}[/tex]

Solution

[tex](6x^3-16x^2+17x-6) \div (3x-2)=\dfrac{6x^3-16x^2+17x-6}{3x-2}=2x^2-4x+3[/tex]

[tex]\large \begin{array}{r}x^3+3x^2-2x+4\phantom{)}\\2x-5{\overline{\smash{\big)}\,2x^4+x^3-19x^2+18x+5\phantom{)}}}\\{-~\phantom{(}\underline{(2x^4-5x^3)\phantom{-bbbbbbbbbbb.bb.)}}\\6x^3-19x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(6x^3-15x^2)\phantom{))))bbbb..).}}\\-4x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(-4x^2+10x)\phantom{)))..}}\\8x+5\phantom{)}\\-~\phantom{()}\underline{(8x-20)}\\25\phantom{)}\end{array}[/tex]

Solution

[tex]\begin{aligned}(2x^4+x^3-19x^2+18x+5) \div (2x-5) & =\dfrac{2x^4+x^3-19x^2+18x+5}{2x-5}\\ & =x^3+3x^2-2x+4+\dfrac{25}{2x-5}\end{aligned}[/tex]

Answer:

7

Step-by-step explanation:

(2t+3r) divide 4

so if r=2 and t=11 the new equation will be :

(2times11 + 3times 2) divide 4

(22+6) divide 4

= 28 divide 4 = 7

Answer: 37°  53°  90°

Step-by-step explanation:

Given:

ΔABC    m∠C=90°    

Solution:

m∠A+m∠B+m∠C=180°

m∠A+m∠B+90°=180°

m∠A+m∠B+90°-90°=180°-90°

m∠A+m∠B=90°

Let m∠A=x°

Hence,

m∠B=(x+16)°

Thus,

x°+(x+16)°=90°

(2x)°+16°=90°

(2x)°+16°-16°=90°-16°

(2)(x)°=74°

Divide both parts of the equation by 2:

x°=m∠A=37°

m∠B=37°+16°

m∠B=53°

The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.

The formula of the n-th term of a geometric sequence is:

a(n) = a₁ . r^(n-1)

Where:

a₁ is the first term

r  is the ratio = a(n)/a(n-1)

Parameters given in the problem:

a₁ =1024, r=0.5

Plug these parameters into the formula, then we get the explicit formula of the n-th term:

a(n) = 1024 . (0.5)ⁿ⁻¹

The first 5 terms:

a₁ = 1024

a(2) = 1024 . (0.5)²⁻¹

       = 1024 . (0.5)¹ = 512

a(3) = 1024 . (0.5)³⁻¹

       = 1024 . (0.5)² = 256

a(4) = 1024 . (0.5)⁴⁻¹

       = 11024 . (0.5)³ = 128

a(5) = 1024 . (0.5)⁵⁻¹

       = 1024 . (0.5)⁴ = 64

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The sum of the infinite geometric series 6+5+ 25/6 + . .  is S = 36

The given geometric series is:

  1 - 1/2 + 1/4 - . . ..

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 1

a(2) = -1/2

a(3) = 1/4

Hence, the common ratio is

   r = a(2) / a(1) = -1/2

Since 0 < | r | < 1, the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 1 and r = -1/2 into the formula:

S = 1 / (1 - (-1/2))

   = 1 / (3/2)

   = 2/3

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In the given arithmetic series, the first term is a(1) = 3x and the sum of the first 15 terms is S(15) = 45x - 210y

The given series is:

    3x + (3 x-2 y) + (3x-4y) + ......

Notice that this is an arithmetic series with:

the first term, a(1) = 3x

the second term, a(2) = 3x - 2y

the 3rd term, a(3) = 3x - 4y

Hence, the common difference is:

     d = (3x - 2y) - 3x = -2y

Recall that the nth term of an arithmetic series is given by:

a(n) = a(1) + (n -1) . d

Substitute n = 15, a(1) = 3x, and d = -2y:

a(15) = 3x + (15 - 1) . (-2y)

a(15) = 3x - 28y

The sum of the first n terms in an arithmetic series is given by:

S(n) = n/2 [a(1) + a(n)]

Substitute n = 15

S(15) = 15/2 [a(1) + a(15)]

S(15) = 15/2 . (3x + 3x - 28y)

S(15) = 15 . (3x - 14y) = 45x - 210y

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The possible value of angle ∠K, to the nearest degree is 31 degrees

The given parameters are

Triangle = ΔKLM,

Length k = 56 inches,

Length m = 51 inches

Angle ∠M =28

To calculate the possible value of angle K, we make use of the following sine rule

k/sin(K) = m/sin(M)

Substitute the known values in the above equation

So, we have

56/sin(K) = 51/sin(28)

Cross multiply in the above equation

So, we have

51 x sin(K) = 56 x sin(28)

Evaluate the product in the above equation

So, we have

51 x sin(K) = 26.29

Divide both sides of the above equation by 51

So, we have

sin(K) = 0.52

Take the arc sin of both sides

So, we have

K = 31

Hence, the possible value of angle ∠K, to the nearest degree is 31 degrees

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Answer:24939.5 i think

Step-by-step explanation:

The value of h based on the information illustrated is 24 1/2.

It should be noted that the fraction given is illustrated as:

3/4h - 12 = 8 5/8

Add 12 to both sides

3/4h - 12 + 12 = 8 5/8 + 12

3/4h = 20 5/8

Multiply both side by 4/3

3/4h × 4/3 = 20 5/8 × 4/3

h = 165/8 × 4/3

h = 27 1/2

Therefore, the value of h is 24 1/2.

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The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.

The given arithmetic series is 6+7.4+8.8+ . . .

The summation notion of given series is ∑6+1.4n , here n starts from 0.

The sum of arithmetic series can be written as,

[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]

n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.

We have, n=11, [tex]a_{1}[/tex] = 6

To calculate sum of arithmetic series, we need to find [tex]a_{11}[/tex] .

[tex]a_{11} = a_{1} + (n-1)d[/tex]

d = 1.4 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get

[tex]a_{11}[/tex] = 6 + (11-1)(1.4)

[tex]a_{11}[/tex] = 6 + 14 = 20

On substituting values in sum of arithmetic series formula, we get

[tex]S_{7}[/tex] = (11(6 + 20))/2 = 143

The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.

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The percent of 16, which is equal to the 80 percent of 42 is 210.

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.

Let x be the percent of 16, which is equal to the 80 percent of 42.

80% of 42 = x % of 16

80/100 [tex]*[/tex] 42 = x/100 [tex]*[/tex] 16

80(42)/100 = 16/100 [tex]*[/tex] x

Multiplying both sides of the equation by 16/100, then we get

80(42)/100 [tex]*[/tex] (16/100) = 16/100 [tex]*[/tex] x [tex]*[/tex] (16/100)

simplifying the above equation, we get

80(42)/100 [tex]*[/tex] (16/100) =  x

80(42)/16 =  x

210 = x

The value of x = 210.

Therefore, the correct answer is option b. 210.

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Answer:

210

Step-by-step explanation:

We can start by finding 80% of 42:

80% of 42 = (80/100) x 42 = 33.6

So, the question now becomes: what percent of 16 is 33.6?

Let's call the unknown percentage "x".

We can set up the following equation:

x/100 x 16 = 33.6

Multiplying both sides by 100/16, we get:

x = (33.6 x 100)/16

x = 210

Answer:2,4,8,16,32,64,128,256,512,1024,2048,4096

Step-by-step explanation:

You just mutiply the number with 2

Answer:

81 feet & 19 feet

Step-by-step explanation:

Based on the definition of supplementary angles:

Algebraic equation: A. x + (1/2x + 3) = 180

The measure of the smaller angle is: 62°

The measure of the larger angle is: 118°.

The sum of the two angles that are supplement of each other is equal to 180 degrees, hence they are called supplementary angles.

One of the angles = x

The second angle = 1/2x + 3

Since they are supplementary angles, we will have the following algebraic equation:

x + (1/2x + 3) = 180

Solve for x

x + 1/2x + 3 = 180

3/2x = 180 - 3

3/2x = 177

2/3(3/2x) = 2/3(177)

x = 118°

The second angle = 180 - 118 = 62°

Therefore, based on the definition of supplementary angles, we have the following:

Algebraic equation: A. x + (1/2x + 3) = 180

The measure of the smaller angle is: 62°

The measure of the larger angle is: 118°.

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The decimal number with repeating digits can be written as:

0.344... = 31/90

Here we have the number:

0.3444....

Where the 4 keeps repeating.

First, we need to multiply this by 10, so we get:

10*0.344... = 3.444...

Now if we subtract the original number we get:

10*0.344... - 0.344... = 3.444... - 0.344...

9*(0.344...) = 3.1

Now, isolating the original number:

0.344... = 3.1/9

Finally, we multiply and divide the fraction by 10 so we get two whole numbers:

0.344... = (10/10)*(3.1/9) = 31/90

0.344... = 31/90

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