what is the unit rate for meters per second if a car travels 424 meters in 8 seconds

Answer:

  y < 1/2x +6

Step-by-step explanation:

You want the inequality graphed in the given figure.

The line is dashed, and the shading is below it, so the inequality will have the form ...

  y < ...

This is because the boundary line is not included, and the y-values in the solution are less than those on the boundary line.

The y-intercept is at +6, where the line crosses the y-axis.

The line goes 2 units to the right for each 1 unit up, so its slope is ...

  m = rise/run = 1/2

The slope-intercept equation for the boundary line is ...

  y = mx +b . . . . . . slope m; y-intercept b

  y = 1/2x +6 . . . . . equation of the boundary line in the graph

Putting the boundary line expression into the inequality form gives the inequality that describes the graph:

  y < 1/2x +6

The value of x on the line segment and the triangle is 17.3 units

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

A triangle (see attachment for the triangle)

Also from the question, we understand that:

BD bisects ∠ABC

Using the bisector theorem, we have

x/13 = 20/15

Multiply both sides of the equation by 13

So, we have the following representation

13 * x/13 = 20/15 * 13

Evaluate the products

So, we have the following representation

x = 20/15 * 13

Evaluate the other products

So, we have the following representation

x = 52/3

This gives

x = 17.3

Hence, the length x is 17.3 units

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False, the function f(x)=[tex]-3x^3 + x^2 +2x[/tex] does not rises as x grows very small.

First, we need to know that functions are described as laws, expressions or rules that are used to show the relationship between two variables in an equation.

These variables are known as;

The function f(x) =[tex]-3x^3 + x^2 + 2x[/tex]  does not rise as x grows very small. When x approaches negative infinity, the dominant term is [tex]-3x^3[/tex], which becomes increasingly negative.

Therefore, the function decreases as x grows very small in the negative direction.

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Answer:

Step-by-step explanation:

Given

[tex]x=1-sin(a)\\y=1+cos(a)[/tex]

Solve for [tex]a[/tex] in the second equation.

[tex]y=1+cos(a)[/tex]

[tex]y-1=cos(a)[/tex]

[tex]a=cos^{-1}( y-1)[/tex]

Insert our answer for [tex]a[/tex] into the first equation.

[tex]x=1-sin(a)[/tex]

[tex]x=1-sin(cos^{-1}( y-1))[/tex]

[tex]cos^{-1}=arccos[/tex]

[tex]x=1-sin(arccos( y-1))[/tex]

Lets simplify [tex]1-sin(arccos( y-1))[/tex]

A piece of graph paper would be helpful in my opinion.

Here is how I would go about doing so

Draw a triangle in the plane with vertices [tex](y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)[/tex] and the origin.

[tex]arccos(y-1)[/tex] is is the angle between the positive x-axis and the ray beginning at the origin and passing through [tex](y-1,\sqrt{1^2-(y-1)^2})[/tex]. Therefore [tex]sin(arccos(y-1))[/tex] is [tex]\sqrt{1-(y-1)^2}[/tex]

Now we have

[tex]x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)[/tex]

We can write [tex]1[/tex] as [tex]1^2[/tex]. Since both terms are now perfect squares, we can factor using the difference of squares formula.

[tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=1[/tex] and [tex]b=y-1[/tex]

[tex]x=1-\sqrt{(1+y-1)(1-(y-1))}[/tex]

After simplifying we get

[tex]x=-\sqrt{y(-y+2)}+1[/tex]

[tex]x=-\sqrt{y(-y+2)}+1[/tex]

[tex]a=arccos(y-1)[/tex]

I think this is what your question was. If not let me know.

The roots of the quadratic equation x² - x - 56 = 0 is x = -7 or x = 8

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

x² - x - 56 = 0   be equation (1)

On simplifying the equation , we get

x² - 8x + 7x - 56 = 0

Taking the common terms in the equation , we get

x ( x - 8 ) + 7 ( x - 8 ) = 0

Now , on factorizing the equation , we get

( x + 7 ) ( x - 8 ) = 0

We have two factors which can solve the equation ,

when ( x + 7 ) = 0

Subtracting 7 on both sides of the equation , we get

x = -7

And , when ( x - 8 ) = 0

Adding 8 on both sides of the equation , we get

x = 8

Therefore , the roots of the equation are x = -7 and x = 8

Hence , the quadratic equation is solved

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Answer:

x = 8

x = -7

Step-by-step explanation:

To find the solutions of the quadratic equation x^2 - x - 56 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = -1, and c = -56. Plug these values into the formula and calculate the discriminant (the value inside the square root):

Discriminant (D) = b^2 - 4ac = (-1)^2 - 4(1)(-56) = 1 + 224 = 225

Now, calculate the two possible solutions:

x1 = (-(-1) + √225) / (2(1)) = (1 + 15) / 2 = 16 / 2 = 8

x2 = (-(-1) - √225) / (2(1)) = (1 - 15) / 2 = -14 / 2 = -7

So, the correct solutions to the equation x^2 - x - 56 = 0 are:

x = 8 (x = 0 is not a solution)

x = -7

The three consecutive number are 17 , 18 and 19 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be = x

Let the second number be = ( x + 1 )

Let the third number be = ( x + 2 )

Now ,

A = 4 times the first decreased by the second is 12 more than twice the third

Substituting the values in the equation , we get

4x - ( x + 1 ) = 12 + 2 ( x + 2 )

On simplifying the equation , we get

4x - x - 1 = 12 + 2x + 4

3x - 1 = 16 + 2x

Subtracting 2x on both sides of the equation , we get

x - 1 = 16

Adding 1 on both sides of the equation , we get

x = 17

Therefore , the value of x is 17

Hence , the consecutive numbers are 17 , 18 and 19

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Option -A is correct that is the order of the children by age, from oldest to youngest is Paul, Phillip, Annie, Chris.

Given that,

There are 4 children's. The names of the children's are Philip, Annie, Paul and Chris.

Philip is twice as old as Annie. Paul is 4 years older than Phillip and Chris is 2 years younger than Annie.

We have to find which represents the order of the children by age, from oldest to youngest.

We know that,

Lets us take the ages if the children's as a,b,c,d of Philip, Annie, Paul and Chris.

Philip is twice as old as Annie.

That means a = 2b

Paul is 4 years older than Phillip and

That mean c =4+a

Chris is 2 years younger than Annie.

That means d=b-2

So,

If we take the age of Philips as 20

Then Annie is 10, Paul is 24 and Chris is 8.

Therefore, Option -A is correct that is the order of the children by age, from oldest to youngest is Paul, Phillip, Annie, Chris .

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The total number of units of energy produced in the two days is 71,402.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Monday:

Energy = 37,124

Tuesday:

Energy = 37,124 - 2846 = 34278

The total energy produced.

= 37124 + 34278

= 71402

Thus,

The total number of energy in two days is 71,402.

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Answer:

B. 1/6

D. 3/12

F. 4 3/11

PLEASE MARK BRAINLIEST

The density in terms of  pounds per cubic foot is 101.2 pounds/ft³

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here; 6900 g for every 4.05 quarts thus expressing in terms of pounds per cubic foot we get = 15.22/0.15039

                                                  = 101.2

Hence, The density in terms of  pounds per cubic foot is 101.2 pounds/ft³

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Answer: 48 cm

Step-by-step explanation:

12 + 12 + 12 + 12 = 48

The total surface area of the cube will be 37.5 cm²

Here the edge of the cube is given

Edge = 2.5 cm

We have to find out the total surface area of the cube

Total surface area of cube = 6a², where a is the edge of the cube

                                            = 6 × 2.5 × 2.5

                                            = 37.5 cm²

Hence, the total surface area of the cube will be 37.5 cm²

The complete question is,
Find the surface area of a cube of Edge 2.5 CM​

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The value of c obtained from the linear inequality (3/5)·c + 7 ≤ 2/5 is the option;

c ≤ -11

An inequality is a (non equal) comparison between two expressions that have different values.

The specified inequality can be expressed as follows;

[tex]\dfrac{3}{5} \times c + 7 \leq \dfrac{2}{5}[/tex]

Simplifying the above inequality by subtracting  7 from both sides, we get;

[tex]\dfrac{3}{5} \times c + 7 - 7 \leq \dfrac{2}{5} - 7[/tex]

Evaluating and simplifying the right hand side into a fraction, we get;

[tex]\dfrac{3}{5} \times c + 0 \leq \dfrac{2}{5} - 7 = \dfrac{2 - 35}{5} = \dfrac{-33}{5}[/tex]

[tex]\dfrac{3}{5} \times c \leq \dfrac{-33}{5}[/tex]

Multiplying both sides by 5, we get;

[tex]5\times \dfrac{3}{5} \times c \leq 5 \times \dfrac{-33}{5}[/tex]

[tex]\dfrac{5}{5} = 1[/tex], therefore;

3·c ≤ -33

Dividing both sides of the above inequality by 3, we get;

3·c ÷ 3 ≤ -33 ÷ 3

c ≤ -11

The correct option is; c ≤ -11

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Answer:

-2

Step-by-step explanation:

To find the slope, subtract y1 - y2, then divide by x1-x2

The y numbers in this set is -10 & 8

The x numbers in this set is 9 & 0

-10-8= -18

9-0 = 9

-18/9 = -2

The slope would be -2

The graph of g(x) = 4x, is the translation of f(x) by subtracting 3.5 units, 2 of 3.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled.

As per the given question, the required solution would be as:

g(x) = 4x , is the translation of f(x) by subtracting 3.5 units, 2 of 3.

The graph of g(x) would be identical to the graph of f(x), but shifted 3.5 units downward, 3 of 3.

This is because the flat fee for the rental of bowling shoes is not present in the function g(x), so the y-intercept of the graph would be at (0,-3.5) instead of (0,0) in f(x) function.

The slope and the shape of the function will remain the same.

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Step-by-step explanation:

false.

3a²b≠3ab².

If a is 3 and b is3 it is not equal

Answer:

1

Step-by-step explanation:

1/1260 = 0.00079365079

0.00079365079 * 1260 = 1

Answer:

(8, -2)

Step-by-step explanation:

Given:

[tex]\textsf{If P = (8, 2), Find $\sf R_{x-axis}(P)$}[/tex]

[tex]\sf R_{x-axis}(P)[/tex] means to reflect the given point P in the x-axis.

When a point is reflected in the x-axis, the x-value is unchanged, but the y-value becomes negative:

Therefore:

[tex]\sf R_{x-axis}(P)=(8,-2)[/tex]

The baker can make 13 loafs of bread using 85 cups of flour using 6 1/4 c of flour for each loaf of bread.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A baker has 85 cups (c) of flour to make bread she uses 6 1/4 c of flour for each loaf of bread.

Now, The fraction 6 1/4 can be written as 25/4.

Therefore, The number of bread loaf the baker can make is,

= (85/25/4).

= 85×(4/25).

= (17×4)/5.

= 68/5.

= 65/5 + 3/5.

= 13 + 3/5.

So, he can make 13 bread loafs.

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The missing side length is 5.7.

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7½

7×2+1/2

14+1/2

15/2

12½

12×2+1/2

24+1/2

25/2

The unit rate for 4543.08 km in 52.4 hours is 86.7 km.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

4543.08 km = 52.4 hours

Divide 52.4 into both sides.

86.7 km = 1 hour

Thus,

The unit rate is 86.7 km.

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There are total 12 lines of symmetry may be found in the image.

We have to given that;

A image is shown in figure for find the lines of symmetry .

Since, We know that;

Exactly dividing a form in half, a line of symmetry exists. This indicates that the form would fold perfectly in half if you did so along the line.

Hence, By definition of line of symmetry we get;

There are total 12 lines of symmetry may be found in the image.

Thus, The correct answer is,

⇒ 12 line of symmetry

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Answer:

The tourists will meet at the midpoint of the bridge, which is 2738/2 = 1369 meters from each end.

At their respective walking speeds, it will take the first tourist 1369/0.9 = 1521.67 seconds to reach the midpoint, and it will take the second tourist 1369/1.1 = 1242.73 seconds.

Therefore, it will take them a total of 1521.67 + 1242.73 = 2764.4 seconds to meet.

Since there are 60 seconds in a minute, the time in minutes is 2764.4 / 60 = 46.07 minutes.

Therefore, it will take the tourists 46 minutes and 0.4 seconds to meet.

Uday Tahlan

All of the equations which the number 10³ makes true include the following:

B. 0.305 × __ = 305

C. 0.54 × __ = 540

In this exercise, you are required to determine the equations which the number 10³ makes true. This ultimately implies that, we would substitute the number 10³ into each of the given equations as follows;

6.01 × 10³ = 601

By expanding the exponent, we have the following equation:

6.01 × 1,000 = 601

6010 = 601 (False).

0.305 × 10³ = 305

By expanding the exponent, we have the following equation:

0.305 × 1,000 = 305

305 = 305 (True).

0.54 × 10³ = 540

By expanding the exponent, we have the following equation:

0.54 × 1,000 = 540

540 = 540 (True).

0.097 × 10³ = 970

By expanding the exponent, we have the following equation:

0.097 × 1,000 = 970

97 = 970 (False).

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Hi. This is an informal letter .

The body of letter goes like this

Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .

The body of letter goes like this

Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .

The body of letter goes like this

Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .

The body of letter goes like this

Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacation

The percentage of the total finance charge on the loan that the service charge will be is about 15.65%. Option D is correct.

D. 15.56%

A loan is an item borrowed for a charged amount, such as an amount borrowed to be repaid with a specified interest fee.

The compound interest formula for the semiannual interest rate is presented as follows;

A = P·[1 + R/n]^(n·t)

Where;

P = The initial amount borrowed on loan = $15,360

t  = The interest rate on the loan = 9.58% = 0.0958

n = The number of periods in a year = 2 for semiannual interest rate

t = The duration of the loan = 8 years

The equal semi annual installment (ESI) formula is presented as follows;

[tex]ESI = P\times \dfrac{\dfrac{r}{2} \times\left(1 + \dfrac{r}{2} \right)^n }{\left(1+\dfrac{r}{2} \right)^n-1}[/tex]

Therefore;

ESI = 15360 × ((0.0958/2)×(1 + 0.0958/2)¹⁶)/((1 + 0.0958/2)¹⁶-1) ≈ 1396.16

The total amount Sam pays = 16 × 1396.16 ≈ 22338.6

The finance charge ≈ 22338.6 - 15360 = 6978.6

The percentage of the finance charge represented the service charge is therefore;

(1294.64/(6978.6 + 1294.64))×100 ≈ 15.65%

The percentage of the total finance charge represented by the service charge is therefore about 15.65%

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Answer:

28.012

Step-by-step explanation:

9.4*2.98 = 28.012

The set of rational expressions are closed under subtraction because the subtraction will result to a rational expression

The ratio of two polynomials is a rational expression.

A rational expression can be expressed in the form p/q, where p and q are polynomials,

Closure property of rational expression

According to the closure property, a - b is also a rational number for any pair of two rational numbers, a and b. The outcome is a rational number. Therefore, under subtraction, the rational numbers are closed.

In the polynomial subtraction

= P(x) /q(x) - r(x)/s(x)

= (P(x) * s(x) - r(x) * q(x)) / (q(x) * r(x))) also a rational number

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