when making a long trip, you should stop for a rest: about every four hours or two hundred miles only when you stop for meals and gasoline do not stop until you get to your destination about every two hours or one hundred miles submit answer

If [tex]h(x)=\frac{-5}{6} x+\frac{7}{8}[/tex]  then the value of h(3) = -13/8  , h(4) = -59/24 ,  h(-1/2) = 31/24 .

In the question , the equation is given as

[tex]h(x)=\frac{-5}{6} x+\frac{7}{8}[/tex]      ....(i)

Part(a)

To find the value of h(3)

we substitute the value of x=3 .

On substituting the value of x=3 in equation (i),

we get ,

h(3) = (-5/6)3+7/8

= -15/6+7/8

taking LCM of 6 and 8 as 24, we get

= -60/24 + 21/24

= (-60+21)/24

= -39/24

Writing in the simplest form we get

= -13/8

so, the value of h(3)= -13/8 .

Part(b)

for h(4) ,we substitute the value of x=4 .

On substituting the value of x=4 in equation (i) ,

we get ,

h(4) = (-5/6)4+7/8

= -20/6+7/8

taking LCM of 6 and 8 as 24, we get

= -80/24 + 21/24

= (-80+21)/24

= -59/24

so , the value of h(4)= -59/24 .

Part(c)

for h(-1/2) ,we substitute the value of x as -1/2 .

On substituting the value of x = -1/2 in equation (i) ,

we get ,

[tex]h(\frac{-1}{2} )=\frac{-5}{6} *\frac{-1}{2} +\frac{7}{8}[/tex]

= 5/12 +7/8

taking LCM of 12 and 8 as 24, we get

= 10/24 + 21/24

= (10+21)/24

= 31/24

so , the value of h(-1/2)= 31/24 .

Therefore , if h(x) = (-5/6)x+7/8 the the value of h(3)= -13/8  , h(4)= -59/24 and h(-1/2)= 31/24 .

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Answer:

There are 14 problems worth 5 points and 15 problems worth 2 points.

Step-by-step explanation:

x - the number of 5 points worth problems

y - the number of 2 points worth problems

The test has 29 problems.

x+y=29x+y=29

The test is worth 100 points.

5x+2y=100

The system of equations:

x+y=29

5x+2y=100

The solution:

x+y=29 ∣×(−2)

5x+2y=100

Substract −2x−2y=−58 from 5x+2y=100

−2x−2y=−58

5x+2y=100

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

3x=42

3x/3 = 42/3

x=14

x+y=29

14+y=29

14+y-14 = 29 - 14

y=15

There are 14 problems worth 5 points and 15 problems worth 2 points.

Answer:

x = 3

Step-by-step explanation:

Answer:

204 ÷ 34 = 6

Step-by-step explanation:

204 ÷ 34 = 6

Check:

34

x 6

------

204

hope this helps :)

Answer : 6

Explanation :

34 + 34
68
68 + 34
102
102 + 34
136
136 + 34
170
170 + 34
204

OR just simply use Multiplication
34 x 6

Answer:

15 points

Step-by-step explanation:

It's 60 points over 4 days. We can divide 60 by 4, which is

15

The order of the numbers from least to greatest is:

 85% < Two and one fifth < 3.24 < Nineteen over 4

The given data set of numbers are: nineteen over 4, two and one fifth, 85%, and 3.24

In order to compare these numbers, we will change all of them into float (decimal) format.

nineteen over 4 = 19/4 = 4.75

two and one fifth = 2 [tex]\frac{1}{5}[/tex] = 11/5 = 2.2

85% = 85/100 = 0.85

And 3.24 are the numbers set.

Now the order of numbers from least to greatest is clear.

Since 0.85 < 2.2 < 3.24 < 4.75, we can conclude

   85% < 2 [tex]\frac{1}{5}[/tex] < 3.24 < 19/4

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Marsha pay $30 each month for a car wash membership.

In one month Marsha pay $30

In eight month Marsha pay 8*$30 = $240

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Answer:

A. |-30| - 8 = $22

Step-by-step explanation:

You are told to subtract 30 and 8, and the 30 is represented as |-30| - 8 = $22

(if this is incorrect am sorry ;-;)

Answer:

26 cups

Step-by-step explanation:

1 quart = 4 cups

6 quarts x 4 cups =  24 cups

1/2 a quart = 2 cups

Answer:

12

Step-by-step explanation:

Answer:

A. $7.46

Step-by-step explanation:

184.54 - 5.50 = 179.04

179.04 / 24 = 7.46

The answer WITHOUT SUBTRACTING THE DELIVERY FEE is: $7.69 (B).

If you're supposed to subtract the delivery fee, then the answer is $7.46 (A).

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

Hope this helps!

Have a great day and God bless! :)

According to the given statement;

Billy bought 8 flower pots, which will hold a total of 67 litres of dirt. The flower pot Billy  bought his flower pot is x=5.

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For example, 2x+3=8 is a linear equation having a single variable in it.

According to given value ;

    Let x = number of clay pots. Since Billy bought 8 pots in total , the                    number of ceramic pots Billy bought is 8-x

    67 =(8 litre )*(x clay pots)+(9 litres)*(8-x);

       67=8x+72-9x

       67=(-x)+72

      -x =(-72+67)

      ( -x) = -5

         x =5

Hence 8 litre of dirt clay pots is 5 then 9 litres of ceramic flower pot is is 3.

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Answer:

-1/5

Step-by-step explanation:

Minus a negative is plus.

-3/5 - (-2/5) =

= -3/5 + 2/5

= -1/5

Answer:

Step-by-step explanation:

solve the equation for x if 2 to the power x = 8​

2^x = 8

log(2x)=log(8)

x*log(2)=log(8)

x=((log(8))/((log(2))

x=3

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

check

2^3 = 8

2 * 2 * 2 = 8

8 = 8

the answer is good

A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 is 62.

To find the whole number:

Therefore, a whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 is 62.

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Hence ,  the difference in length between segments AB and AD is 1.17 units .

The diagram of the given question is given below .

Applying sin rule in triangle ABC , we get

sin(x°) = AC/AB

sin(45°) = 4 / AB

1 /√2 =  4 / AB

AB = 4√2

AB ≈ 5.657

Similarly, apply sin rule  in triangle ACD, we get

sin(y°) = AC /CD

sin(63°) = 4 / CD

AD = 4.489

Now distinction in lengths of AB and AD = 5.657 - 4.489

                                                                     = 1.168

                                                                     ≈ 1.17

Therefore, distinction within the lengths of AB and AD are going to be 1.17 units.

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Answer: D = -6

Step-by-step explanation:

[tex]\frac{D-8}{-2} =12[/tex]  

1) Divide both sides by -2

[tex]D - 8=-6[/tex]

2) Add 8 to both sides

[tex]D=-6[/tex]

Greetings from Brasil...

The small green lines on the line segments indicate that TR = RA, as well as the small red lines indicate that MR = RH, then

TR = RA

3X + 5 = X + 17

X = 6

Answer:

188.57 in

Step-by-step explanation:

Circumference = 2πr = 2πd/2 = πd

[tex] = \frac{22}{7} \times 60 \: in[/tex]

= 188.57 in ( approx.)

The statement that is true is completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case. Option A

From the information given, we have that;

The linear equation is ;

-2x + 3 = 6

Let's solve for x

First, collect like terms

-2x = 6 - 3

-2x = 3

Divide both sides by - 2

x = 3/ -2

The linear inequality is;

-2x + 3 < 6

collect like terms

-2x < 6 - 3

Make 'x' the subject by dividing both sides by -2

-2x/ -2 = 3/ -2

x = 3/ -2

We can see that the linear equation and the linear inequality have the same solution and steps.

Thus, the statement that is true is completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case. Option A

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The coordinates of the vertex P is calculated as (0,2√3).

The distances among two points as a characteristic of their coordinates are given by an algebraic expression (like coordinate system).

Now, according to the given question;

The coordinates of the points Q and R  is given as;

Q and R as (-2, 0) and (2, 0).

Now, as the all three points P,Q and R forms the equilateral triangle. Then, the distance of each side or the distance between two consecutive points are equal.

Calculate the distances between the points;

QR = √(2 + 2)² + (0 - 0)²

QR = 4

Let the coordinated of P be (x, y);

Then,

QP = √(x + 2)² + (y + 0)²

QP = QR = 4

4 = √(x + 2)² + (y)²     ........(equation 1)

RP = √(x - 2)² + (y + 0)²

RP = QR = 4

4 = √(x - 2)² + (y)²     ........(equation 2)

Equating equation 1 and 2.

√(x + 2)² + (y)² = √(x - 2)² + (y)²

Squaring both side;

(x + 2)² + (y)² = (x - 2)² + (y)²

x² + 4 - 4x + y² = x² + 4 - 4x + y²

Simplifying the equation;

x = 0.

Put the value of x in equation 1;

4 = √(x + 2)² + (y)²

y = 2√3.

Therefore, the coordinates of the point P are found to be (0, 2√3).

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The values of a=60, b=750, c=3, a+b+c= 813 as determined by Pythagorean Theorem..

What is Pythagorean Theorem?

A geometric theorem states that the square of a right triangle's hypotenuse equals the sum of the squares of its other two sides.

Call the circle's center O, the unicorn's tether point A, and the final spot where the rope reaches tower B. Triangle OAB is a right triangle since BA is a tangent line at point B and OB is a radius. We determine the horizontal component of AB has length [tex]4\sqrt{5}[/tex] using the Pythagorean Theorem.

The cylinder is "unrolled" to become a flat surface. Let C be the rope's bottom tether, D the point below A on the ground, and E the point directly beneath B. Triangles CDA and CEB share characteristics of right triangles. The Pythagorean Theorem states that CD=8cdotsqrt6.

Let x represent the size of CB.[tex]CD=8\cdot\sqrt{6}[/tex]

[tex]\[\frac{CA}{CD}=\frac{CB}{CE}\implies \frac{20}{8\sqrt{6}}=\frac{x}{8\sqrt{6}-4\sqrt{5}}\implies x=\frac{60-\sqrt{750}}{3}\][/tex]

Therefore,

a=60, b=750, c=3,a+b+c= 813 as determined by Pythagorean Theorem.

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Answer: A sequence is a enumerated collection of objects in which repetitions are allowed/order matters while a series is a infinite series. A series is definite if its based on the concept of sequences.

A series could be finite or infinite because its mainly  often represented in compact form which is also known as a  sigma notation(∑)to indicate the summation involved. infinite series is the sum of an infinite sequence.

Step-by-step explanation:

Answer:

y=-1/3x+1

Step-by-step explanation:

Slope-Intercept Form: y=mx+b

m is the slope

b is the y-intercept

In the given statement it tells us the point is (-3,1).

-3 is the x-intercept while 1 is the y-intercept

In the given statement it tells us the slope is -1/3

Plug in the m for -1/3 and the b for 1

y=-1/3x+1

Hope this helps.

The coordinates of the image of the point (- 4, 5) is (- 5, 15).

In this question we find the coordinates of the original point and the translation vector. Please notice that translations are examples of rigid transformations, meaning that Euclidean distance is conserved in the resulting image. A translation can be done by the following formula:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that P(x, y) = (- 4, 5) and T(x, y) = (- 1, 10), then the resulting point is:

P'(x, y) = (- 4, 5) + (- 1, 10)

P'(x, y) = (- 5, 15)

There is a typing mistake in the statement. Correct form is shown below:

(- 4, 5) is translated by the vector (- 1, 10). What coordinate would it be at?

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The major difference between inequality and equality is that equality represents a particular value(s) while inequality represents a range of values that are in a specific direction.

This must be noted when solving questions on equality and inequality.

For example:

x  =  a means that the value of x is a. It represents a particular value which is a

x  <  a represents all the values  that are less than a.

x  ≤ a  represents values from a and below.

x  >  a represents all the values that are greater than a

x ≥ a means that the values of x are greater than or equal to a.

From the examples given above, it is obvious that a change in the direction of the inequality sign changes the values of the data represented by the inequality.

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Answer:

I believe it's B

4x - 5y = 16

Step-by-step explanation:

First you divide the whole term by -1 to get rid of negative in front of equation and then you add the c term (-16) to both sides to get the final answer.

I hope you get this right.

Answer:

Since we need to Round the Nearest Tenths, First we need to find what is the thenths.

So the order of numbers are

Hundreds - Tens - Ones - . - Tenths - hundreths

So tenths is the digit after the decimal Dot

When we convert .964 to the nearest tens

since there is .064, the number will be greater than .964

so the rounded number will be 1.000

we did this with only .964m but when we add 28.964 then the answer will be

28.000 = 1.000 - 29.000

Hope U will be clear

The equation that illustrates the amount to be paid for the number of kilometers will be 7.25 + 7x.

Fixed rate for taxi = 7.25

Additional charges per kilometers = 7

Number of kilometers = x

Therefore, the equation that illustrates the amount to be paid for the number of kilometers will be:

= 7.25 + (7 × x)

= 7.25 + 7x

Therefore, the equation is 7.25 + 7x.

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To solve for x in: [tex]2x + 8 = 3x + 10[/tex]

Collect like terms

[tex]→8 - 10 = 3x - 2x \\ - 2 = x[/tex]

Therefore:

[tex]x = - 2[/tex]