On a family vacation, Rollin's family drove 480 miles from Cincinnati, Ohio to Charlotte, North Carolina. His dad drove 65% of the way and his mom drove 20% of the distance his dad drove. If his sister drove the remaining miles, about how many miles did his mom, dad, and sister each drive?

We're given:

We can use the distance equation to help us solve this question:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Plug in the given points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d=\sqrt{(8-(-4))^2+(-7-(-2))^2}\\d=\sqrt{(8+4)^2+(-7+2)^2}\\d=\sqrt{(12)^2+(-5)^2}\\d=\sqrt{144+25}\\d=\sqrt{169}\\d=13[/tex]

The length of line segment BC is 13 units.

Using the distance formula, the length of BC is: 13 units.

Given that:

B(8, -7) = (x1, y1)

C(-4,-2) = (x2, y2)

The distance formula that would be used to find BC is, d =[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Thus, applying the distance formula, we have:

BC = √[(−4 − 8)² + (−2 − (−7))²]

BC = √[(−12)² + (5)²]

BC = √(144 + 25)

BC = √169

BC = 13 units

Therefore, using the distance formula, the length of BC is: 13 units.

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Answer:

  23

Step-by-step explanation:

Given line segment DEFG and lengths DF=12, EG=15, EF=4, you want the length DG.

The segment addition theorem tells you the whole is the sum of the parts.

  DF = DE +EF

  12 = DE + 4

  8 = DE . . . . . . subtract 4

And ...

  DG = DE +EG

  DG = 8 +15 = 23

The length DG is 23 units.

Answer:

No solution

Step-by-step explanation:

To isolate the variable, begin by adding 9x to each side

-6 - 9x = -9x - 4

-6 - 9x (+ 9x) = -9x (+ 9x) - 4

-6 ≠ -4

The equation in your answer has no solution. If you are supposed to find the value of x, you might want to double check for typos.

Answer: the 2nd one

Step-by-step explanation: first term (a1) is -1

recursive formula goes like this

is the nth term

is the term before that

we normally have

we see each term is multipying by -3 to get next one

so that would be

where a1=-1

the 3rd option is correct except that it is the explicit formula

so answer is 2nd one.

Answer:

45

Step-by-step explanation:

run plus duck equals to the implement

The percentage of people living on boat in Florida is 15.4%. The equivalent of this percentage to decimal is 0.154 and to fraction is 77/500.

55% live in a house, 25% live in an apartment, 4.6% in condo while the rest live on a boat. If all the percentages are summed up, they must be equal to 100%.

Let a% equals to the percentage of adult living on boat

55+25+4.6+a = 100

84.6 + a = 100

Collect like terms

a = 100 - 84.6

a = 15.4%

Therefore, the percentage of adult living on boat is 15.4%

To convert the percentage to decimal equivalence, one must divide it by 100%

15.4%/100%

= 15.4/100

= 0.154

To convert the percentage to fraction equivalence, one have to divide it by 100%

15.4%/100%

= 15.4/100

One has to make both the numerator and denominator of the fraction whole numbers, to do that one has to shift the decimal place behind the last digit, for a number without decimal point a 0 is added to the back of the number.

= 154/1000

Reducing the fraction to its lowest term, this is done by diving the numerator and denominator by a common factor

= 77/500

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Answer:

h =2

Step-by-step explanation:

10=h ×5

10=h5

DBS by 5

10÷5=h5÷5

h=2

Rewrite the given polynomial in the form ax² + bx + c:

To find the zeros, set the function to zero and solve for x using the quadratic formula.

Quadratic formula:

Therefore,

a = 2√3

b = 5

c = - 4√3

Substituting the values into the quadratic formula:

The sum of the roots of a polynomial is -b/a:

The sum of the found roots is:

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is: c/a

The product of the found roots is:

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.

The is a parallel to b and m is parallel n.

Given that

To find

So, according to the question

We have,

and the value of two angles m∠2 and m∠4.

From diagram we can see a is parallel to b and m is parallel to n.

So, we can say that

   m∠4 = m∠3    { they are vertical congruent angles } and

   m∠3 = m∠2    { they are congruent angles}

∴  m∠4 = m∠2 -------------(1)

Now, putting the values in equation(1)

So, will be get

                m∠4 = m∠2 -------------(1)

              11x+16 = x²+5x

  x²+5x - 11x-16 = 0

         x²- 6x-16 = 0  

    x²-8x+2x-16 = 0  

  x(x-8)+2(x-8) = 0

        (x-8)(x+2) = 0

If               (x+8) = 0

                      x = 8

And if        (x+2) = 0

                      x = -2

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Answer:

I believe it’s 20

Step-by-step explanation:

1st: 2x-2

2nd: 2x

3rd: 2x+2----

sum = 54

6x = 54

x = 9

1st: 2x-2 = 16

2nd: 2x = 18

3rd: 2x+2 = 20

Pull 4 4/5ths apart - now it is 4 and 4/5ths. Divide both by four - 4/4 = 1, 4/5 / 4 = 1/5th

Now add your answers together;

1 1/5

It should be noted that calculating 215 * 107 in scientific notation will be 2.15 × 10⁴

It should be noted that from the information, we want to calculate 215 * 107 in scientific notation.

It should be noted that 215 = 2.15 × 10²

It should be noted that 107 = 1.07 × 10²

Therefore, calculating 215 * 107 in scientific notation will be:

= 215 × 107.

= 2.15 × 10² × 1.07 × 10²

= 2.15 × 10⁴

Therefore it should be noted that calculating 215 * 107 in scientific notation will be 2.15 × 10⁴

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Answer:

She is correct.

In order to turn a fraction into its simplist form, you need to not be able to divide the numerator or the denominator by ANY integer. A prime number is not divisible by anything, so it is its simplist form.

[tex]|7x+35|=7 \\7x_{1} + 35 = 7 \\ 7x_{1} = - 28 \\ x_{1} = - 4[/tex]

[tex]|7x+35|=7 \\7x_{2} + 35 = - 7 \\ 7x_{2} = - 42\\ x_{2} = - 6[/tex]

[tex]distance = | x_{1}-x_{2}| = | - 4-( - 6)| \\ distance = | 2| = 2[/tex]

The midpoint between two points A(0,0) and B(8,4) is (4,2)

The distance between two points A(0,0) and B(8,4) is 4√5

To find the midpoint of two points,

We need to take an average of both the x and y components of both points

Two points A(x ₁,y₁) and B(x₂ ,y₂) are (0,0) and (8,4) respectively

Let M be the mid-point M(x, y),

x = x₁+x₂/2

 = 0+8/2

= 8/2

= 4

Similarly

y = y₁+y₂/2

  = 0+4/2

  = 4/2

  = 2

So, the midpoint of the two points A(0,0) and B(8,4) is (4,2)

To find the distance between two points,

We need to take the square root of the difference square of x and y, which is

d² = Δx² + Δy²

d = √(Δx²+Δy²)

Δx = x₂-x₁

    = 8-0

   = 8

Δy = y₂-y₁

    = 4-0

    = 4

Thus,

d = √(8²+4²)

d = √(64 + 16)  

d = √80

d = 4√5

So the distance between the two points is 4√5

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Answer:

230

The 72nd term in the following arithmetic sequence is 230.

Step-by-step explanation:

Formula: an = a1 +(n−1)d

a1=17

n=72

d=3

a72=17+(72-1)3

Simplify.

a72=17+(71)3

a72=17+213

a72=230

The 72nd term in the following arithmetic sequence is 230.

Hope this helps!

Please mark as brainliest if correct!

Answer:

Step-by-step explanation:

The inequality that is represented by the given graph is; y > 2x + 1

From the given graph, we have the following points coordinates;

(x1, y1) = (2, 5)

(x2, y2) = (6, 13)

The formula to calculate the slope is;

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

Thus;

m = (13 - 5)/(6 - 2)

m = 8/4

m = 2

On the graph, we have the following observations:

The line of the graph is a dashed line (this represents > or <)

The upper part is shaded (this represents >)

Thus, the inequality is; y > 2(x - 2) + 5

y > 2x - 4 + 5

y > 2x + 1

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Answer:7y7=3y-16

Step-by-step explanation:

Solve  for

Subtract  from both sides

Answer: -4

Step-by-step explanation: Tell me if it's correct. :)

A possible real world scenario is that the product of your age and 16 is 8 more than the product of your age and 14

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

16x = 14x + 8

In the above equation, the variable of the equation is x while the number 8 is a constant

A possible real world scenario is that:

The product of your age and 16 is 8 more than the product of your age and 14

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Answer:

12

Step-by-step explanation:

Divide both sides by 6 to isolate x

Answer:12

Step-by-step explanation:

divide 6 from 72

An oceanic -oceanic convergence give rise to volcanic island arcs.

What kind of convergence results in the arcs of volcanic islands?

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In the given particular sum we have to give reason why asolving 4 = 2x uses the division property of equality.

The reason for that why it is using division property of equality we wneed to know what is division property of equality : It states that when both side of the equation is divided by a real number other than 0 then the quotients remain same . It can be written as following : if a,b,c are real numbers where a = b , c ≠ 0 then ac = bc

for example suppose we have two breads of same size . We cut each of them into halfs and give it to  our friends , if we measure the remaining portions we will see that we are left with same portions of bread . Here at initial both the breads were same and we divide it by 2 and find that they are still same.

Solving 4 = 2x using the division property because in order to get the last portion that answer we have divide the both sides by 2 to get x by itself .

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Answer:

You would need to score a 10.

The equation is going to have a total of 5 values where one is unknown. We will call this unknown x and include it as a value in the equation.

Since we are going to have to find an average, we will need a fraction. We also know we will take five total tests. This will equal 12 as this is the desired average.

To start, create the fraction that will add all five values together and divide that by the number of values.

[tex]\displaystyle \frac{12+14+11+13+x}{5}[/tex]

Then, set this equal to 12.

[tex]\displaystyle \frac{12+14+11+13+x}{5}=12[/tex]

To solve, we will first combine all like terms.

[tex]\displaystyle \frac{50+x}{5}=12[/tex]

Then, divide the fraction.

[tex]\displaystyle 10+\frac{x}{5}=12[/tex]

Now, move the constants to the right side of the equation. To do this, subtract 10 from 12.

[tex]\displaystyle \frac{x}{5}=2[/tex]

Finally, multiply both sides of the equation by 5 to get rid of the denominator.

[tex]x=10[/tex]

Therefore, on test 5, you must score a 10 to maintain an average of 12.

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Answer:

Step-by-step explanation:

Answer: f(x) = x

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

The sides of the equation are unbalanced, therefore, the equation has no solution. Here's an example(The problem is not designed to mathematically make sense).

[tex]x + 1 = -y \times z\\(w)x+1-1=-y+(z)x-1\\0 = -b[/tex]

Since the first side which was equal to 0 is unbalanced to the other side, the rule is that [tex]a = \mathrm{false\:if}\:a < 0[/tex], and since this rule applies in such a scenario, the equation ends up having no solutions.

Hope this helps!

A situation in the real world that the equation can simulate. A corporation charges 19.25 per hour, whereas another charges 17.25 per hour plus a one-time fee of 26.77. This is represented by 19.25x =17.25x +26.77. How many hours do they cost the same?

An equation is used to show the relationship between the variables that are illustrated.

In this instance, a situation from the actual world that the equation can simulate.

A corporation charges 19.25 per hour, whereas another charges 17.25 per hour plus a one-time fee of 26.77.

This is represented by 19.25x =17.25x +26.77. How many hours do they cost the same?

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The perimeter of the whole figure includes the sum of the side lengths and the value is -2 - 4m units

The area of a shape is the amount of space on the shape.

For most regular shapes, the area is the product of their width and the length

The area of this rectangle is given as

Area = 3m - 7m - 6

Evaluate the like terms

So, we have

Area = -4m - 6

The common factor of 4 and 6 is 2

So, we have the following equation

Area = 2(-2m - 3)

The area of the rectangle is

Area = Length * Width

So, we have

Length, L = 2

Width, W = -2m - 3

The perimeter of the rectangle is calculated as

P = 2 x (L + W)

So, we have

P = 2 x (2 - 2m - 3)

Evaluate the like terms in the above expression

So, we have

P = 2 x (-1 - 2m)

Open the bracket in the above expression

So, we have

P = -2 - 4m

Hence, the perimeter of the whole figure is -2 - 4m units

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If the 6% sales tax had been computed on the sale price instead of on the regular price, the tax will be $0.04 lower.

It should be noted that from the information, Samwell bought a packet of pens and his receipt is shown above as $2.04.

Assume that sales tax is rounded to the nearest cent, If the 6% sales tax had been computed on the sale price instead of on the regular price, the difference will be:

Sales price = $1.89

Tax = $1.89 × 0.06 = $0.11

Therefore, the difference will be:

= Former tax amount - New tac amount

= $0.15 - 0.11

= $0.04

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