In the race Math , drivers must complete laps of miles each. Dave drove the first laps at mph and the last laps at mph. What was Dave's average speed for the race, in miles per hour

The value of the variable x equation 0.2x+0.2+0.5x=-0.3x+1.2 is x=1.

Given a linear equation 0.2x+0.2+0.5x=-0.3x+1.2

Equation is a combination between two or more variables which is usually expressed in equal to form. Equation of two variable looks like ax +by=c. It is solved to find the quantity of x.

Given equation is as under:

0.2x+0.2+0.5x=-0.3x+1.2

It is a linear equation and will have only 1 solution. Linear equation is a equation which is having a straight line graph.

Adding the coefficients of variable

0.7x+0.2=-0.3x+1.2

Take -0.3 to other side

0.7x+0.3x=1.2-0.2

Adding the coefficients of variables

x=1

Hence the value of x in the equation 0.2x+0.2+0.5x=-0.3x+1.2 is x=1.

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The recursive function of a ball with a 67% rebound is a(n) = 0.67a(n-1)

The rebound is given as:

r = 67%

Express as decimal

r = 0.67

So, the recursive function is:

a(n) = Previous height * r

This gives

a(n) = a(n-1) * 0.67

Evaluate

a(n) = 0.67a(n-1)

Hence, the recursive function is a(n) = 0.67a(n-1)

Basketball

The initial height is given as:

a(1) = 54

So, we have:

a(2) = 0.67 * 54 = 36.18

a(3) = 0.67 * 36.18 = 24.24

Tennis ball

The initial height is given as:

a(1) = 58

So, we have:

a(2) = 0.67 * 58 = 38.86

a(3) = 0.67 * 38.86 = 26.04

Table-tennis ball

The initial height is given as:

a(1) = 26

So, we have:

a(2) = 0.67 * 26 = 17.42

a(3) = 0.67 * 17.42 = 11.67

Hence, the complete table is:

Bounce               n             Height

First bounce       1               Basketball: 54 inches

                                           Tennis ball: 58 inches

                                           Table tennis ball: 26 inches

Second bounce   2            Basketball: 36.18 inches

                                           Tennis ball: 38.86 inches

                                           Table tennis ball: 17.42 inches

Third bounce       3            Basketball: 24.24 inches

                                           Tennis ball: 26.04 inches

                                           Table tennis ball: 11.67 inches

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Missing part of the question

A ball is dropped such that each successive bounce is 67% of the previous bounce's height.

Answer:

2300

Step-by-step explanation:

53%=1219

100=X

X=[(1219)(100)]/53=2300

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

53% = 1219

100% = 2300

The total number of seats in the theater is 2300

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of seats filled by all the students = 1219

1219 is 53% of the total seats in the theater.

This means,

53% = 1219

Now,

Total number of seats in the theater = 100%

53% = 1219

Multiply 100/53 on both sides.

100/53 x 53% = 100/53 x 1219

100% = 2300

Thus,

The total number of seats in the theater is 2300

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A quadratic equation in the form of ax²+bx+c. The zeroes of the polynomial are -2.4 and -7.5.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c. The Root of the quadratic equation are given as,

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The zeroes of the polynomial are:

f(x)=x² + 9.9x + 18

0 = x² + 9.9x + 18

[tex]x= \dfrac{-9.9\pm \sqrt{(9.9)^2-4(1)(18)}}{2(1)}\\\\[/tex]

x = -2.4, -7.5

Hence, the zeroes of the polynomial are -2.4 and -7.5.

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The Linear inequality that is graphed with y > –x – 2 to create the given solution set is; y < x + 1

From the attached graph of inequalities, we see that one of the lines has its' y - intercept as -2 with a slope of -1. Thus, the equation in slope intercept form is; y = -x - 2.

The shaded region will have the inequality; y > -x - 2.

The other line has its' y - intercept as 1 and a slope of 1.

Thus, the equation of line is; y = x + 1.

The shaded part is above the line and as such the inequality region is represented by the inequality y < x + 1.

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Answer:

D

Step-by-step explanation:

Step-by-step explanation:

the y intercept is found by equating X to 0

hence, y = 3

answer is: (0,3)

Hello,

[tex]3(3x + 5y)[/tex]

if x = 1 and y = 5 :

[tex]3(3 \times 1 + 5 \times 5) = 3(3 + 25) = 3 \times 28 = 84[/tex]

⊰__________________________________________________________⊱

Answer:

Step-by-step explanation:

[tex]\large\displaystyle\text{$\begin{gathered} \sf {Substitute \ the \ values-\!\!:} \\ \sf{3(3*1+5*5)} \\ \sf{3(3+25)=3(28)=84} \end{gathered}$}}[/tex]

[tex]\pmb{\tt{done \ !!}}[/tex]

⊱__________________________________________________________⊰

Applying the midsegment theorem, the perimeter of triangle JKL is: D. 19.

The perimeter of triangle JKL = JK + JL + KL

Find the lengths of JK, JL, and KL using the triangle midsegment theorem.

JK = 2(3.5) = 7 units

JL = 2(4) = 8 units

KL = 2(2) = 4 units.

Perimeter of triangle JKL = 7 + 8 + 4

Perimeter of triangle JKL = 19 units.

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Answer:  D. 19

Step-by-step explanation:  Answer is correct on Edge. Trust Me! :)

MO, MN, and ON are the midsegments of △JKL.

Triangle M N O is inside triangle J K L. Points M, N, and O are the midpoints of sides J K, J L, and K L.

Q: What is the perimeter of △JKL?  

A:  D. 19

The recursive formula of the arithmetic sequence 13, 6, -1, -8,... is a(n) = 20 - 7n.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have an arithmetic sequence:

13, 6, -1, -8,...

The first term:

a = 13

The common difference:

d = 6 - 13 = -7

The recursive formula of the arithmetic sequence:

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

a(n) = 13 + (n - 1)(-7)

a(n) = 20 - 7n

Thus, the recursive formula of the arithmetic sequence 13, 6, -1, -8,... is a(n) = 20 - 7n.

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Using it's concept, the mean amount of precipitation (in inches) on March 9 for the areas listed the table was of:

C. 1.56.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

The observations given in the problem are:

0.45, 0.63, 1.34, 3.53, 2.57, 0.84.

Hence the mean is:

M = (0.45 + 0.63 + 1.34 + 3.53 + 2.57 + 0.84)/6 = 1.56.

Which means that option C is correct.

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The vertex form of the Quadratic equation is y =  [tex](x-3)^{2}[/tex] +5. The vertex is (3, 5), which is a maximum point.

A quadratic equation is an algebraic equation with the power of its variable 2.

it can be written in standard form which is called vertex form or in the general form.

Analysis:

y = [tex]x^{2}[/tex] -6x +14

y = [tex]x^{2}[/tex] -6x +9 +5

Simplifying this perfect square expression y = [tex]x^{2}[/tex] -6x +9

y  = [tex]x^{2}[/tex] -3x -3x +9

y = x(x-3) -3(x-3) + 5

y = (x-3)(x-3) +5

y = [tex](x-3)^{2}[/tex] + 5

In conclusion, the Vertex form of the equation is y = [tex](x-3)^{2}[/tex] + 5

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Answer:

K-A would make a circle because it goes across

[tex]\bf{9x > -36 }[/tex]

Divide both sides by 9.

[tex]\bf{\dfrac{9x}{9} > \dfrac{-36}{9} }[/tex]

[tex]\bf{x > -4 \ \ \to \ \ \ Answer}[/tex]

Answer:

{x | x > -4}

Step-by-step explanation:

{a few basic reminders:  > means greater than; < means less than; ≥ means greater than or equal to; ≤ means less than or equal to

for example: 4 < 7

                     4 ≤ 4

                     4 ≥ 3

                     4 > 3}

When we see an inequality, such as 9x > -36, we are trying to figure out what possible numbers x can be to make this statement true.

We can either use logic / words (see below), or in a much more efficient manner, we can solve this algebraically [as though it were an equation]

So, like when working with any other variable, we want to isolate x:
9x > -36

÷9    ÷9

   x > -4  

just in case none of this makes sense (it can be quite confusing at first),

here's how we can think about it logically

we know that whatever multiplies with 9 must be more than -36, and because -4 multiples with 9 to be exactly -36, any number greater than -4 also will be greater than -36

meaning that x must be more than -4, which we express as: x > -4

So, the solution set (solution set means set of possible solutions) is

{x | x > -4}

hope this helps!! have a lovely day :)

Answer:

Simplifying

x2 + 6x + 13 = 20

Reorder the terms:

13 + 6x + x2 = 20

Solving

13 + 6x + x2 = 20

Solving for variable 'x'.

Reorder the terms:

13 + -20 + 6x + x2 = 20 + -20

Combine like terms: 13 + -20 = -7

-7 + 6x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0

-7 + 6x + x2 = 0

Factor a trinomial.

(-7 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying

1 + -1x = 0

Solving

1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -1x = 0 + -1

-1x = 0 + -1

Combine like terms: 0 + -1 = -1

-1x = -1

Divide each side by '-1'.

x = 1

Simplifying

x = 1

Solution

x = {-7, 1}

Step-by-step explanation:

hope this helps if not let me know have a blessed day

The solution to the given inequality will be x ≤ -2 and x > -5

Inequality are expressions not separated by an equal sign

Given the expression below

2≤-4-3x<11

Split

2≤-4-3x and -4-3x<11

Solve both inequalities

-4-3x≥2

-3x ≥ 6

x ≤ -2

Similarly

-4-3x<11

-3x < 15

x > -5

The solution to the given inequality will be x ≤ -2 and x > -5

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Answer:

40

Step-by-step explanation:

Answer:

i 4 boys

ii 3 boys

III 5 boys

Step-by-step explanation:

3y-13>-9

3y-13<-1

3y>4

3y<12

12>3y>4

y=2,3,4

Answer:

[tex]\left[ \dfrac{4}{3},4 \right][/tex]

Step-by-step explanation:

Inequality 1

[tex]3y-13\geq -9[/tex]

Add 13 to both sides:

[tex]\implies 3y-13+13\geq -9+13[/tex]

[tex]\implies 3y\geq 4[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3y}{3}\geq \dfrac{4}{3}[/tex]

[tex]\implies y \geq \dfrac{4}{3}[/tex]

Therefore, y is equal to or bigger than 4/3.

Inequality 2

[tex]3y-13\leq -1[/tex]

Add 13 to both sides:

[tex]\implies 3y-13+13\leq -1+13[/tex]

[tex]\implies 3y\leq 12[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3y}{3}\leq \dfrac{12}{3}[/tex]

[tex]\implies y\leq 4[/tex]

Therefore, y is equal to or smaller than 4.

Therefore, the solution to the inequalities in interval notation is:

[tex]\left[ \dfrac{4}{3},4 \right][/tex]

The number is 5 if two increased by a number is a dozen. In other words, the correct answer is 5 by solving equations.

Step 1: Write the given information as an equation. "Two increased by a number" can be represented as 2 + x, where x is the unknown number.

Step 2: Translate "Two increased by a number is a dozen" into an equation. The word "a dozen" refers to the number 12.

[tex]2 + x = 12.[/tex]

Step 3: Solve the equation for x. To isolate x, subtract 2 from both sides of the equation:

[tex]2 + x - 2 = 12 - 2.[/tex]

This simplifies to x = 10.

Step 4: Verify the solution. Substitute the value of x back into the original equation:

2 + 10 = 12.

This equation is true, so x = 10 is indeed the solution.

Therefore, the number is 10.

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The number line that represents the solution set of the inequality can be seen below.

Here we have the inequality:

15 > n ≥ 3

Then we need to have a open dot at the number 15 on the number line, and then a line that goes to the left until the value 3, where we must have a closed dot (because n = 3 is a solution of the inequality). The number line can be seen below.

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Answer:

17.25

Step-by-step explanation:

The probability that more than 210 people will pass in front of his store is 0.2272.

In the question, we are given that a coffee shop owner wants to examine the number of customers who pass in front of his store in the morning from 7:00 A.M to 7:30 A.M.

We are asked to find the probability that more than 210 people will pass in front of his store if the mean number of customers during this time is 210.

This experiment follows a Poisson Distribution with a mean (λ) = 200, and the random variable X = 210.

To find the probability that more than 210 people will pass in front of his store, we will find P(X > 200).

P(X > 200) = 1 - P(X ≤ 210).

Now, P(X ≤ 210) can be calculated using the function poissoncdf(200,210) on the calculator.

As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).

The value of poissoncdf(200,210) = 0.77271.

Thus, the value of P(X > 210) = 1 - 0.77271 = 0.22729.

Thus, the probability that more than 210 people will pass in front of his store is 0.2272.

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An equation is formed of two equal expressions. The value of the constant of proportionality is 0.41.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given there exists a proportional relationship between the number of juice bottles bought, j, and the total cost in dollars and cents. Therefore,

c ∝ j

c = kj

As the relation is represented by the equation c=0.41j. Therefore, the value of the constant of proportionality is 0.41.

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Answer: B

Step-by-step explanation:

The statement which best describes the similarity of the two triangles is; Choice D; There is not enough information to determine whether the triangles are similar.

The two triangles given in the task content are expected to be assessed to determine if they are similar.

From the concept of congruence in triangles, two triangles are congruent only if all 3 angle measures in one are similar to that in the other, or if the ratio of all corresponding pairs of sides are equal.

Hence, since neither of the conditions is satisfied by the information given, it follows that Choice D is correct.

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By critically observing the two triangles, we can deduce that they: B. might not be congruent.

In Geometry, two triangles are said to be similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

By critically observing the two triangles, we can logically deduce that the three angles of both triangles are congruent in accordance with AAA similarity postulate:

However, AAA isn't a congruence postulate and as such all similar triangles might not be congruent.

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The subtraction property of inequality can be used to proof that x = 7 from  x + 8 = 15

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that x + 8 = 15

Hence:

x + 8 - 8 = 15 - 8 (subtraction property of inequality)

x = 7

The subtraction property of inequality can be used to proof that x = 7 from  x + 8 = 15

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Answer:

Step-by-step explanation:

    Cost =  fixed rate + number of guests* cost per meal.

Let  x be the number of guests.

a)  Pin hall:

       Fixed rate = $ 500

      Cost per meal = $15

      Cost = 500 + 15*x

    [tex]\sf \boxed{\bf C = 500 + 15x}[/tex]

Bloom place:

       Fixed rate = $350

   Cost per meal = $18

         [tex]\sf \boxed{\bf C = 350 +18x}[/tex]

b) Given the charges are same at both halls.

  350 + 18x = 500 + 15x

             18x = 500 + 15x - 350

              18x = 150 + 15x

        18x -15x = 150

                3x  = 150

                  x = 150 ÷ 3

                  x = 50

When the number of guests is 50, the cost is same at both the halls

Hello!

Forming the equations :

y = mx + b

m = rate per hour

b = fixed charge

[tex]\fbox {y = 15x + 500}[/tex]

[tex]\fbox {y = 18x + 350}[/tex]

Solving for number of guests at which cost is the same :

15x + 500 = 18x + 350

3x = 150

x = 25 guests