Using the formula r=d/t, where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 227.5 miles in 3.5 hours?

A. In the given question, we know that the Club washed cars and vans. They charge $5 for cars and $7 for vans. They earned a total of $243. Also, they washed a total of 45 vehicles. We have to find out the Equations for the Linear system

Let, the Number of Cars = 'c', and the Number of Vans = 'v', then the equation representing the total number of vehicles will be:

=> v + c = 45          => Equation (1)

Now, if the cost of washing 1 car is $5 and the van is $7 then,

Cost of washing 'c' car: 5c

Cost of washing 'v' van: 7v

then the equation representing total Earning will be:

=> 7v + 5c = 243          => Equation (2)

B. Now, we have to calculate the system of Linear equations to find out the number of cars and vans.

by equation (1) we get:

=> v + c = 45

=> v = 45 - c               => Equation (3)

Putting this value in Equation(2) we get:

=> 7(45-c) + 5c = 243

=> 315 - 7c + 5c = 243

=> 2c = 72

=> c = 36

Put this value of c = 36 in Equation (3), and we get:

=> v = 45 - 36

=> v = 9

Hence, the system of equations is v + c = 45, and 7v + 5c = 243 and the number of Cars washed is 36 and vans is 9

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The inequality that is represented by the graph is; y ≤ 1.5x - 3

Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region.

Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

Now, the given line is a dashed line and shaded below the line and as such we will use the inequality symbol ≤ .

The equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the graph, we have that;

c = -3

m = 1.5

Thus, we have the inequality as y ≤ 1.5x - 3

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The value of 9792381 ÷ 13 with the remainder will be 753260 remainder 1.

In contrast to multiplication, division is the process of dividing a given sum into equal pieces.

To solve the division will be illustrated as thus;

The formula to calculate the division of two numbers is: Dividend ÷ Divisor = Quotient + Remainder.

Calculate the division as usual using your calculator. Once you have the result in decimal form, take the entire number out and multiply the decimal value that remains by the original problem's divisor. The outcome is your remainder.

In this case, the value when we divide 9792381 by 13 is 753260 remainder 1.

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The number obtained by multiplying 5 and square root 164 is 64.

The square root operator in mathematics can be defined as a factor of a number that, when multiplied by itself, gives the original number.

The square root operator in mathematics is denoted by the symbol "√".

The problem 5 (square root of 164) is calculated as follows;

5 ( square root of 164) = 5√164

5√164 = 5(12.8) = 5 x 12.8 = 64

Thus, we can conclude that using the mathematics operator  "√", the number obtained from 5 (square root of 164)  will be greater than 5 but less than 164.

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Answer:

0.62853934

Step-by-step explanation:

Use a calculator.

I didn't get very far by hand. I've attached my partial solution.

The answers of the given question are a followed

2. Same side interior angle theorem

3. Same side interior angle theorem

4. Vertical angle theorem

5. Vertical angle theorem

6. Substitution

The Vertical Angle Theorem states that two intersecting lines' opposing angles must be congruent, or of equal value. The angles opposite to each other will always be congruent, or equal in value, regardless of the manner in which or the location at which two straight lines intersect one another:

Two straight lines that cross each other create two linear pairs, according to the Vertical Angle Theorem. As a result, the adjacent angles created by the intersection of two lines are supplementary angles, meaning that their angles sum to 180 degrees:

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Answer:

x = 3

Step-by-step explanation:

6 + 8x

---------  =  5x

   2

6 + 8x

---------  =  5x (2)

   2 (2)

6 + 8x = 10x

   -8x      -8x

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

6 = 2x

÷2  ÷2

-----------

3 = x

I hope this helps!

A. The equation in standard form: x + 0.50y = 150

B. The equation in slope-intercept from: y = -2x + 300.

C. y = 220 sodas

D. x-intercept is (150, 0)

E. y-intercept is (0, 300).

The standard form for an equation is: Ax + By = C, where C is a constant and A and B are integers.

The slope-intercept form is, y = mx + b, here, m = slope or unit rate, and b = y-intercept.

A. x = number of hotdogs

y = number of sodas

Cost of one hotdog = $1.00

Cost of one soda = $0.50

Total cost = $150

To write the equation in standard form, substitute A = 1, B = 0.5, and C = 150 into Ax + By = C:

x + 0.50y = 150

B. Rewrite x + 0.50y = 150 in slope-intercept form:

x + 0.50y - x = -x + 150

0.50y = -x + 150

Divide both sides by 2

y = -2x + 300 [slope-intercept form]

C. Substitute x = 40 into x + 0.50y = 150:

40 + 0.50y = 150

0.5y = 150 - 40

0.5y = 110

y = 220 sodas

D. Substitute y = 0 into x + 0.50y = 150:

x + 0.50(0) = 150

x = 150

The x-intercept is 150, it means when 0 number of soda is sold, 150 hot dogs is sold.

E. Substitute x = 0 into x + 0.50y = 150:

0 + 0.50y = 150

y = 150/0.5

y = 300

The y-intercept is 300, it means when 0 number of hot dog is sold, 150 sodas are sold.

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Answer: -12

Step-by-step explanation:

0.5(x+6) = 1 + 0.25(x-4)

0.5x + 0.5×6 = 1+ 0.25x - 0.25×4

0.5x - 0.25x = 1 - 1 -3

0.25x = -3

x = -12

Answer:

y ≥ 5

Step-by-step explanation:

y ≥ 5

domain

x ≥ -7

Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain: [ − 7 , ∞ ) , { x | x ≥ − 7 }

Range: [ 5 , ∞ ) , { y | y ≥ 5 }

The algebraic expression for the quotient of 1 and the square of a number is written as 1/y²

An algebraic expression can best be defined as an arithmetic or mathematical expression that is known to consist of variables, coefficients, constants, factors as well as terms.

These expressions also said to be made up of numerous mathematical or arithmetic operations, which includes;

From the information given, we have that;

The quotient of 1 and the square of a number

Now, let the number in this case be y

This expression can be represented as;

1/ (y)²

expand the bracket

1/y²

Hence, the expression is 1/y²

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Answer:i don't know if right but 19  

Step-by-step explanation:

Answer: 1/24

Step-by-step explanation:

1/2 * 1/12 = 1/24

The value of b could be 0 so that the equation x + 3 - (1/2)x  = 3/4(bx - 5) has exactly one solution.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The equations are:

x + 3 - (1/2)x  = 3/4(bx - 5)

Let

b = 0

x + 3 - (1/2)x  = 3/4(- 5)

x/2 = -15/4 - 3

x/2 = -27/4

x = -27/2

Thus, the value of b could be 0 so that the equation x + 3 - (1/2)x  = 3/4(bx - 5) has exactly one solution.

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Answer:

The decimal terminates and does not repeat

Step-by-step explanation:

1/8 = .125

The property that could be used to solve the problem when Erica rode her bike for 5 hours last week is B. additive identity property.

From the information, Erica rode her bike for 5 hours last week and this week, she did not ride her bike.

It should be noted that the additive identity property illustrates that when a number is added to zero, the value is the same number.

In this case, the number of hours that she ride her bike in the past two weeks is:

= 5 + 0

= 5

In conclusion, the correct option is B.

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The the coordinates of the other endpoint of a line segment with an endpoint of (-1,8) and a midpoint of (5, 2) is ( 11,-4 ).

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2

Given the data in the question;

Midpoint (5,2)

Endpoint 1 ( -1,8)

Endpoint 2 ( x₂,y₂)

To determine the coordinate of endpoint 2, plug the given points into the midpoint formula above and solve for x₂ and y₂.

First, we get the x-coordinate.

x = (x₁+x₂)/2

5 = ( -1 + x₂ )/2

( -1 + x₂ ) = 5 × 2

( -1 + x₂ ) = 10

x₂ = 10 + 1

x₂ = 11

Next, we get the y-coordinate

2 = ( 8 +y₂ )/2

8 +y₂ = 2 × 2

8 + y₂ = 4

y₂ = 4 - 8

y₂ = -4

Therefore, the coordinates of the other endpoint is ( 11,-4).

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∠1 and ∠4 are vertical interior angle.

∠1 ≅ ∠5 follows Transitive property of congruence

g ║h  by corresponding angle theorem

The diagram is to prove alternate interior angles converse.

Therefore,

∠4 ≅ ∠5 (Alternate interior angles)

By, the vertical interior angle congruence, ∠1 ≅ ∠4

Vertically opposite angles are congruent. Vertically opposite angles share the same vertex.

Then by the Transitive property of congruence, ∠1 ≅ ∠5.

So, by the corresponding angles theorem, g ║h

Corresponding angles are usually congruent.

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Based on angle relationship, the measures for each angle are:

m∠1 = 103°; m∠4 = 103°; m∠7 = 103°; m∠5 = 77°; m∠6 = 77°; m∠3 = 77°; m∠2 = 77°.

The relationship between angles that are formed by two paralleled lines and a transversal can be used to determine the measures of each of the angles.

Using angles relationship, we have:

Angle 1 = 103° [corresponding angles are equal]

Angle 4 = 103° [alternate interior angles are equal]

Angle 7 = 103° [vertical angles are equal]

Angle 5 = 180 - 103 = 77° [supplementary angles]

Angle 6 = angle 5 = 77° [vertical angles are equal]

Angle 3 = angle 5 = 77° [alternate interior angles are equal]

Angle 2 = angle 5 = 77° [corresponding angles are equal]

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When Ian scores 44 out of 60, his score as a 1 decimal point is 0.3.

From the information, Ian scores 44 out of 60. This will be illustrated as:

Ian's score = 44

Total score = 60

The decimal will be illustrated as:

= Ian's score / Total score

= 44 / 60

= 4 / 15

= 0.3

Therefore, the score is 0.3

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1) At x = -2, 0, and 5, the solutions are; f(-2) = -2, f(0) = 1 and f(5) = 8.5

2) At x = -2, 0, and 5, the solutions are; g(-2) = 18, g(0) = 13, g(5) = -2

3) At x = -2, 0, and 5, the solutions are; h(-2) = -3, h(0) = -5 and h(5) = -10

We want to evaluate each of the given functions when  x = -2, 0, and 5.

1) f(x) = 1.5x + 1

At x = -2, we plug in -2 for x in the linear equation to get;

f(-2) = 1.5(-2) + 1

f(-2) = -2

At x = 0, we plug in 0 for x in the linear equation to get;

f(0) = 1.5(0) + 1

f(0) = 1

At x = 5, we plug in 5 for x in the linear equation to get;

f(5) = 1.5(5) + 1

f(5) = 8.5

2) g(x) = 11 - 3x + 2 = 13 - 3x

At x = -2, we plug in -2 for x in the linear equation to get;

g(-2) = 13 - 3(-2)

g(-2) = 18

At x = 0, we plug in 0 for x in the linear equation to get;

g(0) = 13 - 3(0)

g(0) = 13

At x = 5, we plug in 5 for x in the linear equation to get;

g(5) = 13 - 3(5)

g(5) = -2

3) h(x) = -3 - x - 2 = -5 - x

At x = -2, we plug in -2 for x in the linear equation to get;

h(-2) =  -5 - (-2)

h(-2) = -3

At x = 0, we plug in 0 for x in the linear equation to get;

h(0) =  -5 - 0

h(0) = -5

At x = 5, we plug in 5 for x in the linear equation to get;

h(5) =  -5 - 5

h(5) = -10

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We have the expression:

If we apply the logarithm with base 30 to both sides, we obtain:

Answer: an equivalent logarithmic expression is log_30(y) = 1/6

Answer:

p = 0

Steps shown below

Step-by-step explanation:

5p + 7 - 3p = 3(2 - p) + 1

5p + 7 - 3p = 6 - 3p + 1 (Distributive Property of Equality)

2p + 7 = 7 - 3p (Combine Like Terms)

2p + 7 + 3p = 7 - 3p + 3p (Addition Property of Equality)

5p + 7 = 7 (Simplify)

5p + 7 - 7 = 7 - 7 (Subtraction Property of Equality)

5p = 0 (Combine Like Terms)

5p/5 = 0/5 (Division Property of Equality)

p = 0 (Simplify)

P(X < 4) = 0.8059

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

In which

P(X < 4) = 0.8059

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Answer:

y=mx+b so the answer is 28980/420 which equals 69 lol

Step-by-step explanation:

Answer:

a.  See below.

b.  See attachment.

c.  (1, 2)  (2, 0)  (0, 0)  (0, 1)

d.  The maximum value of P is 11.

Step-by-step explanation:

[tex]\textsf{Maximize}: \quad P=-x+6y[/tex]

[tex]\textsf{Subject to}:\begin{cases}\begin{aligned} \quad y &\leq -2x+4\\y&\leq x+1\\x&\geq 0\\y & \geq 0\end{aligned}\end{cases}[/tex]

Graph the lines:

[tex]\textsf{Draw the line } \;\;y=-2x+4 \;\;\textsf{and shade under the line}.[/tex]

[tex]\textsf{Draw the line } \;\;y=x+1 \;\;\textsf{and shade under the line}.[/tex]

[tex]\textsf{Draw the line } \;\;x= 0 \;\;\textsf{and shade above the line}.[/tex]

[tex]\textsf{Draw the line } \;\;y=0\;\;\textsf{and shade above (to the right of) the line}.[/tex]

Therefore, the feasible region is bounded by the vertices:

Determine the value of P at the vertices by substituting the x and y values of the points into the equation for P:

[tex]\textsf{Value of $P$ at $A(1, 2)$}: \quad -(1)+6(2)=11[/tex]

[tex]\textsf{Value of $P$ at $B(2, 0)$}: \quad -(2)+6(0)=-2[/tex]

[tex]\textsf{Value of $P$ at $C(0, 0)$}: \quad -(0)+6(0)=0[/tex]

[tex]\textsf{Value of $P$ at $D(0, 1)$}: \quad -(0)+6(1)=6[/tex]

Hence, the maximum value of P is 11 at vertex (1, 2).

Answer:

There are 240 blue beads and 300 total beads.

Step-by-step explanation:

We know that 60 beads are red, and that represents 1/5 of the total beads. To get the total number, multiply 60 by 5 to get 300. To find the number of blue beads, which we know is 4/5 of the total, we multiply 300 (total) by 4/5 (or .8) and get 240 beads.