y < x² - 2x
find the vertex

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 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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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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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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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 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:

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.

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:

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

Step-by-step explanation:

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

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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Answer: 1/24

Step-by-step explanation:

1/2 * 1/12 = 1/24

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!

the answer would be C ( i am not 100% sure though) c= -36x-9

d);

12(3x) = 36x

-12(-3/4) = 9

∠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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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

Answer:

0.62853934

Step-by-step explanation:

Use a calculator.

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

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:

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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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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Solving for the probability using the z-table, the proportion of iPhone owners who use their iPhone between 4 and 7 hours in a day is 0.787.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value (4 and 7)

μ = mean = 5.4

σ = standard deviation = 1.2

z-score = (4 - 5.4) / 1.2     where x = 4

z-score = -1.4 / 1.2

z-score = -7/6 or -1.1667

z-score = (7 - 5.4) / 1.2     where x = 7

z-score = 1.6 / 1.2

z-score = 4/3 or 1.3333

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = -7/6 or -1.1667     probability = 0.12197

z-score = 4/3 or 1.3333     probability = 0.90853

To determine the proportion of iPhone owners who use their iPhone between 4 and 7 hours in a day is the difference between the probabilities of the two values.

proportion = 0.90853 - 0.12197

proportion = 0.787

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Answer:

Nickels are equal to 5 cent and pennies are equal to 1 so:

5 times 100 = 500

1 times 60 = 60

500 + 60 = 560

560 converted to dollars would be $5.60!

Step-by-step explanation:

Hope it helps! =D

Answer:

Since r and s are parallel lines, angle 1 = angle 2 (corresponding angles)

75 - 2x = 91 - 3x

x = 16

Angle 1 = 75 - 2(16) = 43°

Angle 2 = Angle 1 = 43°

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 }

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

If new mobile device has a value of $256.25 and its value changes by [tex]22\frac{1}{2}[/tex]% each year, then the value of phone after two years is $153.76

The value of new mobile device = $256.25

The percentage of value change =  [tex]22\frac{1}{2}[/tex]%

Convert the mixed fraction to decimal form

[tex]22\frac{1}{2}[/tex]% = 22.5%

After one year mobile value = 256 - (256×22.5/100)

= 256-57.6

= $198.4

After two year the mobile value = 198.4-(198.4×22.5/100)

= 198.4-44.64

= $153.76

Hence, if new mobile device has a value of $256.25 and its value changes by [tex]22\frac{1}{2}[/tex]% each year, then the value of phone after two years is $153.76

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