Christopher has $780 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $446.45.
He buys 2 bicycle reflectors for $16.82 each and a pair of bike gloves for $24.60.
He plans to spend some or all of the money he has left to buy new biking outfits for $43.70 each.

Write and solve an inequality which can be used to determine oo, the number of outfits Christopher can purchase while staying within his budget.

Answer:its c

Step-by-step explanation:

Answer:

1.  c < -4

2.  -4 < c < 0

3.  c = 0

4.  c > 0

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.8 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}[/tex]

Given quadratic equation:

[tex]-x^2+4x+c=0[/tex]

If the quadratic equation has no real roots, then the discriminant is less than zero:

[tex]\implies b^2-4ac < 0[/tex]

[tex]\implies (4)^2-4(-1)(c) < 0[/tex]

[tex]\implies 16+4c < 0[/tex]

[tex]\implies 4c < -16[/tex]

[tex]\implies c < -4[/tex]

If the quadratic equation has two real roots, then the discriminant is greater than zero:

[tex]\implies b^2-4ac > 0[/tex]

[tex]\implies (4)^2-4(-1)(c) > 0[/tex]

[tex]\implies 16+4c > 0[/tex]

[tex]\implies 4c > -16[/tex]

[tex]\implies c > -4[/tex]

Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.  If c < 0 there would be 2 sign changes and therefore a maximum of 2 negative roots.

Therefore, for the two roots to have the same sign, -4 < c < 0.

If c = 0 then:

[tex]\implies -x^2+4x=0[/tex]

[tex]\implies -x(x+4)=0[/tex]

[tex]\implies x(x+4)=0[/tex]

Therefore, the roots would be 0 and -4 so there would be one negative root and one root equal to zero.

Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.

Therefore, for the equation to have two roots with opposite signs, c > 0.

The daughter's age is 7 years old.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a parent is 20 years older than twice his daughter's age, and he was half of his present age 17 years back.

Let the age of the parent be x,

He/she was half of the age 17 years back, then,

x/2 = x-17

x = 34

Therefore, parent's present age is 34 years.

He is  20 years older than twice his daughter's age,

Let his daughter's age be y,

2y+20 = 34

2y = 14

y = 7

Hence, his daughter's age is 7 years old.

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The function rule for the transformation of the graph f(x) = 2x

reflection over the x - axis (x, y) → (x, -y)

vertical compression of a factor of 1/4

Considering the given function  f(x) = 2x that requires reflection and vertical compression

The transformation rule for reflection over the x - axis

(x, y) → (x, -y)

comparing to the equation y = f(x) = 2x

-y = -2x

hence f(x) = -2x

vertical compression involves multiplying by 1/4

= 1/4 * f(x)

= 1/4 - 2x

= -x/2

Hence g(x) = -x/2

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The linear function that models the problem of movie theater sells popcorn is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = cost of the bucket = $3.50

m = cost of refills = $2.50

y = 2.50x + 3.50

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The linear function that represents the situation is of:

C(y) = 13y + 145.

The intercept is of:

C(0) = 145, meaning that the flat fee to pay the game is of $145.

The slope-intercept representation of a linear function is given by the rule presented as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

Two points of the function, from the table, are given as follows:

(8, 249) and (13,314).

The slope is given by the change in y of the two points divided by the change in x, hence:

m = (314 - 249)/(13 - 8) = 13.

Hence:

C(y) = 13y + b

When y = 8, C(y) = 249, hence the intercept b of the function is obtained as follows:

249 = 13(8) + b

b = 249 - 13 x 8

b = 145.

Meaning that the flat fee to pay the game is of $145.

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Answer:

5.12

Step-by-step explanation:

If u times 1.6 and 3.2 you get 5.12 also i got it correct on my test

Answer: A 50 miles

Step-by-step explanation:

Its A becuase 60%=0.6 and 0.6 times 50 is 30 which means 60 percent of 50 is 30.

Answer: 6u^3

Step-by-step explanation:

You have to add the exponents when you multiply them.

But before that, you can multiply the coefficients of 2 and 3 so you get 6.

Now you have u and u^2 left.

u = u^1

u^2 = u^2

1+2 =3

[tex]i=\sqrt{-1}[/tex]

[tex](9\sqrt{-81})(-10\sqrt{64})[/tex]

⇒ Take out i from the first square root:

[tex]= (9i\sqrt{81})(-10\sqrt{64})[/tex]

⇒ Evaluate the square roots:

[tex]= (9i\times9)(-10\sqrt{64})\\= (9i\times9)(-10\times 8)[/tex]

⇒ Multiply:

[tex]= (81i)(-10\times 8)\\= (81i)(-80)\\= -6480i[/tex]

-6480i

Answer:

-2

Step-by-step explanation:

use the formula

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

Answer:

Step-by-step explanation:

to find x;

-4x - 2 -1 =8

-4x + 3 = 8

+4  + 3 = +4

x + 3 = 12

   -3 + -3

    x  =  10

to find y;

y = x2 - 3

y = (10)2 - 3

y = 20 - 3

y = 17

Answer:

40% off of 75 is 45$

Step-by-step explanation:

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of the given expression is  1479.40

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Sum of [tex]2(\frac{4}{3})^n[/tex] from n = 0 to n = 6.

This can be written as,

= [tex]2(4/3)^0 + 2(4/3)^1 + 2(4/3)^2 + 2(4/3)^3 + 2(4/3)^4 + 2(4/3)^5 + 2(4/3)^6[/tex]

= 2 x 1 + 8/3 + 2 x 16/9 + 2 x 64/27 + 2 x 256/81 + 2 x 1024/243 +

2 x 4096/729  

= 2 + 2.67 + 3.56 + 4.74 + 6.32 + 8.43 + 1458

= 1479.40

Thus,

The value of the given expression is  1479.40

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The value of the logarithm in one logarithm will be [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex].

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

As per the given logarithm,

7[tex]log_{6} z[/tex] + (1/2)[tex]log_{6} x[/tex] + 3[tex]log_{6}y[/tex]

Since,[tex]alog_{b}c = log_{b}c^\frac{1}{a}[/tex]

Thus,

7[tex]log_{6} z[/tex] + (1/2)[tex]log_{6} x[/tex] + 3[tex]log_{6}y[/tex] =d [tex]log_{6}z^7 +log_{6}x^\frac{1}{2}+log_{6}y^3[/tex]dddd

Since,[tex]log_{a}b+log_{a}c=log_{a}bc[/tex]

Therefore,

[tex]log_{6}z^7 +log_{6}x^\frac{1}{2}+log_{6}y^3[/tex]= [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex].

Hence "The value of the given logarithm in one logarithm will be [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex]".

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The time taken by the Reagan to cover the distance of 28 meters will be 7 seconds.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that Reagan is running toward school twice as fast as her brother. If her brother is running at 2 meters per second.

The time taken to cover the distance of 28 meters will be calculated as,

R = 2B

Brother's speed = 2 m / s

Reagan's speed = 2 x 2 = 4 m/s

The time will be,

T = Distance / Speed

T = 28 / 4

T = 7 seconds

Therefore, the time taken by Reagan to cover the distance of 28 meters will be 7 seconds.

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Answer:

n = 44

Step-by-step explanation:

the 'dashes ' through the 2 legs of the triangle indicate they are congruent.

then n = 44 mm

The minutes when Anjam travel from Sheffield at 10.15am and arrived in Watford 3.55pm in minutes is 320 minutes.

It is important to note that the question is simply about the calculation of the time involved. Based on this situation, it should be noted that:

60 minutes = 1 hour.

Given that due to road works and a diversion, Anjam's drive from Sheffield to Watford took a lot longer than planned. He left Sheffield at 10.15am and arrived in Watford 3.55pm in minutes.

The time for the journey will be:

= 3.35pm - 10.15am

= 5.20 hours.

We will change this to minutes:

= (5 × 60) + 20

= 320 minutes

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Answer:

[tex]y=-x-\frac{7}{12}[/tex]

Hope this helps!

BD ≅ CE is proved and is shown below.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are two triangles as shown in the figure.

Triangles ΔMPN and ΔSTU are congruent. We can write -

2x - y = 13

2x - 50 = 24

Now -

2x - 50 = 24

2x = 74

x = 3The measurements of [x] and [y] are 37 and 61 respectively.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is isosceles △ABC with legs AB and AC, BD ⊥DC and CE ⊥ BE.

In △BDC and △CEB, we can write -

∠D = ∠E = 90°

BC = BC {Common}

∠B = ∠C  {Angles opposite to equal sides are equal}

By SAS criteria △BDC ≅ △CEB.

So, we can write -

BD ≅ CE

Therefore, BD ≅ CE is proved and is shown above.

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Answer:

x- intercept = - [tex]\frac{1}{14}[/tex]

Step-by-step explanation:

to find the x- intercept, that is where the line crosses the x- axis, let y = 0 in the equation and solve for x

14x - 11(0) = - 1

14x = - 1 ( divide both sides by 14 )

x = - [tex]\frac{1}{14}[/tex] is the x- intercept

The domain of the function f(t) is best described as 608 ≤ t ≤ 620

From the question, we have the following parameters that can be used in our computation:

Rate = 2.5 kilograms per hour

Mass of the car (including the fuel) = 1550 kg

Mass of the car (not including the fuel) = 1520 kg

Calculate the times using the rate and the masses above

So, we have the following representations

Time 1 = 1550/2.5

Time 1 = 620

Time 2 = 1520/2.5

Time 2 = 608

Express as an interval

608 ≤ t ≤ 620

Hence, the domain is 608 ≤ t ≤ 620

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x/5 - 4 represents 4 less than the quotient of x and 5.

The measurements of [x] and [y] are 37 and 61 respectively.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are two triangles as shown in the figure.

Triangles ΔMPN and ΔSTU are congruent. We can write -

2x - y = 13

2x - 50 = 24

Now -

2x - 50 = 24

2x = 74

x = 37

then -

2 x 37 - y = 13

74 - 13 = y

y = 61

Therefore, the measurements of [x] and [y] are 37 and 61 respectively.

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Answer: -7

Step-by-step explanation:

7 ÷ (-9 - -8)³

(-9 - -8)³ = -1

7 ÷ -1 = -7

Answer:

-7

Step-by-step explanation:

We have to solve this according to the B O D M A S theorem.

That is:

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Also, we know that,

( + ) × ( + )  = ( + )

( - ) × ( - ) = ( + )

( + ) × ( - ) = ( - )

Let us solve it now.

7 ÷ ( - 9 - ( - 8 ) )³

7 ÷ ( - 9 + 8 )³

7 ÷ ( - 1 )³

7 ÷ ( - 1 )

- 7

The lengths of CF, EF and A.F are 6 units, 28 units and 16 units, respectively

From the question, the given parameters to solve the question are represented as

DF = 3

BF = 14

GF = 8

The point F in the triangle is the centroid of the triangle

This means that the point F divides the lines that passes through it in the ratio 1 : 2 or 2 : 1 (as the case may be)

The claim above also  means that

CF = 2 * DF

EF = 2 * BF

A.F = 2 * GF

Substitute the known values in the above equation, so, we have the following representation

CF = 2 * 3 = 6

EF = 2 * 14 = 28

A.F = 2 * 8 = 16

Hence, the lengths are 6 units, 28 units and 16 units

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Answer:

Step-by-step explanation:

there is no  oblique asymptote

Haha ITS MATHXL

Anyways, constant rate of +90 and currently has 1560.

Say y will be the amount of students, and x is how many years later.

y=90x+1560

So for a), the answer is y=90x+1560

For b), plug in 3 for x, since 2017 is 3 years after 2014.

y=90(3)+1560
y=270+1560
y=1830

Amount of students in 2017: 1830

For c), plug in 2010 for y.

2010=90x+1560
Subtract 1560 both sides
450=90x

Divide both sides by 90
x=5

Answers

a) y=90x+1560
b) 1830
c) 5 Years Later, or 2019

Hope this helps!

Answer:

y=6

Step-by-step explanation:

75-3.5y-4y=4y+6

Combine like terms on each side

75-7.5y=4y+6

Add 7.5y to both sides since it is the inverse of subtraction

75-7.5y=4y+6

   +7.5y. +7.5y

75=11.5y+6

Isolate y on one side by subtracting 6 from both sides

75=11.5y+6

-6.          -6

69=11.5y

Divide both sides by 11.5

69=11.5y

/11.5. /11.5

6=y

hopes this helps please mark brainliest

TQ/VQ=TV/VR is true for the given triangle. Option B is correct

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Two pairs of corresponding angles are equal

Three pairs of corresponding sides are proportional

Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

From these we can say that the sides TV is proportional to Rs and TQ is proportional to VQ

Hence, TQ/VQ=TV/VR is true for the given triangle. Option B is correct

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