A music company offers lessons. They charge a registration fee $30 and the $40 per lesson. The equation y=40x+30 represents the total cost y of x lessons.

What is the y intercept and what does it represent in the context of the problem?

What is the slope and what does it represent in the context of the problem?

What is the total cost if 6 lessons where taken?

Answer:

First choice, 47/100

Step-by-step explanation:

16 + 9 + 22 + 26 + 15 + 12 = 100

The even numbers are 2, 4, and 6. They rolled two 9 times, four 26 times, and six 12 times. Added together and they're 47, so 47/100

There's no simplification of this fraction as theres no number that can be used to divide both 47 and 100

Answer:

The amount of cookies in the small tray = x = 19 cookies

The amount of cookies in the Large tray = y = 40 cookies

Step-by-step explanation:

Let

The amount of cookies in the small tray = x

The amount of cookies in the Large tray = y

We are told:

A caterer is making cookie trays for upcoming holiday parties.

This morning, she made 4 small trays and 4 large trays, which contain a total of 236 cookies.

This is represented Mathematically as:

4x + 4y = 236..... Equation 1

In the afternoon, she made 4 small trays and 1 large tray, which contain a total of 116 cookies.

This is represented Mathematically as:

4x + y = 116 ........ Equation 2

y = 116 - 4x

We solve the above equations using the substitution method

We substitute 116 - 4x for y in Equation 1

4x + 4y = 236..... Equation 1

4x + 4(116 - 4x) = 236

4x + 464 - 16x = 236

Collect like terms

4x - 16x = 236 - 464

-12x = -228

x = -228/-12

x = 19 cookies

Solving for y

y = 116 - 4x

y = 116 - 4 × 19

y = 116 - 76

x = 40 cookies

The number of cookies the different sized trays contained is given as:

The amount of cookies in the small tray = x = 19 cookies

The amount of cookies in the Large tray = y = 40 cookies

Step-by-step explanation:

Side length of heptagon = 20.3cm / 7 = 2.9cm.

The heptagon is made out of 7 congruent triangles, each with height 3.0cm and base 2.9cm

Hence area of heptagon

= 7 * [(0.5)(3.0cm)(2.9cm)]

= 7 * 4.35cm²

= 30.45cm².

Answer:

18.875 feet left, not sure if you need to round that or not

Answer:

Step-by-step explanation:

Total length of the wall to be painted = 75 1/2 feet

Already painted part = 3/4 of total length

Remaining part to be painted:

Remaining part in feet:

Answer:

Fabian got $7.

Step-by-step explanation:

Isaiah gave $18 to his friends--Ricardo got $4, Jeremiah got $7, and Fabian got the rest. This needs a math equation!

4 + 7 + f = 18

where f is the amount of money Fabian got.

4 + 7 + f = 18

(subtract 4 from both sides)

7 + f = 14

(subtract 7 from both sides)

f = 7

It looks like Fabian got $7! Let's check just to make sure.

4 + 7 + f = 18

4 + 7 + (7) = 18

18 = 18

It checks out!

Answer:

[tex]x^3 + 3x\²y + 3xy^2 + y[/tex] [tex]=283[/tex]

[tex]When\ x = 3\ and\ y = 4[/tex]

Step-by-step explanation:

Given

[tex]x^3 + 3x\²y + 3xy^2 + y[/tex]

Required

Solve when x = 3 and y = 4

To do this, we simply substitute  3 for x and 4 for y in [tex]x^3 + 3x\²y + 3xy^2 + y[/tex]

[tex]3^3 + 3 * 3^2 * 4 + 3 * 3 * 4^2 + 4[/tex]

[tex]27 + 3 * 9 * 4 + 3 * 3 * 16 + 4[/tex]

[tex]27 + 108 + 144+ 4[/tex]

[tex]283[/tex]

Hence:

[tex]x^3 + 3x\²y + 3xy^2 + y[/tex] [tex]=283[/tex]

[tex]When\ x = 3\ and\ y = 4[/tex]

Answer:

he can play 12 games

Step-by-step explanation:

but he is gonna have some tokens left over.

Answer:

Consequently, any trigonometric identity can be written in many ways. To verify the trigonometric identities, we usually start with the more complicated side of the equation and essentially rewrite the expression until it has been transformed into the same expression as the other side of the equation.

Step-by-step explanation:

Answer:

2893.14/321.46=9

Step-by-step explanation:

in 9 months he will run out of money

Answer:

(Choice A) A 16:10

(Choice C) C 48:30

(Choice D) D 32:20

Step-by-step explanation:

Given ratio

8 : 5

Select three ratios that are equivalent to 8:5

Check all options

(Choice A) A 16:10

= 16 / 10

Dividing by 2

= 8 / 5

= 8 : 5

(Choice B) B 50:80

= 50 / 80

Dividing by 10

= 5 / 8

= 5 : 8

(Choice C) C 48:30

= 48 / 30

Dividing by 6

= 8 / 5

= 8 : 5

(Choice D) D 32:20

= 32 / 20

Dividing by 4

= 8 / 5

= 8 : 5

(Choice E) E 64:35

= 64 / 35

The equivalent ratios to 8 : 5 are

(Choice A) A 16:10

(Choice C) C 48:30

(Choice D) D 32:20

Answer:

Yes

Step-by-step explanation:

the equation for Bruce would be 3b+3b-2= numbers of tiles used.

and Felocias equation would be 5b+5= numbers of tiles used

so therefore if there were 7 tiles in each box they both could have used the same number of tiles

Answer:

The value of [tex]4x+12-x^2[/tex] is 16.

Step-by-step explanation:

The given expression is [tex]4x+12-x^2\ at\ x=2[/tex].

Put x = 2 in the above expression as follows :

[tex]4x+12-x^2=4(2)+12-(2)^2\\\\=8+12-4\\\\=16[/tex]

Hence, the final answer is 16.

Answer:

X can be anything above

2

Answer:

right triangle  

tep-by-step explanation:

i just took the test and worked this out

Answer:

The account will take 7 years to reach a value of $4,020

Step-by-step explanation:

Compound Interest

When it occurs interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Ella invested P=$2,700 in an account with an interest rate of r=5.4% (0.054) compounded monthly. Since there are 12 months in a year, n=12.

It will be calculated when will the account have a value of A=$4,020. Substituting all the values in the formula:

[tex]{\displaystyle 4,020=2,700\left(1+{\frac {0.054}{12}}\right)^{12t}}[/tex]

Calculating:

[tex]{\displaystyle 4,020=2,700\left(1.0045)^{12t}}[/tex]

Dividing by 2,700:

[tex]{\displaystyle \frac{4,020}{2,700}=\left(1.0045)^{12t}}[/tex]

To solve this equation for t, we need to apply logarithms:

[tex]{\displaystyle \log\frac{4,020}{2,700}=\log\left(1.0045)^{12t}}[/tex]

Applying the logarithm power rule:

[tex]\displaystyle \log\frac{4,020}{2,700}=12t\log 1.0045[/tex]

Dividing by 12log 1.0045:

[tex]\displaystyle t=\frac{\log\frac{4,020}{2,700}}{12\log 1.0045}[/tex]

Calculating:

t= 7.39 years

Rounding to the nearest year, the account will take 7 years to reach a value of $4,020

Answer:

7  

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

Since the 2 legs are congruent, then

3x + 12 = 33 ( subtract 12 from both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer: 45 degree and continuous

Step-by-step explanation: i used a protractor

disclamer:pls dont sue me i dont think im right

9514 1404 393

Answer:

  EL/EF and OS/OJ

Step-by-step explanation:

In the similar triangles, angle F and angle J have the same measure, so will have the same tangent. The tangent is the ratio of the opposite side to the adjacent one.

In ΔFEL, the desired ratio is ...

  tan(F) = EL/EF . . . . . 2nd choice

In ΔJOS, the equivalent ratio is ...

  tan(J) = tan(F) = OS/OJ . . . . . 7th choice

Answer:

The answer is 3

Step-by-step explanation:

1/4(16 + 4)-2 = 3

Hope this helped ya

Answer:

1/4(16+4)-2

1/4(20)-2

5-2

3

Step-by-step explanation:

Answer:

B = Blue paint = 3.5 gallons

Y= Yellow paint = 24.5 gallons

Step-by-step explanation:

Let B = Blue paint

Y= Yellow paint

Your mixing blue paint and yellow paint to get a total of 28 gallons.

B + Y = 28 gallons

You want to use 7 times yellow paint as blue.

This means, 7B = Y

How many gallons of each should you use ?

Hence,

B + Y = 28

B + 7B = 28

8B = 28

B = 28/8

B = 3.5 gallons

B + Y = 28 gallons

Y + 3.5 gallons = 28 gallons

Y = 28 gallons - 3.5 gallons

Y = 24.5 gallons

B = Blue paint = 3.5 gallons

Y= Yellow paint = 24.5 gallons

Given:

Consider the given function is

[tex]y=|8x-3|-3[/tex]

To find:

The vertex , axis of symmetry, and transformations of the parent function?

Solution:

We have,

[tex]y=|8x-3|-3[/tex]

[tex]y=\left|8\left(x-\dfrac{3}{8}\right)\right|-3[/tex]

[tex]y=8\left|x-\dfrac{3}{8}\right|-3[/tex]      ...(i)

It is an absolute function.

The vertex form of an absolute function is

[tex]y=a|x-h|+k[/tex]       ...(ii)

where, a is a constant, (h,k) is vertex and x=h is axis of symmetry.

From (i) and (ii), we get

[tex]a=8,h=\dfrac{3}{8},k=-3[/tex]

So,

[tex]\text{Vertex}:(h,k)=\left(\dfrac{3}{8},-3\right)[/tex]

[tex]\text{Axis of symmetry}:x=\dfrac{3}{8}[/tex]

Parent function of an absolute function is

[tex]y=|x|[/tex]

Since, a=8 therefore, parent function vertically stretched by factor 8.

[tex]h=\dfrac{3}{8}>0[/tex], so the function shifts [tex]\dfrac{3}{8}[/tex] unit right.

k=-3<0, so the function shifts 3 units down.

Therefore, the vertex is [tex]\left(\dfrac{3}{8},-3\right)[/tex] and Axis of symmetry is [tex]x=\dfrac{3}{8}[/tex]. The parent function vertically stretched by factor 8, shifts [tex]\dfrac{3}{8}[/tex] unit right and  3 units down.

Answer:

Please find attached the required new cereal boxes for the Yum Yum Cereal Company created with Microsoft Visio

Step-by-step explanation:

The required volume of the cereal box = 2,400 cm³

The box is to be drawn and labeled as follows using Microsoft Visio

Box #1 Length = 16 cm, Width = 15 cm, Height = 10 cm

The volume = Length × Width × Height = 16 cm × 15 cm × 10 cm = 2,400 cm³

Box #2 Length = 30 cm, Width = 10 cm, Height = 8 cm

The volume = Length × Width × Height = 30 cm × 10 cm × 8 cm = 2,400 cm³

Answer:

345 in total. If there are already 121 in: 345-121=224 pounds.

Answer:

128%

Step-by-step explanation:

Because -5/4 is a negative, no matter what is in front of the % in the128%, as long as it's a positive, it is bigger than -5/4

Answer:

f(g(5)) = 4

Step-by-step explanation:

It says to find the value of f(g(5)). In this case, we first have to find g(5).

Plug 5 into g(x) = -x+5

g(5) = 0

Now, f(g(5)) is f(0), since g(5) was found out to be 0.

Plug in 0 into 2x² + 7x + 4

2(0)² + 7(0) + 4 = 0 + 0 + 4 = 4

So the answer is 4.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b

where m is the slope and b the y- intercept

Answer:

m is the slope of the line and b is constant / y intercept value which shows that the line is passing through origin

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

Step-by-step explanation:

Answer:

[tex]\frac{492}{65}[/tex]

Step-by-step explanation:

Using the trigonometric identity

sin²A + cos²A = 1 , then

sinA = [tex]\sqrt{1-cos^2A}[/tex] thus

sinA = [tex]\sqrt{1-(5/13)^2}[/tex]

        = [tex]\sqrt{1-\frac{25}{169} }[/tex]

        = [tex]\sqrt{\frac{144}{169} }[/tex] = [tex]\frac{12}{13}[/tex] , then

tanA = [tex]\frac{sinA}{cosA}[/tex] = [tex]\frac{\frac{12}{13} }{\frac{5}{13} }[/tex] = [tex]\frac{12}{5}[/tex]

Thus

2tanA + 3sinA

= 2 × [tex]\frac{12}{5}[/tex] + ( 3 × [tex]\frac{12}{13}[/tex] )

= [tex]\frac{24}{5}[/tex] + [tex]\frac{36}{13}[/tex]

= [tex]\frac{312}{65}[/tex] + [tex]\frac{180}{65}[/tex]

= [tex]\frac{492}{65}[/tex]