Julian spent $15.00 to purchase some notebooks that cost $3.50 each and some pens that cost $4.50 each. Assuming he bought at least one notebook, what is the greatest number of pens Julian could have purchased?

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=0.25(x+5)^2\implies y=0.25[x-(\stackrel{h}{-5})]^2+\stackrel{k}{0}~\hfill \stackrel{\textit{vertex}}{(-5,0)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{the y-intercept occurs when x =0}~\hfill }{y=0.25(0+5)^2\implies y=0.25(5)^2}\implies y=6.25~\hfill \stackrel{\textit{y-intercept}}{(0, 6.25)}[/tex]

To identify the vertex and the y-intercept for the function \( y = 0.25(x + 5)^2 \), we will use our knowledge of quadratic functions and their properties.
Vertex:
The given function is in the form of \( y = a(x - h)^2 + k \), where (h, k) is the vertex of the parabola. This form is commonly referred to as the vertex form.
For the given function, \( y = 0.25(x + 5)^2 \), we can see that it is equivalent to \( y = 0.25(x - (-5))^2 + 0 \), indicating that the vertex (h, k) is at (-5, 0). This means the parabola opens upwards (because the coefficient of \( (x + 5)^2 \) is positive) and has its vertex point at x = -5 and y = 0.
Y-intercept:
The y-intercept of a function is found by evaluating the function when x = 0.
So we'll substitute x = 0 into the function to find the y-coordinate of the y-intercept:
\( y = 0.25(0 + 5)^2 \)
Now, we'll calculate the value inside the parentheses:
\( 0 + 5 = 5 \)
Then, we raise it to the power of 2:
\( 5^2 = 25 \)
Finally, we multiply by 0.25:
\( y = 0.25 \times 25 = 6.25 \)
Therefore, the y-intercept where the graph crosses the y-axis is at the point (0, 6.25), where the x-coordinate is 0 and the y-coordinate is the value we just calculated, 6.25.
In summary, the vertex of the function \( y = 0.25(x + 5)^2 \) is (-5, 0), and the y-intercept is at (0, 6.25).

Answer:

36°

Step-by-step explanation:

134° is the exterior angle of the triangle.

By the exterior angle theorm

134° = 98° + y

y = 134° - 98°  = 36°

Final answer:

To find the sum of the first 16 terms of the arithmetic series with a common difference of 6, use the sum formula for an arithmetic series S_n = (n/2) * (2a_1 + (n - 1)*d). By plugging in the values n = 16, a_1 = 1, and d = 6, the sum S_16 is calculated to be 736.

Explanation:

The student has presented an arithmetic series and is asking to find the sum of the first 16 terms (S16). In an arithmetic series, each term increases by a constant difference. The given sequence is 1, 7, 13, 19, and so on, showing a common difference (d) of 6.

Steps to find S16:

Identify the first term (a1) which is 1.

Determine the common difference (d), which is 6 in this case.

Use the formula for the sum of the first n terms of an arithmetic series Sn = (n/2) * (2a1 + (n - 1)*d), where n is the number of terms.

Substitute n = 16, a1 = 1, and d = 6 into the formula and calculate S16.

Now let's calculate S16:

S16 = (16/2) * (2*1 + (16 - 1)*6) = 8 * (2 + 15*6) = 8 * (2 + 90) = 8 * 92 = 736

The sum of the first 16 terms of the given arithmetic series is 736.

Answer:

120

Step-by-step explanation:

A: D: 10 ≤ b ≤ 12

R: 0 ≤ W(b) ≤ 120

B: D: 0 ≤ b ≤ 10

R: 12 ≤ W(b) ≤ 120

C: D: 0 ≤ b ≤ 120

R: 0 ≤ W(b) ≤ 10

D: D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120

W(b) = 12b.

he has enough to build 10 birdhouses, he doesn't have for more than that, he can either build no birdhouses or build 10 birdhouses, since "b" is the independent variable and thus the domain will come from it, what values can "b" safely take?   "b" can be either 0 or more than 0 but nor more than 10, because Owen doesn't have enough for more than that, 0 ≤ b ≤ 10.

let's say owen chooses to build 0 birdhouses, then W(0) = 12(0) => W(0) = 0.

let's say owen chooses to build 10 birdhouses, then W(10) = 12(10) => W(10) = 120.

so the amount of wood needed for those birdhouses, namely the range, can be either 0, if he chooses to build none, or 120 if he chooses to build 10, 0 ≤ W(b) ≤ 120.

Answer:

95.1893

Step-by-step explanation:

The distance between points (16, -43) and (1, 51) is 95.1893

Answer:

It will take 5 years.

Step-by-step explanation:

Let's find how long it will take, but first let's understand the equation.

For simple interest, we use the equation:

T=(1/R)*(((A+B)/B)-1) where,

A= interest amount

B=invested money

R=interest rate (in decimal form)

T=time

Because we want to earn $1800 in interest, then A=1800.

Because we invested $6000, then B=6000.

Because we are investing under an interest rate of 6%, then R=0.06.

'How long will it take' means that T= not given, but its value is in 'years', since an annual rate was given.

Using the equation for simple interest we write:

T=(1/0.06)*(((1800+6000)/6000)-1), the solution is then:

T=5; remember, because is an annual rate, T solution means 5 years.

Answer:

k = 29

Step-by-step explanation:

(5k -3) + (9+k) = 180

5k-3+9+k = 180

6k + 6 = 180

6k = 180 - 6 = 174

k = 29

The value of k is:

                     k = 29

We know that when two angles lie on a straight line then the sum of the two angles is equal to 180 degree.

Here we have two angles on a straight line as:

first angle = (5k-3)°

and second angle= (9+k)°

Hence, we have:

(5k-3)°+(9+k)°=180°

i.e.

5k-3+9+k=180

on combining the like terms on the left hand side of the equation we have:

5k+k+9-3=180

6k+6=180

6k=180-6

6k=174

i.e.

k=174/6

i.e.

k=29

Answer:

Option D is correct.

Step-by-step explanation:

We need to find the quotient of the polynomials:

[tex](12x^3+14x^2 +9)\div(2x+3)\\[/tex]

The division is shown in the figure attached.

The quotient is: 6x^2-2x+3

The remainder is: 0

So, Option D is correct.

Answer:

3/8

Step-by-step explanation:

Slope is the same as rise over run, or y/x. In this case, rise over run is 15 over 40, or 15/40. Simplified, this is 3/8.

For this case we have that by definition, a quadratic expression is of the form:

[tex]ax ^ 2 + bx + c[/tex]

Where "c" represents the constant term.

Then, given the following expression:

[tex]4h ^ 7- \frac {h} {3} + \frac {1} {2}[/tex]

The constant term is given by:

[tex]\frac {1} {2}[/tex]

Answer:

Option D

Answer:

5^-7

Step-by-step explanation:

5^-4 over 5^3   : 5^-4/ 5^3 = 5^-4 × 5^-3 = 5^-7

For this case we must simplify the following expression:

[tex]\frac {\sqrt {10x ^ 3}} {\sqrt {5x}}[/tex]

We combine the expression in a single radical:

[tex]\sqrt {\frac {10x ^ 3} {5x}} =[/tex]

We eliminate common factors of the numerator and denominator:

[tex]\sqrt {\frac {2x ^ 3} {x}} =\\\sqrt {2x ^ 2} =[/tex]

By definition of power properties we have to:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]\sqrt {2x ^ 2} = x \sqrt {2}[/tex]

Answer:

Option A

Answer:

side of the pool = 11 m

Step-by-step explanation:

Square Plot:

side = 35 m

Area = 35 * 35 = 1225 sq.m

Area of  lawn = 1104 sq.m

Swimming pool:

Area of the Swimming pool = 1225 - 1104 = 121 sq.m

 side * side = 121 = 11 * 11

side = √11 * 11

side of the pool = 11 m

In physics, we always measure quantities and compare them with a standard. That standard defines a unit of the quantity. Suppose you want to measure the length of a car, so you use a meter stick, which is the standard for measuring distances. Then, why are units of measure important when solving real-world problems? Well, because when solving problems that involve equations, they need to be dimensionally consistent, but what does it mean? it means that you can't add two terms having different units. For instance, you can't add apples with tables!

Answer:

C.1/16

Step-by-step explanation:

When a coin is tossed 4 times, the number of outcomes are:

2^4 = 16

So,

From the outcomes, only one outcome will be when there will be all heads

So, the probability will be:

One out of the 16 outcomes

Hence, the probability of a coin landing on heads all 4 times is:

C.1/16

Answer:

[tex]\boxed{\text{8.7 gal}}[/tex]

Step-by-step explanation:

The volume V of a prism is the area of the base b times the height h.

V=bh

Step 1. Calculate the volume of the prism.

Data:

b = 100 in²

h = 20 in

Calculation:

V = 100 in² × 20 in =2000 in³

Step 2. Convert cubic inches to gallons

1 gal = 231 in³

[tex]V = \text{2000 in}^{3} \times \dfrac{\text{1 gal}}{\text{231 in}^{3}}} = \textbf{8.7 gal}\\\\\text{The water jug will hold } \boxed{\textbf{8.7 gal}}[/tex]

Answer:

8.7gal

Step-by-step explanation

I uhm need points please

The vertex where the two triangles touch forms a pair of vertical angles, so that the angles on opposites sides of the vertex are congruent. You're shown that two legs of both triangles are congruent. All this tells you that the two triangles are isosceles, and furthermore that they are similar because of the congruence of their "base" angles.

This means

[tex]82^\circ=m\angle 2[/tex]

[tex]\implies82=10x+12[/tex]

[tex]\implies10x=70[/tex]

[tex]\implies\boxed{x=7}[/tex]

Answer: 3x4 - 13x3 + 28x2 - 23x + 10

Step-by-step explanation:

(3x2 - 4x + 5)(x2 - 3x + 2)

(3x4 - 9x3 + 6x2)

+       (-4x3 + 12x2 - 8x)

                    (10x2 - 15x + 10)

3x4 - 13x3 + 28x2 - 23x + 10

Answer: 3x^4 - 13x^3 + 23x^2 -23x + 10

For me at least

Step-by-step explanation: Good luck! :)

the associative property of addition. Try and memorize the different properties. youll need to know them later on. I hope this helped!

Answer:

(13, -8, 5)

Step-by-step explanation:

Given

[tex]u = (5,-2,3)\\and\\v = (1,1,2)[/tex]

We have to find 3u-2v

So,

[tex]3u = 3(5,-2,3)\\3u= (15,-6,9)\\\\And\\\\2v= 2(1,1,2)\\2v= (2,2,4)\\\\3u-2v = (15,-6,9) - (2,2,4)\\= (15-2, -6-2 , 9-4)\\= (13, -8, 5)[/tex]

The ordered triple that represents 3u-2v is:

(13, -8, 5) ..

Answer:

C on edge

Step-by-step explanation:

Did the practice :)

Final answer:

The linear equation is solved by distributing the number outside the parentheses, combining like terms, and then isolating the variable x. The final answer is x = 1/4.

Explanation:

To solve the linear equation 3(−4x + 5) = 12, let's follow the standard steps for solving a linear equation.

Distribute the 3 to both terms inside the parentheses: 3 × (−4x) + 3 × 5 = 12, which simplifies to −12x + 15 = 12.

Subtract 15 from both sides of the equation to get the x term by itself: −12x + 15 − 15 = 12 − 15, which simplifies to −12x = −3.

Finally, divide both sides of the equation by −12 to solve for x: −12x / −12 = −3 / −12, which simplifies to x = 1/4.

By following these steps, we've found that the value that satisfies the equation is x = 1/4.

Final answer:

To solve the equation 3(−4x + 5) = 12, distribute the 3, subtract 15 from both sides, and then divide by −12, yielding the solution x = 1/4 or 0.25.

Explanation:

To solve the linear equation 3(−4x + 5) = 12, we'll start by expanding the equation and then isolating x.

Therefore, the solution to the equation 3(−4x + 5) = 12 is x = 0.25.

Answer:

amount of miles traveled

Step-by-step explanation:

The dependent variables depends on another variable.

What that variable depends on is called the independent variable.

So the cost of the cab fare depends on the mile traveled variable.

The amount of miles traveled is the independent variable because the cost of the cab fare depends on it.

Answer:

The independent variable is the initial fee of $4

Step-by-step explanation:

Initial fee of $4

Additional fare of $0.25 per mile

Check the picture below.

recall that OM is an angle bisector, so those two "green" angles are equal, the same goes for ON which is also an angle bisector, those two "red" angles are also equal.

Answer:

hello

Step-by-step explanation:

i'm just making this answer so the other guy who obviously worked VERY hard on his answer can get a brainliest. :) don't mind me

Answer:

13 and 14

Step-by-step explanation:

13+ (2*13) +6= 45 which is less than 50

14+ (2*14) +6= 48 which is also less than 50.

When you do the same with 15,16, and 17 the answers all come out to be  51, 54, and 57 which are all greater than 50

Answer:

13 and 14

Step-by-step explanation:

Given : [tex]x + 2x + 6 < 50[/tex]

To Find : From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are .

Solution:

Inequality :  [tex]x + 2x + 6 < 50[/tex]

Substitute x =  13

[tex]13 + 2(13) + 6 < 50[/tex]

[tex]45 < 50[/tex]

Substitute x = 14

[tex]14 + 2(14) + 6 < 50[/tex]

[tex]48 < 50[/tex]

Substitute x = 15

[tex]15 + 2(15) + 6 < 50[/tex]

[tex]51 > 50[/tex]

Substitute x = 16

[tex]16+ 2(16) + 6 < 50[/tex]

[tex]54 > 50[/tex]

Substitute x = 17

[tex]17+ 2(17) + 6 < 50[/tex]

[tex]57 > 50[/tex]

So,  the values of x for which the inequality holds true are 13 and 14.

The answer is:

The option that represents the matrix is the option D:

[tex]3x+6y-z=8\\-2x+3y=4\\4x+5y+4z=-2[/tex]

From the statement we know that the matrix is formed with the information obtained from a system of equations:

Being the values of the first column the values of the variable "x"

Being the values of the second column the values of the variable "y"

Being the values of the third column the values of the variable "z"

Being the values of the fourth column the values of the constant numbers (after the equality)

Knowing that, we are looking for a system equation that contains the following equations:

First equation:

[tex]3x+6y-z=8[/tex]

Second equation:

[tex]-2x+3y=4[/tex]

Third equation:

[tex]4x+5y+4z=-2[/tex]

Hence, we can see that the option that matches with the matrix is the option D.

[tex]3x+6y-z=8\\-2x+3y=4\\4x+5y+4z=-2[/tex]

Have a nice day!

Answer:

(9,7)

Step-by-step explanation:

F(a)=b means the point (a,b) is on the graph of F

The point that is on the graph of the function f, given f(9)=7, is (9, 7). This results because 9 is the input (x-coordinate) and 7 is the output (y-coordinate) of the function.

In mathematics, particularly in graphing functions, each point on the graph of a function f is represented by an ordered pair: the input (x-coordinate) and the output (y-coordinate). When you are given that f(9)=7, this essentially means that when the input is 9, the output is 7. Therefore, the point that is on the graph of the function f is (9, 7).

https://brainly.com/question/8613034

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Answer:

0.1 or 1/10

Step-by-step explanation:

100% --> 1

9/10 --> 0.9

1 - 0.9 = 0.1

Answer:

The value of b is 28.28

Step-by-step explanation:

We would use Law of sines to find the value of b

The law of sines is:

[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]

We are given

a= 20

A = 30°

B = 45°

b=?

Putting values in the formula:

[tex]\frac{20}{sin(30)}=\frac{b}{sin(45)}\\\frac{20}{0.5}=\frac{b}{0.707}\\b = \frac{20}{0.5} * 0.707\\b = 40 * 0.707\\b= 28.28\\[/tex]

The value of b is 28.28