Rachel received a $90 gift card for a coffee store. She used it in buying some coffee that cost $7.74 per pound. After buying the coffee, she had $66.78 left on her card. How many pounds of coffee did she buy?

[tex]

2x^2+5x+8=0 \\

x=\dfrac{-5+\vee-\sqrt{5^2-2\cdot2\cdot8}}{2\cdot2} \\

x=\dfrac{-5+\vee-\sqrt{25-64}}{4} \\

x=\dfrac{-5+\vee-\sqrt{-39}}{4}\Longrightarrow x\notin\mathbb{R} \\

x\notin\mathbb{R}\Longrightarrow x\in\mathbb{C}

[/tex]

So no real solutions for x. But two complex solutions for x.

[tex]

x_1=\boxed{\dfrac{-5-39i}{4}} \\ \\

x_2=\boxed{\dfrac{-5+39i}{4}}

[/tex]

Hope this helps.

r3t40

Answer:

8x^2 +14x +3

Step-by-step explanation:

(2x + 3)* (4x + 1)​

FOIL

first 2x *4x = 8x^2

outer  2x*1 = 2x

inner  3*4x =12x

last = 3*1 =3

Add them together

8x^2 +2x+12x +3 = 8x^2 +14x +3

[tex]\sqrt{36}=6[/tex] and [tex]\sqrt{49}=7[/tex], so it stands to reason that [tex]\sqrt{42}[/tex] lies somewhere between 6 and 7.

Answer: C) 6.0025

Step-by-step explanation:

The equation for the area of a circle requires the radius, you put in the full diameter. Just divide 4.9 by 2, which gives you 2.45. 2.45 squared is equal to 6.0025 and then slap your pi on to the end of it.

Answer:

[tex]6.0025\pi \: {m}^{2} [/tex]

Step-by-step explanation:

The formula for the area of a circle:

[tex]\pi \times {r}^{2} [/tex]

We are given the diameter of the circle, which is two times its radius. To find the radius, we divide the diameter by 2.

4.9 ÷ 2 = 2.45 m^2.

Now we need to square the radius:

[tex] {2.45}^{2} = 6.0025[/tex]

So, the area in terms of pi would be

[tex]\pi \ \times {6.0025}^{2} \: {m}^{2} [/tex]

Or

[tex]6.0025 \times \pi \: {m}^{2} [/tex]

Hope this helps!

Answer:

100

Step-by-step explanation:

10,000 is merely 100 x 100 = 100²

so √10,000 = √100² = 100

255 square centimeters

First, break this into two shapes: a triangle and a rectangle.

The rectangle is 22 cm by 10 cm.  [tex]22 * 10 = 220[/tex] square centimeters

The triangle's base is 10 cm ([tex]22-12=10[/tex]) and its height is 7 cm ([tex]17-10=7[/tex]).  [tex]\frac{1}{2} * 10 * 7 = 5 * 7 = 35[/tex] square centimeters

Add the areas together. [tex]220 + 35 = 255[/tex] square centimeters

Since f(d) and g(d) represent two types of discounts that you will receive off of the price, the composite function is f(g(d)) = 0.8d - 15.

In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.

In this exercise, we would determine the corresponding output values for the composite functions by using the substitution method as follows;

f(g(d)) = 0.8d - 15

In this context, we can reasonably infer and logically deduce that the composite function is f(g(d)) = 0.8d - 15.

Complete Question:

You go to a store to buy sneakers f(d) and g(d) represent two types of discounts that you will receive off of the price of the sneakers that you want.

Find f(g(d))

f(d)=d-15

g(d)=0.8d

Answer:

C. 6 equilateral triangles

6 Equilateral triangles needed to construct the hexagon option (C)  6 Equilateral triangles is correct.

A hexagon is a six-sided polygon with six inner angles totalling 720° and six outside angles totalling 360° in geometry. Regular, irregular, concave, convex, and complicated hexagons are two-dimensional shapes.

We have a given a hexagon in the figure.

As we know hexagon is a polygon made up from six sides also hexagon can be made using six equilateral triangles by joining them.

Thus, 6 Equilateral triangles needed to construct the hexagon option (C)  6 Equilateral triangles is correct.

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Answer:65

Step-by-step explanation:

The triangle is isosceles triangle and the base angles must be the same

The measure of angle z is 65°.

Given that, in ΔXYZ XZ=XY=7 cm.

We need to find the value of ∠Z.

In an isosceles triangle with two equal sides. The angles opposite the equal sides are also equal.

Since XZ=XY=7 cm.

Here, ∠Y=∠Z=65°

Therefore, the measure of angle z is 65°.

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Answer:

yes

Step-by-step explanation:

a

The answer is:

Yes, the given equation is also a function. (it's a quadratic function)

We know a function exists when there is only one value of y (output) for each x (input).

We can easily know if an equation (relation) is also a function using the graphic method:

To know if a relation is a function, we need to graph it a draw a vertical line, if the line cut the graph in only one point, the relation is a function, otherwise, if the vertical line cuts the graph in two or more points, the relation is a not a function. Remember, the condition for a function is that there is only one output for each input.

Note: I have attached a picture for better understanding.

Have a nice day!

Answer:

There is an association because the relative frequencies by column are different.

Step-by-step explanation:

For checking the association of a two-way table we have to calculate the relative frequency of the table. Here we see that there is an association between timing and day pf watching the movie. Also here relative frequencies of both columns are similar.

Answer:

12.625

mean=total sum value /total data set

The mean of given data set is: 12.625.

The correct option is (B)

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Mean = (Sum of all the observations/Total number of observations)

Given data: 5,7,8,10,11,17,19,24.

Mean=

sum of observation/ Total number of observation

=5+7+8+10+11+17+19+24/8

=101/8

=12.625.

Hence, the mean is 12.625.

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Answer:

[tex]\large\boxed{\left(7,\ \dfrac{13}{3}\right)}[/tex]

Step-by-step explanation:

You must use the algebraic method: substitution or elimination.

I will solve a given system of equations the substitution method.

[tex]\left\{\begin{array}{ccc}y=\dfrac{1}{3}x+2&(1)\\\\y=\dfrac{4}{3}x-5&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\\dfrac{4}{3}x-5=\dfrac{1}{3}x+2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}x-(3)(5)=3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x+(3)(2)\\\\4x-15=x+6\qquad\text{add 15 to both sides}\\\\4x=x+21\qquad\text{subtract x from both sides}\\\\3x=21\qquad\text{divide both sides by 3}\\\\x=7\\\\\text{put the value of x to the first equation}\\\\y=\dfrac{1}{3}\cdot7+2\\\\y=\dfrac{7}{3}+\dfrac{6}{3}\\\\y=\dfrac{13}{3}[/tex]

Answer with explanation:

A tangent to a circle is a Line which touches a circle at a single point.

       There can be Infinite number of tangents to a circle which are external only.

In the given figure:

⇒ There are three circles having Centers A, B and C.Circle having Center B lies inside the circle having center C.

⇒The three circles intersect at point T.

⇒The common tangent of these three circles passes through Point T.

⇒Circles having Center B and Center C , have a common external Tangent.

Option A,B and C:

→A and B

→A and C

→B and C

Tangent is the line that intersects the circle at a single point. Thus, Option A, B, and C all apply.

Three different circles are given in the question that is A, B, and C.

We have to determine the pair of circles that have a common external tangent.

Therefore, take circles A and B from the given figure.

Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.

Hence, Option A applies.

Now, take circles A and C from the given figure.

Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.

Hence, Option B applies.

Further, take the circles B and C from the given figure.

Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.

Hence, Option C applies.

Thus, Option A, B, and C all apply.

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Answer:

y=-ax(x-500)^2(x-1000)

Step-by-step explanation:

Answer:

27/4 or 6 3/4

Step-by-step explanation:

 ( 19 x 4 ) - ( 11 x 2 )

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

          2 x 4

         54/8

 54/2

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

  8/2

Answer:

Theoretical  P(3) = 1/6

Experimental P(3) = 67/450

Step-by-step explanation:

A die has 6 possibilities that can come up {1,2,3,4,5,6}  They are all equally likely, so each has a probability of 1/6

a  P(getting a 3) = 1/6

We rolled a 3 67 times out of 450.  This is our experimental probability

b P (getting a 3) = 67/450

This does not simplify

As your math teacher, let's solve this problem together step by step.

a. Theoretical Probability of Rolling a 3:
A standard number cube, often referred to as a die, has six faces numbered 1 through 6. Since all faces are usually designed to be equally probable, the theoretical probability of rolling a three (or any specific number) is the ratio of the number of successful outcomes (rolling a 3) to the total number of possible outcomes (any number from 1 to 6).

So,

Theoretical Probability = Number of successful outcomes / Total number of possible outcomes
                       = 1 / 6

This is already in the simplest form since 1 and 6 have no common divisors other than 1.

b. Experimental Probability of Rolling a 3:
The experimental probability, in contrast to the theoretical probability, is determined based on actual trials or experiments. In this case, the cube was rolled 450 times, and the number 3 appeared 67 times.

So,

Experimental Probability = Number of times a 3 was rolled / Total number of rolls
                        = 67 / 450

Now, to simplify the fraction, you would find the greatest common divisor (GCD) of 67 and 450 and divide both numerator and denominator by that GCD.

Looking at the numbers, they do not immediately suggest a common factor, and since 67 is a prime number, we can reasonably conclude that the fraction is already in its simplest form. Therefore, the experimental probability is:

                        = 67 / 450

So there you have it, answers to both questions in their simplest form:

a. The theoretical probability of rolling a 3 on a number cube is 1/6.
b. The experimental probability of rolling a 3 given the cube is rolled 450 times and 3 comes up 67 times is 67/450.

You must remember that a polynomial is written like so...

ax^2 + bx + c

In this case...

a = 1

b = 10

c = 21

To factor you must find two numbers who both add up to b (10) AND multiply to c (21)

3 + 7 = 10

3 * 7 = 21

so...

(x + 3 )(x + 7)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: 12x + 21  or  C. F(x) = (x - 2)(x + 2)

Step-by-step explanation:

x2 + 10x + 21

2x + 10x + 21  

Rearrange to put the coefficient in front/move it in front of the term.

Ex. (× · 4 ⇒ 4×)

     (×( 7 ) ⇒ 7×)

Identify  and group like terms.

 (2x + 10x) + 21

Group the coefficients together.

 (2+ 10)x + 21

Combine 2 + 10 to get 12.

 12x + 21

= 12x + 21

You're Welcome! :))

Answer:

The correct answer is first option

(2, 3)

Step-by-step explanation:

It is given that,

3y = -x + 11  and

x + 4y = 14

To find the solutions

The given equation can be written as,

x + 3y = 11 --------(1)

x + 4y = 14  -------(2)

Subtract (1)  from (2) we get

y = 3

Substitute vale of y in eq(1)

x + 3*3 = 11

x = 11 - 9 = 2

Therefore x = 2 and y = 3

The correct answer is first option

Answer:

first option

(2, 3)

Step-by-step explanation:

We have the following system of linear equations

[tex]\left \{{{3y=-x+11} \atop {x+4y=14}} \right.[/tex]

This is the same as

[tex]\left \{{{x + 3y=11} \atop {x+4y=14}} \right.[/tex]

To solve the system multiply the first equation by -1 and then add it to the second equation.

[tex]-1*(x+3y)=11*(-1)[/tex]

[tex]-x -3y=-11\\x+4y=14[/tex]

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

[tex]y = 14-11[/tex]

[tex]y = 3[/tex]

substitute [tex]y = 3[/tex] in any of the two equations and then solve for x

[tex]x+4(3)=14\\x+12=14\\x =14-12\\x = 2\\[/tex]

[tex]x =2[/tex]

The answer is the first option

(2, 3)

Answer:

the best package is 15 lessons for $80

Answer:

Which package is the best deal? Option  D

(D) 15 lessons for $80    100% Answer

Step-by-step explanation:

Answer:

p=$300 and q=30 clock radio

Step-by-step explanation:

we have

p ----> is the price

q ----> is the quantity

[tex]p+3q=390[/tex] ----> equation A

[tex]p-7q=90[/tex] ----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The intersection point is (300,30)

see the attached figure  

therefore

The solution is

p=$300

q=30 clock radio

Answer:

x = 9

Step-by-step explanation:

Use the equation of the line, and let y = 0. Then solve for x.

y = 2/3 x - 6

Let y = 0:

0 = 2/3 x - 6

Add 6 to both sides.

6 = 2/3 x

Multiply both sides by 3/2.

3/2 * 6 = x

x = 9

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-2y=-4&(1)\\3x+5y=Q&(2)\end{array}\right\\\\\text{From (2, 3), put x = 2 and y = 3 to (2):}\\\\Q=3(2)+5(3)=6+15=21[/tex]

Answer:

-4,-4,-4,-4,-2,-2,-2,-2,3,3,3,3,3,|5|,|5|,|5|,5,|6||6||-6||-6|

Numbers' absolute values are outputted as non-negative numbers. The arrangement of given numbers from least to greatest is: Option A: -4, -2, 3, |5|, |-6|

Modulus of a real number, also called absolute value, is non-negative result of the input value.

This is defined as:

[tex]|x| = x ; \text{ (x is non-negative)}\\\\|x| = -x ; \text{ (x is negative)}[/tex](so that the outer negative makes the negative number positive).

Example:

[tex]|5| = 5\\|-5| = -(-5) = 5[/tex]

A number has both magnitude(its absolute value) and its sign(positive or negative).

If numbers are negative, the more their magnitude increases, the lesser they become.

If numbers are positive, the more their magnitude increases, the greater they become.

Thus, for -5, the magnitude is 5, and sign is –ve.

Also, positive numbers > 0 > negative numbers.

For given case, we get:

Arranging, we get:

-4 < -2 < 3 < 5 < 6

or

-4 < -2 < 3 < |5| < |-6|

Thus,

The arrangement of given numbers from least to greatest is: Option A: -4, -2, 3, |5|, |-6|

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The slope is given as 1.

The Y-intercept is where the line crosses the Y axis when X is 0. This is also given by the point (0,5/6). X is 0 and Y is 5/6, so the Y-intercept is 5/6.

The equation of a line is given as y = mx +b where m is the slope and b is the y-intercept.

The equation is: y = x +5/6

Answer:

y = x+5/6

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx +b

We are given the slope of 1 and the y intercept of 5/6 (The y intercept is when x=0)

y = 1x+5/6

y = x+5/6

Answer:

A

Step-by-step explanation:

Given

[tex]\sqrt{-108}[/tex] - [tex]\sqrt{-3}[/tex]

= [tex]\sqrt{36(3)(-1)}[/tex] - [tex]\sqrt{3(-1)}[/tex]

= 6[tex]\sqrt{3}[/tex] i - [tex]\sqrt{3}[/tex] i

= 5[tex]\sqrt{3}[/tex] i

Answer:

Step-by-step explanation:

√(-108) - √(-3)

= √(-3*36) - √(-3)

= √[(-3)*36] - √(-3)

= √(-3)*(√36 - 1)

= √[(-1)*(3)]*(6-1)

= i*√(3)*(5)

= 5√3i

Answer:

17 is the missing the number

Step-by-step explanation:

Pattern: +1, +3, +5, +7, etc.

Solving for  b  by simplifying both sides of the equation, then isolating the variable.

b  =  −y  +  6x

----

Choosing three values for  x  and substitute in to find the corresponding  y  values.

(0,−3)  ,  (1,0)  ,  (2,3)

____

I hope this helps, as always. I wish you the best of luck and have a nice day, friend..

Answer:

Step-by-step explanation:

y = 6x -b

and -3x +y =-3

on simplifying equation 2 ,we have y = 3x -3

System of equation has infinite number of solution if one equation can be obtained by multiplying by suitable non zero number

if we multiply equation by 2 we get y =6x -6

Since coefficient of x and y is same therefore comparing the value of x b with constant in another equation which is 6 .

therefore b =6

Answer:

right triangles should have one right angle (90 degrees) and it should liik like an L, and then draw a line connecting the gap (the hypotenuse)

Step-by-step explanation:

Answer:

make a 90 degree angle and connect the two points to finish the shape of the triangle.

Step-by-step explanation:

HINT: the corner of a piece of paper is a 90 degree angle