A cash box of $1 and $5 bills is worth $45. The number of $1 bills is 3 more than the number of $5 bills. How many of each bill does it contain?

Answer:

The area of the circle is:

[tex]3.14\, *\,2^2 \,\,in^2[/tex]

Step-by-step explanation:

If the diameter of the circle is 4 inches, then its radius is half of that (that is 2 inches), and we can use the formula for the area of a circle:

[tex]Area=\pi\,R^2\\Area= \pi\,(2\,\,in)^2\\Area=3.14\,(4)\,in^2[/tex]

The area of the circle is : [tex]3.14\, *\,2^2 \,\,in^2[/tex]

Answer: the real solution: x = - 2

Find the attached file for the remaining solution

Step-by-step explanation:

The equation given is:

x3 - 5x2 + 28 = 0 

Let assume that -2 is one of the root of the equation. Substitute -2 for x

(-2)^3 - 5(-2)^2 + 28

-8 - 20 + 28 = 0

Therefore, -2 is one of the root of the equation since the equation tend to zero.

If x = -2, then x+2 is one of the factors of the equation. Therefore, the real solution is x = -2

Please find the attached file for the remaining solution.

Answer:

Yes, the table represents quadratic function.

[tex]Y = 3X^2+10[/tex]

Step-by-step explanation:

Given that table of values:

[tex]\begin{center}\begin{tabular}{ c c}X & Y \\ 1 & 13 \\ 2 & 22 \\ 3 & 37 \\ 4 & 58 \\ 5 & 85 \\\end{tabular}\end{center}[/tex]

To find:

Whether the given table represents a quadratic?

Solution:

First of all, let us plot the given values on the coordinate xy plane.

Kindly refer to the attached image for the graph of given values.

The graph seems parabolic in nature which is the graph of a quadratic equation.

Now, let us try to find the equation from the given set of values from hit and trial.

Let Quadratic equation be:

[tex]y=ax^{2} +b[/tex]

If the coefficient a = 1

[tex]f(1) = 13 = 1^2+12[/tex]

[tex]f(2) = 22 = 2^2+18[/tex]

[tex]f(3) = 37= 3^2+28[/tex]

[tex]f(4) = 58 = 4^2+42[/tex]

[tex]f(5) = 85 = 5^2+60[/tex]

value of b is not same in each case.

Now, let us try coefficient a = 3

[tex]f(1) = 13 = 3 \times 1^2+10[/tex]

[tex]f(2) = 22 = 3\times 2^2+10[/tex]

[tex]f(3) = 37= 3\times 3^2+10[/tex]

[tex]f(4) = 58 = 3\times 4^2+10[/tex]

[tex]f(5) = 85 =3\times 5^2+10[/tex]

Value of b = 10

So, we can clearly say that the given table represents a quadratic equation.

and the quadratic equation is:

[tex]Y = 3X^2+10[/tex]

Answer:

Once we got

[tex]x=-1[/tex]

[tex]y=3[/tex]

[tex]z=2[/tex]

[tex]\boxed{\text{The sum is 4}}[/tex]

Step-by-step explanation:

Given the linear system:

[tex]\begin{cases} 2x + 3y-z = 5 \\ x- 3y + 2z = -6 \\ 3x + y - 4z = -8 \end{cases}[/tex]

Let's solve it using matrices. I will use Cramer's rule

[tex]M=\left[\begin{array}{ccc}2&3&-1\\1&-3&2\\3&1&-4\end{array}\right][/tex]

Considering determinant as D.

[tex]D=\begin{vmatrix}2&3&-1\\1&-3&2\\3&1&-4\\\end{vmatrix}=40[/tex]

[tex]M_x = \left[\begin{array}{ccc}5&3&-1\\-6&-3&2\\-8&1&-4\end{array}\right] \implies D_x = \begin{vmatrix}5&3&-1\\-6&-3&2\\-8&1&-4\\\end{vmatrix}=-40[/tex]

[tex]M_y = \left[\begin{array}{ccc}2&5&-1\\1&-6&2\\3&-8&-4\end{array}\right] \implies D_y = \begin{vmatrix}2&5&-1\\1&-6&2\\3&-8&-4\\\end{vmatrix}=120[/tex]

[tex]M_z = \left[\begin{array}{ccc}2&3&5\\1&-3&-6\\3&1&-8\end{array}\right] \implies D_z= \begin{vmatrix}2&3&5\\1&-3&-6\\3&1&-8\\\end{vmatrix}=80[/tex]

So, we have

[tex]$x=\frac{D_x}{D} =\frac{-40}{40}=-1 $[/tex]

[tex]$y=\frac{D_y}{D} =\frac{120}{40}=3$[/tex]

[tex]$z=\frac{D_z}{D} =\frac{80}{40}=2 $[/tex]

Answer:

0.412

Step-by-step explanation:

Given the stem plot figure out which ones are below 17g.

So: 7g / 17g = 0.412 which is the proportion

Answer:

  1 : 50,000,000

Step-by-step explanation:

The given scale (with units) is ...

  1 mm : 50 km

If we convert both units to meters, so we can give the scale as a pure number, then we have ...

  10^-3 m : 5×10^4 m = 1 : 5×10^7 = 1 : 50,000,000

Answer: 3

Step-by-step explanation: you add 7+3 which is 10 - 7 =3

Answer:

14 elliptical machines

Step-by-step explanation:

t = # of treadmills

e = # of elliptical machines

t + e = 38

t = e + 10

Substitute:

e + 10 + e = 38

2e = 28

e = 14

Answer:

y = -7x + 2

Step-by-step explanation:

Use the slope-intercept form y = mx + b.

Substitute -7 for m, 0 for x and 2 for y.  Then

2 = (-7)(0) + b, so b must be 2.

The desired equation is y = -7x + 2.

Answer:

11 years old

Step-by-step explanation:

Because the dog is 4 years older, add 7+4

Answer:

0.1875

Step-by-step explanation:

The well formatted expression for the series has been attached to this response.

Each term in the series is govern by the rule, Tₙ

Where

n = term position

Tₙ = [tex]\frac{(-1)^{n+1}n}{2^n}[/tex]

To get the first six terms, we substitute n = 1 through 6 into Tₙ as follows:

When n = 1, we have;

T₁ = [tex]\frac{(-1)^{1+1}(1)}{2^1} = \frac{1}{2}[/tex] = 0.50000

When n = 2, we have;

T₂ = [tex]\frac{(-1)^{2+1}(2)}{2^2} = \frac{-2}{4} = \frac{-1}{2}[/tex] = -0.50000

When n = 3, we have;

T₃ = [tex]\frac{(-1)^{3+1}(3)}{2^3} = \frac{3}{8}[/tex] = 0.37500

When n = 4, we have;

T₄ = [tex]\frac{(-1)^{4+1}(4)}{2^4} = \frac{-1}{4}[/tex] = -0.25000

When n = 5, we have;

T₅ = [tex]\frac{(-1)^{5+1}(5)}{2^5} = \frac{5}{32}[/tex] = 0.15625

When n = 6, we have;

T₆ = [tex]\frac{(-1)^{6+1}(6)}{2^6} = \frac{-6}{64} = \frac{-3}{32}[/tex] = -0.09375

Therefore, the approximate sum of the series using the sum of the first six terms is

=> T₁ + T₂ + T₃ + T₄ + T₅ + T₆

=> 0.50000 + -0.50000 + 0.37500 + -0.25000 + 0.15625 + -0.09375

=> 0.1875

Answer:

found this on the web. hopefully it helps

Answer:

3.2 units

Step-by-step explanation:

Given that:

WY bisects UV at Y.

[tex]UV=x-7[/tex] and

[tex]YV = 3x-29[/tex],

To find: UV = ?

Solution:

First of all, let us draw the diagram of the given dimensions and bisector line WY of UV.

As UV is bisected i.e. divided in two equal parts at Y by the line WY

Therefore, UY = YV

UV = UY+YV

OR

UV = 2 YV

Now, let us put the given values to solve for [tex]x[/tex]:

[tex]x-7=2 \times (3x-29)\\\Rightarrow x-7=2 \times 3x-2 \times 29\\\Rightarrow x-7=6x-58\\\Rightarrow 6x-x=58-7\\\Rightarrow 5x=51\\\Rightarrow \bold{x =10.2 }[/tex]

Now, we are given that:

[tex]UV=x-7[/tex]

Putting value of [tex]x[/tex] as solved in above step to get the value of UV:

[tex]UV=10.2-7\\\Rightarrow \bold{UV=3.2}[/tex]

So, answer is UV = 3.2 units

Answer: True.

Step-by-step explanation:

The one-way analysis of variance usually (abbreviated as one-way ANOVA). is a method that is used to compare the means of two or more samples ( by make use of the F distribution). This method only applies to numerical response data, the "Y", usually one variable, and numerical or (usually) categorical input data, the "X", always one variable, hence the reason it’s know as "one-way" beca it takes it account one variae at a time.

Answer: $130.66

Step-by-step explanation:

Answer:

130.66

Step-by-step explanation:

i took the asignment

Answer: 2/3

Step-by-step explanation:

Answer: 2/3

Step-by-step explanation:It can sometimes be difficult to divide fractions, such as 1/4 divided by 3/8. When we divide two fractions, such as 1/4 ÷ 3/8, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other.

Answer:oufonsrgonsrgnrsosgnsogwo0on93rhskgv oaoef

Step-by-step explanation:

iaeiuaefiaef ebf efa fcade emma jog 123e oefofoinsfnfsaefosefnhsfnalnfaogh

Answer:

58.33

Step-by-step explanation:

35 isn't exactly 60% of an number but by rounding you will get 58.33

Hello, please consider the following.

x is obviously different from 0 and then, dividing by x is legit.

For the first 105 miles the speed is x, so the time spent is

[tex]\dfrac{105}{x}[/tex]

For the second part, the speed is 1.4 x, so the time spent is

[tex]\dfrac{105}{1.4x}=\dfrac{75}{x}[/tex]

In total, the time she spent driving is

[tex]\dfrac{105}{x}+\dfrac{75}{x}\large \boxed{=\dfrac{180}{x}}[/tex]

Thank you.

Answer:

12+40= 52

180-52=128

Step-by-step explanation:

Angles in a triangle add up to 180

so if two sides are given , they must be added and subtracted from 180.

which gives us 180-52=128

Answer:

the angle is 128°

the right answer is C

Step-by-step explanation:

the angles of a triangle are always 180°

thus

the angle of the the triangle = 180° - (12°+40°)

= 180- 52° = 128°

Answer:

3x + 5

Step-by-step explanation:

We are doing variables and simplifying.

You have two types of numbers here, you have a coefficient, and you have regular numbers. Now do keep in mind that you can never add a regular number to a coefficient. So the only thing in this problem you will add is 3 and 2. Because 3x is different

3x + (3 + 2)

3x + 5

The simplified form of the expression is 3x + 5.

Option A is the correct answer.

We have,

Expression:

3x + 3 + 2

Add like terms.

3x + (3 + 2)

3x + 5

This is the simplest simplified form of the expression.

Thus,

The simplified form of the expression is 3x + 5.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

Answer:

soln,

y=37/100×x

or, 100y=37x.....is the answer

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 equation of y is 37% of x is

y = 0.37x

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.

2 + 3 - 4 is an expression.

2x4 + 4x = 4 is an expression.

We have,

y is 37% of x.

This can be written as,

y = 37/100 of x

y = 0.37x

Thus,

The equation of y is 37% of x is

y = 0.37x

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

20

Step-by-step explanation:

Given:

As per the picture:

Comparing the two equations above:

x = 20 is the correct answer for this question

Otherwise something is wrong with the question.

Answer:

Values of k can be 0, 1, or 2 such that intersection of the given lines lie in the 1st quadrant.

Step-by-step explanation:

Given two lines:

[tex]x=2k[/tex] and

[tex]3x+2y=12[/tex]

To find:

Values of 'k' such that the intersection of given two lines lie in the first quadrant.

Solution:

In 1st quadrant, the values of [tex]x[/tex] and [tex]y[/tex] both are positive.

So, let us find out intersection of the two lines.

Intersection of the two lines can be found by solving the two equations for the values of [tex]x[/tex] and [tex]y[/tex].

Given that [tex]x=2k[/tex] to be in the first quadrant, the value of k must be positive.

Let us put [tex]x=2k[/tex] in the equation [tex]3x+2y=12[/tex] to find the intersection point.

[tex]3 \times 2k + 2y=12\\\Rightarrow 6k+2y=12\\\Rightarrow 2y=12-6k\\\Rightarrow \bold{y=6-3k}[/tex]

For y to be positive:

[tex]6 - 3k \geq 0\\\Rightarrow 3k \leq 6\\\Rightarrow k \leq 2[/tex]

So, values of k can be 0, 1, or 2 such that intersection of the given lines lie in the 1st quadrant.

Answer:

mark it as brainlist plzz

Answer:

  [tex]1-\dfrac{2}{3}\sqrt{3}[/tex]

Step-by-step explanation:

Maybe you want to simplify ...

  [tex](1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}[/tex]

Multiply numerator and denominator by the 'conjugate' of the denominator:

  [tex](1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}\cdot\dfrac{3-\sqrt{3}}{3-\sqrt{3}}=\dfrac{(1-\sqrt{3})(3-\sqrt{3})}{9-3}=\dfrac{3-4\sqrt{3}+3}{6}\\\\\boxed{1-\dfrac{2}{3}\sqrt{3}}[/tex]

Use the divergence theorem,

[tex]\displaystyle\iint_{\partial\sigma}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\iiint_\sigma\mathrm{div}\mathbf F(x,y,z)\,\mathrm dV[/tex]

We have

[tex]\mathrm{div}\mathbf F(x,y,z)=\dfrac{\partial(3x)}{\partial x}+\dfrac{\partial(2y)}{\partial y}+\dfrac{\partial0}{\partial z}=5[/tex]

so that the flux across [tex]\sigma[/tex] is equal to 5 times the volume of the cube. The cube itself has edge length 5, so its volume is [tex]5^3=125[/tex], making the flux [tex]5^4=\boxed{625}[/tex].

Answer:

true

Step-by-step explanation: