A store owner wants to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $18.90 per pound should be mixed with 22 pounds of trail mix costing $3.30 per pound to create a mixture worth $8.50 per pound.

The owner needs to mix _________ pounds of chocolate (round to the nearest whole pound - NO COMMAS).

[tex]\bf a^3b^{-2}c^{-1}d\implies \cfrac{a^3d}{b^2c}\qquad \begin{cases} a=2\\ b=4\\ c=10\\ d=15 \end{cases}\implies \cfrac{2^3\cdot 15}{4^2\cdot 10}\implies \cfrac{120}{160}\implies \cfrac{3}{4}[/tex]

Answer:

y = - 3x + 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = - 3, hence

y = - 3x + c ← is the partial equation

To find c substitute (4, - 2) into the partial equation

- 2 = - 12 + c ⇒ c = - 2 + 12 = 10

y = - 3x + 10 ← equation of line

Answer:   [tex]y=-3x+10[/tex]

Step-by-step explanation:

The equation of a line in intercept form: [tex]y=mx+c[/tex]

The equation of a line passing through (a,b) and has slope m is given by :_

[tex](y-b)=m(x-a)[/tex]

Similarly, the  equation in slope-intercept form that describes a line through (4, -2) with slope -3 will be :_

[tex](y-(-2))=-3(x-4)\\\\\Rightarrow\ y+2=-3x+12\\\\\Rightarrow\ y=-3x+12-2\\\\\Rightarrow\ y=-3x+10\ \ \text{In intercept form}[/tex]

Hence, the equation in slope-intercept form that describes a line through (4, -2) with slope -3 = [tex]y=-3x+10[/tex]

Answer:

53.4 and 62.6

Step-by-step explanation:

Answer:

53.4 and 62.6

Step-by-step explanation:

Got it right :/

Answer:

z = 5/3 or 1 2/3

Step-by-step explanation:

2/3·z=10/9

Multiply each side by 3/2

3/2*2/3·z=10/9*3/2

z = 30/18

We can simplify by dividing the top and bottom by 6

z = 5/3

Changing to a mixed number

z =1 2/3

Answer:

1⅔ [OR 5⁄3]

Step-by-step explanation:

2 × ? = 10

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

3 × ? = 9

That would be 1⅔.

I am joyous to assist you anytime.

Answer:3x+y=3 is the red line.

6x+y=-4 is the blue line.

Step-by-step explanation:I answer it on the test it is right..

Answer:

The correct option is A.

Step-by-step explanation:

We need to find the cheapest per month over all.

Assume a month has 30 days.

In option A:

Rent = 11.95 a day

Monthly rent = 11.95 × 30 = 358.5

Total renting amount is 358.5.

In option B:

Lease = 149.00 a month 3180 due at signing

Total amount = 149 + 3180 = 3329

Total leasing amount is 3329.

In option C:

Buying = 16,000

In option D:

Finance = 389.00 /month

The cheapest amount for a month is 358.5 .Therefore the correct option is A.

Answer: renting a car

Step-by-step explanation:

Answer:

Lara's share = 25000

Step-by-step explanation:

Partnership's income = 50,000

Lara's guaranteed payment = 20,000

As the Income 50,000 is larger than Lara's guaranteed payment i.e 20,000. Since Lara is 50% partner so she will receive half the amount of the partnership's income.

Partnership's Income = 50,000  

Half of Partnership's income = 50,000/2

                                                = 25,000

Therefore, Lara's distributive share is 25,000.

!!

Answer:

121

Step-by-step explanation:

THIS IS BECAUSE 11*11 = 121

Answer:

121

Step-by-step explanation:

121= 11x11, that is the only option

140 has no square

168 is close, but still isn't a square

195 is 1 away from a square, but not a square

[tex]\bf sin(y)+cos(y)+tan(y)sin(y)=sec(y)+cos(y)tan(y) \\\\[-0.35em] ~\dotfill\\\\ sin(y)+cos(y)+tan(y)sin(y)\implies sin(y)+cos(y)+\cfrac{sin(y)}{cos(y)}\cdot sin(y) \\\\\\ sin(y)+cos(y)+\cfrac{sin^2(y)}{cos(y)}\implies \stackrel{\textit{using the LCD of cos(y)}}{\cfrac{sin(y)cos(y)+cos^2(y)+sin^2(y)}{cos(y)}} \\\\\\ \cfrac{sin(y)cos(y)+\stackrel{cos^2(y)+sin^2(y)}{1}}{cos(y)}\implies \cfrac{sin(y)cos(y)+1}{cos(y)} \\\\\\ \cfrac{sin(y)}{cos(y)}\cdot cos(y)+\cfrac{1}{cos(y)}\implies tan(y)cos(y)+sec(y)[/tex]

Answer:

G !!! Have a good day BLOODY

Answer:

a) The length of the diagonal is 17.71 feet

b)  The area of the trapezoid is 123.14 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- Look to the attached figure

- ABCD is an isosceles trapezoid

∵ DC is the longer base with length 18 feet

∵ AD and BC are the two non-parallel sides with length 8 feet

∵ ∠ ADC and ∠ BCD are the bases angles with measure 75°

- AE and BF are ⊥ DC

# In Δ BFC

∵ m∠BFC = 90° ⇒ BF ⊥ CD

∵ m∠C = 75°

∵ BC = 8

∵ sin∠C = BF/BC

∴ sin(75) = BF/8 ⇒ multiply both sides by 8

∴ BF = 8 × sin(75) = 7.73

∵ cos∠C = CF/BC

∴ cos(75) = CF/8 ⇒ multiply both sides by 8

∴ CF = 8 × cos(75) = 2.07

# In Δ BFD

∵ m∠BFD = 90°

∵ DF = CD - CF

∴ DF = 18 - 2.07 = 15.93

∵ BD = √[(DF)² + (BF)²] ⇒ Pythagoras Theorem

∴ BD = √[(15.93)² + (7.73)²] = 17.71

a)

∵ BD is the diagonal of the trapezoid

* The length of the diagonal is 17.71 feet

b)

- The area of any trapezoid is A = 1/2 (b1 + b2) × h, where b1 and b2

  are the barallel bases and h is the height between the two bases

∵ b1 is CD

∴ b1 = 18

∵ b2 is AB

∵ AB = CD - (CF + DE)

∵ ABCD is an isosceles trapezoid

∴ CF = DE

∴ AB = 18 - (2.07 + 2.07) = 13.86

- BF is the perpendicular between AB and CD

∴ BF = h

∴ h = 7.73

∵ A = 1/2 (18 + 13.86) × 7.73 = 123.14

* The area of the trapezoid is 123.14 feet²

Answer:

y ≤ ¼x + 1

Step-by-step explanation:

Starting from the y-intercept of course, use rise\run until you hit another endpoint [finding the rate of change (slope)]. That means me we go up north one block, then go over four blocks east, and since the slope is already simplified, we do not need to go any further. Now all we have left is to determine the correct inequality symbol, and since we know that the bottom portion of the graph is shared, we automatically know it is less than, but to check this, we need to do what is called a zero-interval test [do not recall the actual term], meaning that we plug in 0 for both y and x, getting 0 < 1, which is a GENUINE statement, so the bottom portion stays shaded, otherwise we would have had to shade the top portion if it were a false statement. Finally, we have to determine if we have to add an equivalence line under the inequality symbol, and we DO because as you can see, the line is SOLID BLACK. If it were DASHED BLACK, then it would stay "<" instead of "≤".

I am joyous to assist you anytime.

Answer:

If the width of the rectangle is x than the length is 4x because 4x*x is 4x^2

Step-by-step explanation:

Answer:

b=3/8a

Step-by-step explanation:

Have a good night/day<3

To find the equation describing the proportional relationship between A and B, we divide B by A and find that the constant of proportionality is 3/8. Thus, the equation is B = (3/8)A.

To find the equation that describes the proportional relationship between A and B, we can start by examining the given pairs of values. For A = 8, B = 3; for A = 24, B = 9; and for A = 40, B = 15. We observe that as A increases, B increases at a constant rate. This suggests a direct proportionality between A and B.

To determine the constant of proportionality (the rate at which B changes with respect to A), we can divide the values of B by the corresponding values of A. Doing so, we find:

All these ratios reduce to 3/8, which is the constant of proportionality. Therefore, B is 3/8 times A, which we can express as:

B = (3/8)A

This equation represents the proportional relationship between A and B, with the constant of proportionality being 3/8.

Points [tex]X(-2,1)[/tex] and [tex](-4,-3)[/tex] are defined therefore we have all data we need to construct equation.

Linear function has a form of,

[tex]y=ax+b[/tex]

First calculate the slope a.

[tex]a=\dfrac{dy}{dx}=\dfrac{-3-1}{-4-1}=\dfrac{-4}{-5}=\dfrac{4}{5}[/tex]

Now plug in the coordinates of either one of the points into the linear function. I'll pick point X.

[tex]y=ax+b\Longrightarrow1=\dfrac{4}{5}\cdot(-2)+b[/tex]

Now just solve for b.

[tex]1=-\dfrac{8}{5}+b\Longrightarrow b=\dfrac{13}{5}[/tex]

The equation is therefore,

[tex]\boxed{y=\dfrac{4}{5}x+\dfrac{13}{5}}[/tex]

Hope this helps.

r3t40

again, bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-2)}{6-3}\implies \cfrac{2+2}{6-3}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=\cfrac{4}{3}(x-3)\implies y+2=\cfrac{4}{3}x-4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf y=\cfrac{4}{3}x-6\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( \cfrac{4}{3}x-6 \right)}\implies 3y=4x-18 \\\\\\ -4x+3y=-18\implies \stackrel{\textit{standard form}}{4x-3y=18}[/tex]

Final answer:

The notation h(40)=1820 means that the function h produces an output of 1820 when the input is 40, although additional context is needed to determine what h represents specifically in this scenario.

Explanation:

The expression h(40)=1820 typically means that a function h is being evaluated at the input value of 40, and the output is 1820. This could represent a variety of contexts, such as the height of a rocket in meters at 40 seconds after launch, the amount of money saved after 40 weeks, or any other situation described by a function where the variable h depends on the number 40. Without additional context, it's impossible to say precisely what 1820 refers to, but it is the result of the function h when the input is 40.

Answer:

10sqrt3+22

Step-by-step explanation:

Ok, let us imagine it as a sort of rectangle split upon its diagonal.

Using that, we can Pythag it out,

11^2+b^2=14^2

121+b^2=196

b^2=75

b=sqrt75

b=5sqrt3

Ok, using this info, we find the perimeter,

5sqrt3+5sqrt3+11+11

10sqrt3+22

The answer is 10sqrt3+22

The answer is:

The perimeter of the rectangle is equal to 39.32".

[tex]Perimeter=39.32in[/tex]

Since we are working with a rectangle, we can use the Pythagorean theorem to find the missing side of the rectangle and calculate its perimeter. We must remember that we can divide a rectangle into two equal right triangles.

According to the Pythagorean Theorem, we have:

[tex]a^{2}=b^{2}+c^{2}[/tex]

Where:

a, represents the hypotenuse of the triangle which is equal to the diagonal of the given rectangle (14")

b and c are the other sides of the triangle.

Now, let be "a" 14" and "b" 11"

So, solving we have:

[tex]a^{2}=b^{2}+c^{2}[/tex]

[tex]14^{2}=11^{2}+c^{2}[/tex]

[tex]14^{2}-11^{2}=c^{2}[/tex]

[tex]14^{2}-11^{2}=c^{2}\\\\c=\sqrt{14^{2} -11^{2} }=\sqrt{196-121}=\sqrt{75}=8.66in[/tex]

Now, that we already know the the missing side of the rectangle, we can calculate the perimeter using the following formula:

[tex]Perimeter=2base+2length\\\\Perimeter=2*11in+2*8.66in=22in+17.32in=39.32n[/tex]

Hence, we have that the perimeter of the rectangle is equal to 39.32".

Have a nice day!

Answer:

Scalene Triangle

Step-by-step explanation:

By definition, scalene triangles have 3 sides of unequal length.

FYI,

Right Triangle : triangle with one of the angles = 90°

Isosceles Triangles: Triangle with 2 sides of the same length.

Equilateral triangle: Triangle with 3 sides of the same length.

Step-by-step explanation:

Look at the picture.

All rhombuses are

parallelograms

quadrilaterals

Answer:

10.5 units

Step-by-step explanation:

Since M is the centre of the circle. The measure to the edge is the radius.

Which in this case is 10.5 units

Answer: A. 10.5 units

Step-by-step explanation: The answer would be 10.5 units because the radius is equal to half the circle. MS is a radius, and MR is a radius. A radius has one point in the center, and one point on the circle.

To isolate the variable terms on one side and the constant terms on the other side of the equation 3x - 5 = -2 + 10, add 2 to both sides, simplify to 3x - 3 = 10, then add 3 to both sides to get the final simplified equation 3x = 13.

The equation 3x - 5 = -2 + 10 needs to be rearranged to isolate the variable terms on one side and the constant terms on the other. To do this, follow these steps:

Now, we have successfully isolated the variable terms (3x) on one side of the equation and the constant terms (13) on the other side.

[tex]\bf r=2sec(\theta )\qquad \begin{cases} x=rcos(\theta )\\ \frac{x}{r}=cos(\theta ) \end{cases}\qquad \implies r=2\cdot \cfrac{1}{cos(\theta )}\implies r=\cfrac{2}{~~\frac{x}{r}~~} \\\\\\ r=\cfrac{\frac{2}{1}}{~~\frac{x}{r}~~}\implies r=\cfrac{2r}{x}\implies x=\cfrac{2~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies x=2[/tex]

To solve the system of equations x + 3y = 5 and x - 3y = -1, we add both equations to get 2x = 4, solve for x to find x = 2, and then substitute x back into one of the equations to find y = 1, resulting in the solution (2, 1).

The solution of the system of linear equations given by x + 3y = 5 and x - 3y = -1 involves manipulating the equations to find the values of x and y that satisfy both equations simultaneously. One common method to solve these is to add or subtract the equations, which eliminates one variable, making it possible to solve for the other.

Starting with the addition method, we align the equations and add them together:

x + 3y = 5

x - 3y = -1

Adding these equations, we get 2x = 4, and solving for x gives us x = 2. We can substitute x = 2 back into one of the original equations to find the value of y, yielding y = 1.

The solution to the system is the intersection point of the two lines represented by the equations, which is the point (2, 1).

Answer:

[tex]\large\boxed{6y+52}[/tex]

Step-by-step explanation:

In this question, we're going to simplify the expression.

We would do this by distributing and solving after.

Solve:

[tex]6(2y + 8) - 2(3y - 2)\\\\\text{Distribute the 6 to the 2y and 8}\\\\12y+48- 2(3y - 2)\\\\\text{Distribute the -2 to the 3y and -2}\\\\12y+48-6y+4\\\\\text{Combine like terms}\\\\6y+48+4\\\\\boxed{6y+52}[/tex]

When you're done solving, you should get 6y+52

This means that the simplified version would be 6y+52

Irrational numbers cannot be expressed as a fraction or ratio of two integers and have decimal representations that go on forever without repeating.

Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. They are decimal numbers that go on forever without repeating. Examples of irrational numbers include π, √2, and √3. These numbers cannot be expressed as a simple fraction or as a terminating or repeating decimal.

Answer:

B

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

Solution = (1, 5 ) → B

[tex]\huge{\boxed{\text{(1, 5)}}}[/tex]

All you need to do is find where the intersection of the lines is located.

Count how many units to the right. [tex]1[/tex] This is our [tex]x[/tex] value.

Count how many units up. [tex]5[/tex] This is our [tex]y[/tex] value.

Answer:

-28

Step-by-step explanation:

[tex]-(2-2^3)^2-4 \cdot (-2)[/tex]

We going to use PE(MD)(AS).

So P means ( ).

We do have operations to perform in the ( ).

We have [tex]2-2^3[/tex] in the first set of ( ) and (-2) in the second set of ( ).

There are no operations in the second  set containing -2.

So we are just focusing on the [tex]2-2^3[/tex] right now.

You have subtract and exponent here.

Exponents come first in PE(MD)(AS) so we will perform that first.

[tex]2-2^3=2-8=-6[/tex]

Let's go back to the original problem now.

[tex]-(2-2^3)^2-4 \cdot (-2)[/tex]

[tex]-(-6)^2-4 \cdot(-2)[/tex]

Now there are no longer any operations grouped together by use of ( ).

It on to the rest of PE(MD)(AS).

So now we are doing the E part, the exponents.

[tex]-(36)-4 \cdot(-2)[/tex]

Now there is multiplication and subtraction left.

(MD) comes before (AS) so we do the multiplication and then the subtraction.  So I'm going to do 4(-2) now:

[tex]-(36)-(-8)[/tex]

Subtraction is addition of the opposite so you could write:

[tex]-(36)+8[/tex]

We don't really need ( ) around the first number:

[tex]-36+8[/tex]

36-8 is 28 but since 36>8 and 36 has a negative sign on it, the answer is -28.

Answer:

[tex]x_1 = 9[/tex] and [tex]x_2 = 11[/tex].

Step-by-step explanation:

Start by adding 1 to both sides of this equation.

[tex](x - 10)^{2} = 1[/tex].

The square of what number or numbers will lead to the number "1"? It turns out that not only [tex]1^{2} = 1[/tex], but [tex](-1)^{2}= 1[/tex] as well. In other words, the value [tex](x - 10)[/tex] can be either 1 or -1. Either way, the equation is still going to hold. That's the reason why there are two solutions to this equation.

Consider the case when [tex]x - 10 = 1[/tex]. Add 10 to both sides of the equation. [tex]x = 11[/tex].

Now, consider the case when [tex]x - 10 = -1[/tex]. Again, add 10 to both sides of the equation, [tex]x = 9[/tex].

Order the two solutions in an increasing order: