A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y. Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season. Which system represents this scenario?

Answer:

C

Step-by-step explanation:

To write the equation of a line use the point slope form of a line substituting m = -1/2 and the point (-2,-3).

[tex]y -y_1 = m(x-x_1)\\y --3=-\frac{1}{2}(x--2)\\y+3 = -\frac{1}{2}(x+2)[/tex]

Convert to standard form by applying the distributive property and rearranging the terms.

[tex]y + 3 = -\frac{1}{2}(x+2)\\y+3 = -\frac{1}{2}x -1\\2y + 6 = -x -2\\x+2y + 6 = -2\\x + 2y = -8[/tex]

The equation x +2y = -8 is the same equation as 4y + 2x = -16 just doubled----> 2x + 4y = -16

x²-8x=768

x²-8x-768=0

(x-32)(x+24)=0

x=32 x=-24

you use 32 because it can be negative

plug in for x

(32)(32-8)(1)=768

32×24=768

this isn't the completing the square method though this is zero product law

a. Equation that represents the volume of the rectangular prism glass is:  (x)(x - 8)(1) = 768

b. The dimensions are, length = 32 cm, width = 24 cm.

Volume = (l)(w)(h)

Given the following dimensions of the glass case:

a. Plug in the values into the volume formula to find the equation

(x)(x - 8)(1) = 768

x² - 8x - 768 = 0

b. Factorize x² - 8x - 768 = 0 to find the x, and find the dimensions of the rectangular prism glass

x² - 8x - 768 = 0

(x + 24)(x - 32) = 0

x= −24 or x = 32

The length cannot be a negative number, so:

Length of the glass = x = 32 cm

Width = x - 8 = 32 - 8 = 24 cm

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Answer:  The answer is A.  

Step-by-step explanation:  The two big things are a one, so it is 2.00, and then the last box is .02.  Add .02 to 2.00, and get 2.02.  That is less.  2 12/100 is basically 2.12, and the last one is either 23, or 230.  But it is over or equal and not under.  

Division! Since litres is a larger unit then millimeters, the value will need to decrease to make up for the change in units. So division is needed.

To convert milliliters to liters, use division because you're converting from a smaller to a larger unit, with 1000 milliliters equaling one liter.

To convert milliliters to liters, you would use division. This is because the process involves going from a smaller unit of measurement to a larger one, and there are 1000 milliliters in one liter. Therefore, you move the decimal point three places to the left. For example, converting 60,000 milliliters to liters, you would calculate 60,000 milliliters / 1000, resulting in 60 liters.

In solving multi-step division problems with compound units or applying compound unit multiplication in word problems, it is essential to convert all values into the same units using multiplication and division. When dealing with compound unit conversions such as milliliters to liters, division helps find the total amount or cost for a given volume in liters after initially representing values in milliliters.

Answer:

The graph would move up 3.

Step-by-step explanation:

When a number is added after the absolute value brackets, the graph shifts up and down. Since it is a positive number, the shift is upwards.

Answer:

graph is shifted up by 3 units.

Step-by-step explanation:

Given : The translation applied to get the graph of g(x) from the graph of f(x) = |x| and g(x) = |x| + 3

To find : Graph of g(x).

Solution : We have given that

Parent function f(x) ans translated function g(x) =  |x| + 3.

By the transformation rule : f(x) →→ f(x) + k it mean graph of f(x) shifted by k units up.

Then, graph is shifted up by 3 units.

Therefore,  graph is shifted up by 3 units.

Answer:

option D

0 < t < 3

Step-by-step explanation:

Given in the question the equation

d = 144 - 16t²

where d is the distance

           t is the time

Since, it is a descent, d should be decreasing until it reaches zero

by plugging d = 0 in the equation

0 = 144 - 16t²

-144 = -16t²

144/16 = t²

t² = 9

take square root on both sides

√t² = √9

t = ±3

since time can't be negative so we will reject -3

t = 3

This means that at 3 seconds the roller coaster was at ground but before that it was in the air

so when t < 3 Greg's car was moving in the air.

[tex]\bf \cfrac{2}{3}\implies \cfrac{1+1}{3}\implies \cfrac{1}{3}+\stackrel{\textit{100\%}}{\cfrac{1}{3}}\impliedby \textit{change of 100\%}[/tex]

Answer:

Option D.  23.4 pounds

Step-by-step explanation:

step 1

Find the pieces of glass for 22.5 pounds of copper in the sculpture.

using proportion

[tex]\frac{12}{1}=\frac{x}{22.5} \\ \\x=22.5*12\\ \\x=270\ piece\ of\ glass[/tex]

step 2

Find the pounds of bronze used in the sculpture

using proportion

[tex]\frac{6.5}{75}=\frac{x}{270} \\ \\x=270*6.5/75\\ \\x=23.4\ pounds[/tex]

graph c, because it is a curved line. The line has to be straight in order to be a function.

A function is a relationship between inputs where each input is related to exactly one output.

The graph in option D shows one-to-many which is not a function.

The graph in option D represents a non-functional relationship.

Option D is the correct answer

A function is a relationship between inputs where each input is related to exactly one output.

Example: f(x) = 2x is a function.

x = input

2x = output

We have,

A function can have two inputs and have the same output.

This property is called many-to-one function

For example f(x) = (-x)²,

x = 1, -1

f(1) = 1

f(-1) = 1

But a function can not have different outputs for the same inputs.

This property is called one-to-many function.

The given graph in the options are:

A - this graph represents a functional relationship.

B - this graph represents a functional relationship as many-to-one function.

C - this graph represents a functional relationship.

D - this graph represents a non-functional relationship because it is a one-to-many function

Thus,

The graph in option D shows one-to-many which is not a function.

The graph in option D represents a non-functional relationship.

Option D is the correct answer

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Hey im happy to help!

your answer here will be 4.

Hope this helps, have a great rest of your day!

Answer:

4

Step-by-step explanation:

Answer:

V_rocket  = 44[tex]\pi[/tex]  ft^3  = 138.2 ft^3

Step-by-step explanation:

Volume  of cone

V_cone = (1/3)*([tex]\pi[/tex]*(radius^2))*h

radius = 2ft

h = height of the cone = 3 ft

pi = 3.1416

V_cone = 4[tex]\pi[/tex]  ft^3

Volume cylinder

V_cylin = ([tex]\pi[/tex]*(radius^2))*h_cyl

h_cyl = height of the cylinder = 10 ft

V_cylin  = 40[tex]\pi[/tex]  ft^3

Volume rocket

V_rocket = V_cone  +  V_cylin  = 4[tex]\pi[/tex]  ft^3 + 40[tex]\pi[/tex]  ft^3

V_rocket  = 44[tex]\pi[/tex]  ft^3  = 138.2 ft^3

Answer:

Vertex Pt (-1,-3) Y=2x^2+4x-1

Step-by-step explanation:

2[ (x+1)^2-1} - 1

2(x+1)^2-2} - 1

2(x+1)^2 - 3

Answer:

$350

Step-by-step explanation:

The interest earned would be $353

See the image attached

Answer:

option A

option C

option D

Step-by-step explanation:

A function is a special relationship where each input has a unique output.

There could not be different y values for same value of x but it may have two x-values assigned to the same y-value.

In option B

for x = 6

have two different outputs y = -6 and y = -1 REJECTED

In option E

for x = 0

have two different outputs y = 0.5 and y = 2 REJECTED

Answer:

25

Step-by-step explanation:

Divide 17 by 68%.

Hope that helps!

Step-by-step explanation:

Let's set up a proportion.

17/x=68/100.

Now if we solve for x it would equal to 25. They played 25 games.

Brainliest? :)

Answer:

The answer is 28

Step-by-step explanation:

To find the answer, take the function and input the -5 for all x's.

f(x) = x^2 - 2x - 7

f(-5) = (-5)^2 - 2(-5) - 7

f(-5) = 25 + 10 - 7

f(-5) = 28

The value of f(-5) is 28 after plugging x = -5 in the polynomial f(x) = x² - 2x - 7

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial:

f(x) = x² - 2x - 7

Plug x = -5

f(-5) = (-5)² - 2(-5) - 7

f(-5) = 25 + 10 - 7

f(-5) = 28

Thus, the value of f(-5) is 28 after plugging x = -5 in the polynomial f(x) = x² - 2x - 7

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Answer:

[tex]4.3\ km[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

[tex]c^{2}=a^{2}+b^{2}-2(a)(b)cos(C)[/tex]

we have

c-----> is the distance between Amanda and Angela

[tex]a=10\ km[/tex]

[tex]b=12\ km[/tex]

[tex]C=20\°[/tex]

substitute the values

[tex]c^{2}=10^{2}+12^{2}-2(10)(12)cos(20\°)[/tex]

[tex]c^{2}=18.4738[/tex]

[tex]c=4.3\ km[/tex]

Answer:

The radius is 5.5 mm

Step-by-step explanation:

The diameter is 11 mm

The radius is 1/2 of the diameter

1/2 d =r

1/2(11) =r

5.5 =r

The radius is 5.5 mm

Answer:

All you have to do is look up the formulas for each one.

Step-by-step explanation:

Plug in the numbers to the correct formulas and you should get your answer.

See the attached figure for your solution

Answer:

4 is your answer

Step-by-step explanation:

Well every 15 minutes he walks 1 step. So divide an hour which is 60minutes by 15 minutes. Then the answer to that you multiply by 1. So the equation would be (60/15)x1= and you will find the answer.

mark brainliest please  :)

Answer:

4000 meters

Step-by-step explanation:

There are 60 minutes in an hour. Divide 60 by 14 and get 4. So she walks 4 km in an hour, but we want to know the answer in meters so we multiply 4 by 1000 to get 4000 meters.

Answer: OPTION B.

Step-by-step explanation:

The number that are inside of the square root are called "radicands".

To subtract the expressions shown in the image attached, the radicands must be the same.

As you can see, both are equal, therefore, you can subtract the numbers that are in front of the square roots.

Then, you obtain the following result:

[tex]3\sqrt{2}-\sqrt{2}=(3-1)\sqrt{2}=2\sqrt{2}[/tex]

The answer is the option B.

Answer:

The correct answer is option B.  2√2

Step-by-step explanation:

It is given an expression, 3√2 - √2

Simplify the expression

The expression is 3√2 - √2

3√2 - √2 = √2(3 - 1)   ( taking √2 as common)

= √2 x  2

= 2√2

Therefore the simplified form of given expression(3√2 - √2) is 2√2

The correct answer is option B.  2√2

Answer:  B) The parabola is narrower.

Step-by-step explanation:

[tex]y=ax^2+bx+c[/tex] is the Standard form of a quadratic function, where a, b and c are coefficients ([tex]a\neq0[/tex]).

With the coefiicient "a" you can determine how narrow or wide the parabola is:

[tex]|a|>1[/tex] makes the parabola narrow.

[tex]0<|a|<1[/tex] makes the parabola wide.

Given the transformation of the parent function: [tex]f(x)=3x^2[/tex], you can identify that:

[tex]a=3[/tex]

Then:

[tex]|a|>1[/tex]

Therefore, as the parent function is multiplied by 3 and know [tex]|a|>1[/tex],   the parabola if narrower than the parabola of the quadratic parent function [tex]f(x)=x^2[/tex].

Answer:

Option B - The parabola is narrower.

Step-by-step explanation:

Given : The function [tex]f(x)=x^2[/tex] is transformed to  [tex]f(x)=3x^2[/tex]

To find : Which statement describes the effect(s) of the transformation on the graph of the original function?

Solution :

When the function of parabola [tex]f(x)=x^2[/tex] is transformed by 'a' unit [tex]f(x)=ax^2[/tex]

Then, [tex]|a|>1[/tex] makes the parabola narrow.

and [tex]0<|a|<1[/tex] makes the parabola wide.

On comparing with given function,

|a|=|3| >1 which is greater than 1.

Which means it makes the parabola narrow.

Therefore, the parabola is narrower.

So, Option B is correct.

Answer:

[tex]\large\boxed{y=2(x+1)^2-3}[/tex]

Step-by-step explanation:

The vertex form of an equation of a parabola:

[tex]y=a(x-h)^2+k[/tex]

(h, k) - vertex

We have

[tex]y=2x^2+4x-1=2\left(x^2+2x-\dfrac{1}{2}\right)[/tex]

We must use the formula: [tex](a+b)^2=a^2+2ab+b^2\qquad(*)[/tex]

[tex]2\left(x^2+2(x)(1)-\dfrac{1}{2}\right)=2\bigg(\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-\dfrac{1}{2}\bigg)\\\\=2\left((x+1)^2-1-\dfrac{1}{2}\right)=2\left((x+1)^2-\dfrac{3}{2}\right)[/tex]

Use the distributive formula a(b + c) = ab + ac

[tex]2(x+1)^2+2\left(-\dfrac{3}{2}\right)=2(x+1)^2-3[/tex]

do u have to use the exact same number for all the substitutions?

The question involves solving a system of two linear equations, 5x - y = -5 and 3x - 6y = 24. By rearranging the first equation to find y in terms of x, and then substituting this into the second equation, we find x = -8/9. Substituting this value into y = 5x + 5, we find y = 5/9.

The question involves a system of linear equations. You solve it using the substitution method. Here are the steps:

So, the solution to the system of equations is x = -8/9 and y = 5/9.

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Answer:

A. 40°

Step-by-step explanation:

Hello, there! The angle is across from (vertical to) the angle given. Therefore, the 2 angles are the same.

I hope I helped!

Let me know if you need anything else!

~ Zoe

Answer:

x = 40°, or A)

Step-by-step explanation:

The Vertical Angle Theorem states that if the angles are vertically (directly) opposite of each other, the measurements will be the same.

Therefore, if the opposite angle of x is 40, then x also = 40.

~

To find the intercept we need to substitute 0 for y and solve for x.

For our x-intercept you should get: (6,0), (-2,0)

For our y-intercept you should get (0,-12).

Answer:

segment AM

Step-by-step explanation:

A median is a line segment which joins the vertex of a triangle to the midpoint of the opposite side. The median to BC is the vertex opposite it A joined to its midpoint M. The segment AM is the median.

Answer:

1. Segment AM.

Step-by-step explanation:

We have been given a triangle ABC. Points L, M and N re midpoints of the triangle. We are asked to find the median of segment BC.

We know that median of a triangle is line segment connecting the midpoint of a segment to the opposite vertex.

We can see that angle A is the opposite angle to side BC and M is the midpoint of side BC, therefore, segment AM is the median to side BC and 1st option is the correct choice.

[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = 0 \\\\\\ \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-(-8)=0(x-6)\implies y+8=0\implies y=-8[/tex]

Answer: Hello there!

we want to find the equation that passes through the point (6, -8) (where this notation stands for (x,y)) with a slope of 0.

a linear equation has the form y = ax+ b

where a is the slope and b is the intercept.

if a = 0, our equation has the form y = b (has no dependence of x)

so we have a constant equation that passes through the point (6, -8) , this means x = 6 and y = -8, but we know that y is constant:

then y = -8 = b

so our equation is y(x) = -8

Answer:

A perfect square is a shape with for 90 degree angles

Step-by-step explanation:

The square of an integer is called a perfect square. For example, 49 is a perfect square because 7² = 49. When a radicand is not a perfect square, you can estimate the square root of the radicand.