Autumn runs a farm stand that sells peaches and grapes. Each pound of peaches sells
for $2 and each pound of grapes sells for $4. Autumn sold 35 more pounds of grapes
than pounds of peaches and made $200 altogether. Graphically solve a system of
equations in order to determine the number of pounds of peaches sold, 2, and the
number of pounds of grapes sold, y.

Answer:

Step-by-step explanation:

Given that :

the  perpendicular distance of the point from x axis = 2 units

the perpendicular distance from y axis is 3 units

The objective is to the write the coordinates of the points if it lies in

(i) | Quadrant  (ii) || Quadrant (iii) ||| Quadrant (iv) |v Quadrant

The position of a point in a plane is conveniently specified by the distances fro two perpendicular lines.The lines are called the x-axis and y-axis and their [point of intersection is called the origin.

The perpendicular distance from the y-axis is called the x- coordinate or abscissa and the perpendicular distance from x-axis is called the y-coordinate or ordinate,The  coordinate form an ordered pair with the abscissa written as first.

With that be said, So In the given question,

the  perpendicular distance of the point from x axis = 2 units

y coordinate = ±2

the perpendicular distance from y axis is 3 units

x coordinate = ±3

The ordered pair of the coordinates = ( ±3, ±2)

Therefore;

in | quadrant ; we have (3,2)   where  x and y are both on the positive axis

in || quadrant ; we have (-3,2)   x is on the negative axis and y is on the positive axis

In ||| quadrant ; we have (-3. -2) both x and y are on the negative axis

In |v quadrant ; we have ( 3, -2)  x is on the positive axis and y is on the negative axis.

Answer: [tex]y-1=\dfrac32(x+3)[/tex]

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]

Since parallel lines have equal slope . That means slope of the required line would be .

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

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]

Required equation: [tex]y-1=\dfrac32(x+3)[/tex]

Answer:

3 24/25 MPH

Step-by-step explanation:

We know Rami runs 6 3/5 miles in 1 2/3 hrs --> Convert into an improper fraction

--> 6 3/5 = 33/5

--> 1 2/3 = 5/3

Speed = Distance divided by Time

Distance = 33/5

Time = 5/3

33/5 / 5/3 = 33/5 x 3/5

33/5 x 3/5 = 99/25

1/25 less than 4 = 3 24/25

Thus, our answer is 3 24/25 MPH

Hope this helps!

Answer:

[tex]\frac{64}{27}[/tex] cm³

Step-by-step explanation:

The volume (V) of the prism is calculated as

V = lbh ( l is length, b is breadth and h is height ), thus

V = [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{4^3}{3^3}[/tex] = [tex]\frac{64}{27}[/tex] cm³

Answer:

Step-by-step explanation:

I am more than happy to answer anymore questions. If needed an explanation I can put one in the comments.

Answer: plot a point at (-8, -5)

The y coordinate flips from positive to negative, or vice versa, when we reflect over the horizontal x axis. The x coordinate stays the same.

The rule can be written as [tex](x,y) \to (x,-y)[/tex]

Step 1:

62cm - (25*2)=12cm

62-25=37cm

Length for both sides 25

Width=37cm=x

Answer:

The value of the derivative at x = 9 is -25

Step-by-step explanation:

Here in this question, we are told to find the derivative of the given equation at the point where x = 9

What we need to do here is simply, differentiate f(x), then substitute that value x = 9 into the differentiated equation

In notation form, what we are to find is f’(9)

So;

f(x) = -2x^2 + 11x

f’(x) = -4x + 11

So therefore;

f’(9) = -4(9) + 11

f’(9) = -36 + 11

f’(9) = 11-36

f’(9) = -25

Answer:

15 flamingos and 12 alligators

Step-by-step explanation:

Because there are 27 heads, that means there is a total of 27 flamingos and alligators. Flamingos have 2 feet and alligators have 4 feet.

1. Set up a system of equations

(x = number of flamingos, y = number of alligators)

1x + 1y = 27 heads

2x + 4y = 78 feet

2. Multiply to get the same coefficient

2(1x + 1y = 27) → 2x + 2y = 54

3. Subtract

 2x + 2y = 54

- 2x + 4y = 78

 0x + -2y = -24

4. Solve for y

-2y = -24

y = 12

5. Plug in y to solve for x

1x + 1(12) = 27

x + 12 = 27

x = 15

==================================================

Work Shown

We'll be using these vector properties

To get the following

-2u + v = -2*(-1, 5) + (2,7)

-2u + v = (-2*(-1), -2*5) + (2,7) .... apply rule 2

-2u + v = (2, -10) + (2, 7)

-2u + v = (2+2, -10+7) .... use rule 1

-2u + v = (4, -3)

Answer:

Step-by-step explanation:

for the first equation x= -2 and y=-7

the second equation x=3 and y is 3 now just plot x and y from the same equation on the same line

Answer:

[tex]\huge\boxed{x = -4; y = 7}[/tex]

Step-by-step explanation:

By plotting the points, we see that both of the lines intersect at (-4, 7)

Which means (X,y) = (-4,7)

So,

x = -4

y = 7

See the attached file so that you can know how would it be graphed.

Answer: Hi!

The only thing we can do to simplify the equation is combine like terms.

5x^2 + 4x^2 = 9x^2

-2y - 7y = -9y

3 - 1 + 7 = 9

Our equation now looks like this:

9x^2 - 9y + 9

We have nothing left to simplify, so we're done!

Hope this helps!

Answer:

Marie´s error was not to consider the number 8:

4x - 8 = 36

it´s equal to:

(4x-8)/4 = 36/4

4x/4 - 8/4 = 36/4

x - 2 = 9

x = 9+2

x = 11

probe:

4*11 - 8 = 36

44 - 8 = 36

Marie did not add 8 on the right-hand side so by considering it the solution of the given equation will be 11.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given equation,

4x - 8 = 36

Marie add +8 on the left-hand side but forgot to add it to the right-hand side.

Thus, add +8 on the left as well as the right-hand side.

4x - 8 + 8 = 36 + 8

4x = 44

x = 11

Hence "Marie did not add 8 on the right-hand side so by considering it the solution of the given equation will be 11".

For more about the equation,

brainly.com/question/10413253

#SPJ2

Answer:

Area= 452.23 ft²

Step-by-step explanation:

Angle at U = 180-48-20

Angle at U = 112°

UT/sin 112=46/sin 48

UT= 0.9272*46/0.7431

UT=57.4 ft

UV= sin 20*46/sin48

UV= 0.3420*46/0.7431

UV= 21.2 ft

S=( 21.2+57.4+46)/2

S=124.6/2

S= 62.3

Area= √((62.3)(62.3-21.2)(62.3-57.4)(62.3-46))

Area= √((62.3)(41.1)(4.9)(16.3))

Area= √204509.5311

Area= 452.23 ft²

Answer:

x = 3

Step-by-step explanation:

Given

5 - (4 - 3x) = 10 ← distribute the terms in the parenthesis by - 1

5 - 4 + 3x = 10, that is

1 + 3x = 10 ( subtract 1 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

Answer:

0.35, 0.359, 1

Step-by-step explanation:

0.359 = 359 thousandths

0.35 = 0.350 = 350 thousandths

1 = 1.000 = 1000 thousandths

Since 350 < 359 < 1000, then from least to greatest you get

0.35, 0.359, 1

Answer:

Total distance = 6,540,000 km

Step-by-step explanation:

Given

Number of bicycles = 9,000,000

Average Distance = 6.5 km (to 1 d.p)

Required

Calculate the upper bound of all bicycle distance

First, we need to determine the range of the distance traveled by each bicycle;

Since, the average distance is approximated, then the Range is:

[tex]Range = (6.45km\ to\ 6.54km)[/tex]

All number in this range approximate to 6.5km

Note that the upper bound of the range is 6.54km;

Hence, total distance is calculated as thus;

[tex]Total\ distance = Number\ of\ bicycle * upper\ bound[/tex]

[tex]Total\ distance = 1,000,000 * 6.54km[/tex]

[tex]Total distance = 6,540,000km[/tex]

Step-by-step explanation:

Hi, there!!!

Here, the question is about the volume of cone,

given that,

diameter = 12m

radius of a circle= 12m/2= 6m

height (h)=9 m

now, we have,

volume of a cone= 1/3×pi× r^2×h

or, v= 1/3×3.14×(6)^2×9

After simplifying it we get,

v= 339.12 m^3

Hope it helps....

Answer:

16%

Step-by-step explanation:

rental charge per year = $80

rental charge at the rate $8 per year = 8 * 12 = 96

the increased amount = 96 - 80 = 16

% = 16 / 100 = 16%

Answer:

49 square meters represent area of the square garden

Step-by-step explanation:

Each side length=7 meters

He multiplied 7 × 7 times to find the amount of space

=49 square meters

Jack is trying to measure the area of his square garden

Area of the square garden = length^2

=Length × length

Recall,

Length=7 meters

Area of the square garden= 7 meters × 7 meters

=49 square meters

Answer:

1/2 cup

Step-by-step explanation:

We can use ratios to solve

2 cups              x cups

---------------   = ----------------

100 cookies        25 cookies

Using cross products

2 *25 = 100x

50 = 100x

Divide by 100

50/100 = x

1/2 = x

Answer:

2/3

Step-by-step explanation:

dy/dx equals derivative of y by x

dy/dx=20t/30t=2/3

Answer:

EF = 2 units

Step-by-step explanation:

Given:

Line segment DF and point E on it.

DF = 11 unit

DE = 9 Unit

Find:

EF

Computation:

We know that,

DF = DE + EF

11 = 9 + EF

EF = 11-9

EF = 2 units

Answer:

1. tan A = 1/(tan B)

Step-by-step explanation:

By definition,

tangent A = opposite / adjacent = a / b

and

tangent B = opposite / adjacent = b / a

Therefore tangent A = a/b = 1/tan(B)

Answer: Tan a=tan b

I belive

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Because the question says you pick a different shirt on Tuesday than on Monday, that means you have one less shirt you can select, so the event is dependent.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Answer:.

Step-by-step explanation:.

Answer:

See below.

Step-by-step explanation:

[tex]f(x)=-x^2+6x-11\\f(x-3)=-(x-3)^2+6(x-3)-11\\f(x-3)=-(x^2-6x+9)+6x-18-11\\f(x-3)=-x^2+6x-9+6x-29\\f(x-3)=-x^2+12x-38[/tex]

Answer:

D

Step-by-step explanation:

-1/2x > 6 (you have to flip the sign when you multiply or divide by negative

x < -12

Answer:

6000

Step-by-step explanation:

Divide top and bottom by the common factor.  

[tex]\dfrac{3 }{4} \times 8000 = 3 \times 2000[/tex]

Simplify

3 × 2000 = 6000

Answer:

C.) 7.14 in²

Step-by-step explanation:

The figure is made up of a square and a circle. The circle is divided in half and each piece is set on one side of the square. This means that the diameter of the circle is equal to the length of the sides of the square, 2 inches.

The area of the square can be found by multiplying length times the width:

[tex]2*2=4[/tex]

The area of the square is 4 inches, and since we multiplied two lengths, we square the value:

A=4in²

Now find the area of the circle using the formula:

[tex]A=\pi r^2[/tex]

The radius is half of the diameter, so the radius is 1. Insert values and solve:

[tex]A=\pi *1^2\\\\A=\pi *1\\\\A=\pi[/tex]

The area of the circle is equal to π. Add the values together:

[tex]4+\pi =7.14[/tex]

The area of the figure is 7.14 in²

:Done

Answer:

3

= 15/5

= [tex]\sqrt[3]{27}[/tex]

= 1.5*2

= 3/1

= 3*1

= 3¹

= 1/3⁻¹

= 3⁴ / 3³

= 3⁵ * 3⁻⁴