A. They sold the least lemonade with the recipe that used 3 lemons
B. They sold the least lemonade with the recipe that used 7 lemons
C. They sold the most lemonade with the recipe that used 3 lemons
D. They sold the most lemonade with the recipe that used 7 lemons

Answer:

The width of the original rectangle on the left is [tex]5\ m[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

Let

z -----> the scale factor

a ----> perimeter of the reduced rectangle on the right

b ----> perimeter of the original rectangle on the left

[tex]z=\frac{a}{b}[/tex]

we have

[tex]a=24\ m[/tex]

[tex]b=30\ m[/tex]

substitute

[tex]z=\frac{24}{30}=0.8[/tex]

step 2

Find the width of the reduced rectangle on the right

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]L=8\ m[/tex]

[tex]P=24\ m[/tex]

substitute and solve for W

[tex]24=2(8+W)[/tex]

[tex]12=(8+W)[/tex]

[tex]W=12-8=4\ m[/tex]

step 3

Find the width of the original rectangle on the left

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Let

z -----> the scale factor

y ----> the width of the reduced rectangle on the right

x ----> the width of the original rectangle on the left

[tex]z=\frac{y}{x}[/tex]

we have

[tex]y=4\ m[/tex]

[tex]z=0.8[/tex]

substitute and solve for x

[tex]0.8=\frac{4}{x}[/tex]

[tex]x=\frac{4}{0.8}[/tex]

[tex]x=5\ m[/tex]

2 units.

Since a triangle is basically a rectangle split in half, we just use the dimensions of the triangle without dividing by 2.

Answer:

its 12 units long and unit c is 5 units long good luck! :D

Step-by-step explanation:

Ad+ae+bd+be so that is your solution

Answer:2, 2

2 factors

2 terms

This expression consist of 2 factors, each factor contains 2 terms

Step-by-step explanation:

Terms are single numbers, variables, or the product of a number and variable.

A factor is one part of a product.

The expression (a+b) (d+e) consists of two parts of a product, and each part is a factor. The first factor is (a+b) and the second is (d+e).

Each of the factors contains the sum of two variables. Variables connected by addition are separate terms. The expression (a + b) contains two terms: a and b. The expression (d + e) also contains tow terms.

The expressions (a+b) (d+e) consists of 2 factors, and each of there factors has 2 terms.

ANSWER

[tex]\left[ { \begin {array} {cc} 10&0& | 10\\-5&-8& | 9\\ \end {array}} \right] [/tex]

EXPLANATION

The given system of equations is

10x=10

-5x-8y=9

We can rewrite this as:

10x+0y=10

-5x-8y=9

The augmented matrix is the combination of the coefficient matrix and the constant matrix.

The coefficient matrix is

[tex] \left[ { \begin {array} {cc} 10&0\\ - 5& - 8\\ \end {array}} \right] [/tex]

The constant matrix is

[tex] \binom{10}{9} [/tex]

The augmented matrix is

[tex]\left[ { \begin {array} {cc} 10&0& | 10\\-5&-8& | 9\\ \end {array}} \right] [/tex]

The augmented matrix is:

         [tex]\begin{bmatrix}10 & 0| & 10\\ -5 &-8| & 9\end{bmatrix}[/tex]

The steps of an augmented matrix are as follows:

The system of equation is:

[tex]10x=10\\and\\-5x-8y=9[/tex]

Hence, the system could be written in the form:

[tex]AX=b[/tex]

where:

[tex]A=\left[\begin{array}{ccc}10&0\\-5&-8\end{array}\right][/tex]

[tex]X=\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

and

[tex]b=\left[\begin{array}{ccc}10\\9\end{array}\right][/tex]

Hence, the augmented matrix  is:

    [tex]\begin{bmatrix}10 & 0| & 10\\ -5 &-8| & 9\end{bmatrix}[/tex]

Answer:

the rule is add 7 i thinso it would be m+7

Step-by-step explanation:

Answer:

? = 7

Step-by-step explanation:

We know it's 7 because,

2 + 7 = 9

4 + 7 = 11

8 + 15 = 7

11 + 7 + 18

Hey, this is easy! Why not ask your parents?

Answer:

x ≈ 11.7

Step-by-step explanation:

When 2 secants are drawn from an external point to a circle then

The products of the measures of one secant's external part and the entire secant is equal to the product of the measures of the other secant's external part and that entire secant, that is

3(3 + x) = 4(4 + 7)

9 + 3x = 4 × 11 = 44 (subtract 9 from both sides )

3x = 35 ( divide both sides by 3 )

x ≈ 11.7

Answer:

Step-by-step explanation:

We know: the sum of the measures of triangle angles is 180°.

Therefore we have the equation:

[tex]2x+(3x-10)+50=180\\\\(2x+3x)+(-10+50)=180\\\\5x+40=180\qquad\text{subtract 40 from both sides}\\\\5x+40-40=180-40\\\\5x=140\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{140}{5}\\\\x=28[/tex]

The sum of all the angles of a triangle is 180°

This means you have to add all the angles together and set it equal to 180. Here is the formula:

50 + 2x + 3x - 10 = 180

Now you solve for x

Step 1: Combine like terms

(50 + (-10) ) + (2x + 3x) = 180

40 + 5x = 180

Step 2: Subtract 40 to both sides

(40-40) + 5x = 180 - 40

5x = 140

Step 3: Isolate x by dividing 5 to both sides

[tex]\frac{5x}{5}  = \frac{140}{5}[/tex]

x = 28

Check: 50 + 2(28) + 3(28) - 10 = 180

50 + 56 + 84 - 10 = 180

180 = 180

Therefore your value of x is 28!

Hope this helped!

it has infinitely many solutions

Answer:it has many solutions

Answer:

The volume of the irregular figure is [tex]470\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the irregular figure is equal to

[tex]V=BL[/tex]

where

B is the area of the front of the L-shaped figure

L is the length of the figure

Find the area B

The area of of the front of the L-shaped figure is equal to the area of two rectangles

[tex]B=(9)(3)+(9-5)(8-3)[/tex]

[tex]B=(9)(3)+(4)(5)[/tex]

[tex]B=27+20=47\ cm^{2}[/tex]

we have that

[tex]L=10\ cm[/tex]

Find the volume

[tex]V=BL[/tex]

[tex]V=(47)(10)=470\ cm^{3}[/tex]

The answer is:

We will have to fill 226.194 cubic inches.

To solve the problem, we need to find the volume of the flower vase, and then, calculate the two third parts of its volume. Also, from the statement we know that the shape of the flower vase is a right cylinder, since the only given information about it, is its diameter and height.

We can calculate the volume of a right cylinder using the following equation:

[tex]V_{Cylinder}=\pi radius^{2}*height[/tex]

So, we are given the following information:

[tex]diameter=6in\\radius=\frac{diameter}{2}=\frac{6in}{2}=3in\\height=12in[/tex]

Then,

Substituting the given information, and calculating, we have:

[tex]V_{Cylinder}=\pi *(3in)^{2}*12in=108\pi=339.292in^{3}[/tex]

Now, calculating how many cubic inches are [tex]\frac{2}{3}[/tex] of the flower vase volume, we have:

[tex]VolumeToFill=CubicInchesToFill=\frac{2}{3}*Volume\\\\CubicInchesToFill=\frac{2}{3}*339.292in^{3} =226.194in^{3}[/tex]

Hence, we have that we will have to fill 226.194 cubic inches.

Have a nice day!

Answer:

[tex]72\pi\ in^{3}[/tex]

Step-by-step explanation:

step 1

Calculate the volume of the cylinder (flower vase)

The volume is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=6/2=3\ in[/tex] -----> the radius is half the diameter

[tex]h=12\ in[/tex]

substitute the values

[tex]V=\pi (3)^{2}(12)=108\pi\ in^{3}[/tex] ------> exact value

step 2

Calculate  2/3 of the volume

[tex]V=(2/3)108\pi=72\pi\ in^{3}[/tex]

8-2x = 10x+3 Subtract 3 from both sides

5-2x = 10x Add 2x to both sides

5 = 12x Divide 12 to both sides

Final answer X=5/12

The solution to the algebraic expression 8-2x=10x+3 is: x = 12/5

An algebraic expression in mathematics is defined as an expression which is made up of variables and constants, along with algebraic operations

We are given the algebraic expression as:

8 - 2x = 10x + 3

Using addition property of equality, add 2x - 3 to both sides to get:

8 - 2x + 2x - 3 = 10x + 3 + 2x - 3

5 = 12x

x = 12/5

x = 2.4

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Answer: 91,445,760 ft³

Step-by-step explanation:

You know that the base of this pyramid is a square, then you can use the following formula to calculate its volume:

[tex]V=\frac{s^2h}{3}[/tex]

Where "s" is the lenght of any side of the base of the pyramid and "h" is the height of the pyramid.

You know that:

[tex]h=480ft\\s=756ft[/tex]

Then, you can substitute these values into the formula. So, you get that the volume of The Great Pyramid is:

[tex]V=\frac{(756ft)^2(480ft)}{3}=91,445,760ft^3[/tex]

Answer:

360 or D.

Step-by-step explanation:

Answer:

π/90 or 0.0035 units

Step-by-step explanation:

equation: length of the arc = ∠of the angle/360 * circumference

Substitute: S = 0.4/360 * 10π --> C = 2πr

Simplify: S = 1/900 * 10π

Simplify: S = π/90 ≈ 0.003489 units

Answer:

put the united states population over the world population you will get a simplified fraction to the ratio between them which is 1/23   easily you can multiply 23 by the USA population to get the world population so it is more than USA population 23 times  

3*10^8 / 6.9*10^9 = 1/23

then   23  *  3*10^8  = 6.9*10^9  

The world population is approximately 23 times larger than the population of the United States.

The question is asking us to determine how many times larger the world's population is compared to the population of the United States. It gives us the population of the United States as 3 x 108 and the world's population as 6.9 x 109. To solve this, we'll divide the world population by the US population.

The calculation is as follows: (6.9 x 109) / (3 x 108) which equals to 23

This means that the world population is approximately 23 times larger than the United States population.

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Answer:

52 sodas

Step-by-step explanation

h=hotdogs

s= sodas

1.5h+.5s=78.5

You know that Emily sold 35 hotdogs so you replace h with 35.

Therefore, 1.5(35)+.5s=78.5

52.5+.5s=78.5

.5s=26

s=52

Answer:

[tex]x1=\frac{-2+\sqrt{26/3}}{2}[/tex]

[tex]x2=\frac{-2-\sqrt{26/3} }{2}[/tex]

Step-by-step explanation:

To find the zeros of the quadratic function f(x)=6x^2 + 12x – 7 we need to factorize the polynomial.

To do so, we need to use the quadratic formula, which states that the solution to any equation of the form ax^2 + bx + c = 0 is:

[tex]x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]

So, the first thing we're going to do is divide the whole function by 6:

6x^2 + 12x – 7 = 0 -> x^2 + 2x - 7/6

This step is optional, but it makes things quite easier.

Then we using the quadratic formula, where:

a=1, b= 2, c = -7/6.

Then:

[tex]x=\frac{-2±\sqrt{2^{2}-4(1)(-7/6)}}{2}[/tex]

[tex]x=\frac{-2±\sqrt{4 +14/3}}{2}[/tex]

[tex]x=\frac{-2±\sqrt{26/3}}{2}[/tex]

So the zeros are:

[tex]x1=\frac{-2+\sqrt{26/3}}{2}[/tex]

[tex]x2=\frac{-2-\sqrt{26/3}}{2}[/tex]

Answer:

52$

Step-by-step explanation:

ok so 2 pins cost 4$ so if you buy one pin its 2$ correct? take 12 and multiply it by 2 and take 14 and multiply by 2,

12×2=24$

14×2=28$

add those two together and you get 52$

hence the answer is 16units

hope helps you!!!!!!

The equation of diagonals of kite are x = 0 and y = 0 and their point of intersection is (0,0)

A straight line is a one-dimensional figure that never ends and has no breadth.

Equation of line : y = mx + c

m - slope of the line

c - y intercept

Let the vertices of the Kite ABCD be A(-4 , 0), B(0 , 4), C(4 , 0), D(0 , -4)

The equation of Diagonal AC is y = 0

The equation of Diagonal BD is x = 0

The point of intersection of diagonals will be ( 0 , 0)

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Answer:

y= |x|-2.5

Step-by-step explanation:

The attached picture is the graph for the function y=|x|

The picture you asked differs in the origin of the graph, which resides in the point (0, -2.5).

So our equation should look like the following

y=a|x|+b

From the first point you have (0, -2.5), This means 0=a*|0|+b, we have obtained that b=-2.5

Now 'a' is the slope, we need to find another point in the graph. that would be (2.5, 0) (obtained from the given graph)

the slope is obtained using the equation

[tex]a=\frac{x_{2}-x_{1} }{y_{2}-y_{1}  }[/tex]

Where (x1, y1)= (0, -2.5), (x2,y2)=(2.5,0)

thus we have that a=1

So our equation is y=|x|-2.5

The answer is 9424.78

Reason:

4x - 8, 4x just means four of x, and eight less means to subtract 8.

Final answer:

The algebraic expression for 'eight less than four times a number' is '4x - 8', where x represents the number.

Explanation:

To write an algebraic expression for "eight less than four times a number," we first consider what the expression tells us:

Four times a number hints at a multiplication of some number, let's call it x, by 4, which we write as 4x.

Eight less than something means we need to subtract 8 from that something.

Therefore, combining these two steps, the algebraic expression that represents "eight less than four times a number" is 4x - 8.

Answer:

A - f

Step-by-step explanation:

Break each term down into its prime factors

7f^2 = 7 *f*f

12f = 2*2*3*f

The common term is f

Factor out the f

f(7f-12)

Since the sum of the opposite angles of a cyclic quadrilateral are supplementary, the value of d is equal to 80°.

In Mathematics, the measure of the sum of two (2) adjacent angles would be equal to 180º when a quadrilateral is inscribed in a circle. Generally speaking, any cyclic quadrilateral would have all of its vertices on the circumference of a circle.

This ultimately implies that, the sum of the opposite angles of a quadrilateral that is inscribed in a circle (cyclic quadrilateral) are supplementary;

m∠c + 96 = 180°

m∠d + 100 = 180°

Now, we can solve for the value of d by by subtracting 100 from both sides of the equation as follows;

m∠d + 100 - 100 = 180° - 100

m∠d = 80°

Answer:

Step-by-step explanation:

Look at the picture.

We have the triangles 30° - 60° - 90° and 45° - 45° - 90°.

The sides are in proportions:

30° - 60° - 90° ⇒ 1 : √3 : 2

45° - 45° - 90° ⇒ 1 : 1 : √2

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

[tex]SR=ST\sqrt3\to ST\sqrt3=2\sqrt3\qquad\text{divide both sides by}\ \sqrt3\\\\ST=2\\\\TR=2ST\to TR=2(2)=4\\\\RQ=TR\to RQ=4\to x=4[/tex]

This answer should be found using the distance formula. Steps are attached. Answer is 7.

Simple! All you need to do is graph the coordinates and then count the spaces in between, and the answer should be seven! Or, try -5 + 7, which would equal 2.

Answer:

From the information we can conclude that the triangle is a isosceles triangle.

First, we can calculate the hypotenuse by using pythagorean theorem:

√(6² + 6²) = √(36 + 36) =√64 = 8 (cm)

To calculate the area of the triangle, we first need to know the height of it.

Since this is a isosceles triangle, the altitude (which is also the height) will also  be the median of that triangle.

Then we also have a 90° angle, this triangle is also a right triangle, and in right triangle, the median will equal half of the hypotenuse.

From the reasoning above, we can now calculate the height of the triangle:

8/2 = 4(cm)

The area of the triangle should be:

S = hb/2 = (4 . 6)/2 = 12 (cm²)

Answer: b 11.9

Step-by-step explanation:

the chord and the line to the center can be used to create a triangle

the radius is the hypotenuse of this triangle

4.5squared + 11 squared= 11.9

Answer:

Step-by-step explanation:

a=12, b=10, c=?

a²+b²=c²

Using pythagorean theorem you can find that c= 2√61

Final answer:

The distance along the hypotenuse of the right triangle with 12 feet vertical height and 10 feet horizontal length is found using the Pythagorean Theorem. The calculated distance is approximately 15.62 feet.

Explanation:

To find the distance along the hypotenuse of a right triangle formed by five people with a total vertical height of 12 feet and a total horizontal length of 10 feet, we use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Thus, the formula is a² + b² = c².

In this case, we have:

Plugging these values into the Pythagorean Theorem gives:

12² + 10² = c²
144 + 100 = c²
244 = c²

Now, find the square root of 244 to get the length of the hypotenuse:

c = √244

c ≈ 15.62 feet (using three significant figures)

Therefore, the distance along the hypotenuse of the human triangle is approximately 15.62 feet.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x=3y&\text{subtract}\ 3y\ \text{from both sides}\\3x-2y=14\end{array}\right\\\\\left\{\begin{array}{ccc}x-3y=0&\text{multiply both sides by (-3)}\\3x-2y=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+9y=0\\3x-2y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad7y=14\qquad\text{divide both sides by 7}\\.\qquad\qquad y=2\\\\\text{put the value of y to the first equation:}\\x=3(2)=6[/tex]