Bea mixes 3 cups of cereal with 2 cups of
trail mix to make a snack for her family,
To make more of the same mix, how
many cups of cereal would she mix with
24 cups of trail mix?
a. 16 cups
B. 25 cups
c. 36 cups
d. 72 cups

Answer:

Triangle ABC has vertices A(0, 0), B(5, 2) and C(7,-3).

Show that ABC is isosceles.

If a triangle has vertices \(A(-2,4), \ B(6,2)\) and \(C(1,-1)\) then \(\triangle ABC\) is an isosceles right triangle.

An Isosceles Right Triangle is a right triangle that have two equal sides.

To know whether it is Isosceles Right Triangle or not we will use ,

Distance formula \(= \sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}\)

We have,

Vertices \(A(-2,4), \ B(6,2)\) and \(C(1,-1)\) of  \(\triangle ABC\).

So

To find \(AB\) coordinates of \(A\) and \(B\) will be used and so on;

\(AB=\sqrt{(6-(-2))^{2} +(2-4)^2} \ =\sqrt{(8)^2+ (-2)^2} \ = \sqrt{64+4} = \sqrt{68}\)

\(BC=\sqrt{(1-6)^{2} +(-1-2)^2} \ =\sqrt{(-5)^2+ (-3)^2} \ = \sqrt{25+9} = \sqrt{34}\)

\(AC=\sqrt{(1-(-2))^{2} +(-1-4)^2} \ =\sqrt{(3)^2+ (-5)^2} \ = \sqrt{9+25} = \sqrt{34}\)

Here,

\(BC=AC\) which means that two sides of  \(\triangle ABC\)  are equal i.e. it is isosceles triangle.

And,

Using Pythagoras theorem;

\(AC^2+BC^2=AB^2\)

\((\sqrt{34} )^2+(\sqrt{34} )^2=(\sqrt{68} )^2\)

\(34+34=68\)

\(68=68\)

So, this is satisfying the Pythagoras theorem.

So, this is Isosceles Right Triangle because it is satisfying the Pythagoras theorem and property of isosceles triangle..

Hence, we can say that if a triangle has vertices \(A(-2,4), \ B(6,2)\) and \(C(1,-1)\) then \(\triangle ABC\) is an isosceles right triangle.

To know more about Isosceles Right Triangle click here

https://brainly.com/question/3504067

#SPJ3

Answer:

-7/25

Step-by-step explanation:

1/5 ÷ (-5/7)

Copy dot flip

1/5 * -7/5

-7/25

A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.

Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.

The equation would be 3 x + 2 = 14.

So we can solve for the equation to be :

3x + 2 - 2 = 14 - 2

3x = 12

3 x / 3 = 12 / 3

x = 4

In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.

Find out more on equation solutions at https://brainly.com/question/2228446

#SPJ1

Answer:

Area = 200 + 50 + x

Step-by-step explanation:

Given

Length = 20

Width = 30

Side Walk = x

Required

Determine the area.

To do this we need to get the new worth and length by adding the length of the sidewalk.

This gives:

Length = 20 + x.

Width = 30 + x

So, area becomes.

Area = (20 + x)(30 + x)

Area = 600 + 20x + 30x + x²

Area = 200 + 50 + x²

The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

For more such questions on Amy:

https://brainly.com/question/25319846

#SPJ8

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Read more about similar shapes here: https://brainly.com/question/21823811

#SPJ1

Algorithm 2 is more efficient than Algorithm 1 because it only needs to loop through the numbers up to upper/11 instead of upper. This means that it will take fewer iterations to reach the result, making it more efficient than Algorithm 1.

Algorithm 1 will make upper/11 more checks than Algorithm 2, resulting in a slower runtime. Additionally, Algorithm 2 avoids the need to check the modulus of each number, further reducing the computation time. Algorithm 2 only needs to loop through the multiples of 11, which are always 11 apart from each other, so it can skip over the other numbers between them.

This makes Algorithm 2 much faster than Algorithm 1 because it is only looping through a fraction of the numbers.

Read more about Algorithm efficiency:

https://brainly.com/question/28992413

#SPJ4

Answer:

Charlotte's age = 30 years

Olivia's age = 50 years

Step-by-step explanation:

Present ages of Charlotte & Olivia = 6:10.

Then, their present ages are:

Charlotte = 6x

Olivia = 10x

Now, in 10 years, their ratio = 4:6

Then,

Ratio of Charlotte's & Olivia's present age + 10 years each = Ratio of their ages in 10 years

\(\frac{6x + 10}{10x + 10} = \frac{4}{6} \\6(6x + 10) = 4 (10x + 10) \: \: \: \: [\mathrm{cross\: multiplication}]\\36x + 60 = 40x + 40\\36x - 40x = 40 - 60\\4x = 20\\\boxed{\bf\:x = 5}\)

So,

Charlotte's present age \(= 6x = 6(5) = {\boxed{\bf\:30 \:years}\)

Olivia's present age = \(10x = 10(5) = \boxed{\bf\:50 \: years}\)

\(\rule{150pt}{2pt}\)

Answer:

If the decimal digits do not repeat in some known pattern, then the number is irrational. We cannot write it as a ratio or fraction of two integers. If it did have a pattern, then we can use algebra to find the fractional representation of that number. Based on what is shown, it looks like there is no pattern so that's why the value is irrational. The number is also a real number as this is the case with any number you'll encounter unless you're dealing with complex numbers (but your teacher may not have introduced that topic yet).

The standard deviation of U(4, 92) is  25.4034

Mean

Mean, in mathematics, is a quantity that has a value intermediate between those of the extreme members of some set. Several kinds of means exist, and the method of calculating a mean depends upon the relationship known or assumed to govern the other members.

Standard Deviation

Standard Deviation is a measure that shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a typical deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Mean Conductivity

Mean Conductivity is the amount of heat that moves through a slab with a unit cross-sectional area per second. Electrical conductivity is the amount of electricity that flows through a comparable slab per second when the potential gradient is unity.

Mean = (4 + 92)/2 = 48

Standard deviation = (92 - 4)/√12 = 25.4034

To learn more about Mean Conductivity visit:

brainly.com/question/591618

#SPJ4

Answer:

It's a spherical triangle and it's used in astronavigation to determine the observers position on the globe

Step-by-step explanation:

Is that right?

The formula that can be used to illustrate consecutive even numbers is a + 2.

It should be noted that the information is incomplete. Therefore, an overview will be given.

It should be noted that consecutive even numbers we the numbers that follow each other and have a difference of 2.

Examples of such numbers include 2, 4, 6,8, 10, etc.

In this case, the formula that can be used to illustrate consecutive even numbers is a + 2.

Learn more about integers on:

brainly.com/question/1558855

#SPJ1

a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

msec = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

for such more question on secant slope

https://brainly.com/question/27877215

#SPJ8

Answer:

i gussing add them together

Step-by-step explanation:

Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

To learn more on Rectangle click:

https://brainly.com/question/20693059

#SPJ1

Answer:

  41/56

Step-by-step explanation:

The LCD is 7×4 = 28. With that denominator, the two fractions are ...

  5/7 = 20/28

  3/4 = 21/28

The average of the two values will be ...

  (5/7 +3/4)//2 = (20 +21)/28/2 = 41/56

_____

Additional comment

  5/7 ≈ 0.714285... (6-digit repeat)

  3/4 = 0.75

Then numbers like 0.72 = 18/25, or 0.73 = 73/100, or 0.74 = 37/50 will all be between the given fractions.

Of course, any terminating or repeating decimal in that range will also be a rational number. For example, 0.727272727272... = 8/11  will be a rational number in the required range.

Answer:

4 1/10 when u have a inproper fraction like that every 10 is one whole number

Answer:

(a) 6.33 miles per hour

(b) $4.33 per hour

(c) $0.68 per mile

Step-by-step explanation:

Li drove 6 hours (5pm - 11pm) for a total of 38 miles
\(\textrm{(a) Her average speed is determined by the formula}\\\\\dfrac{\textrm{Distance Travelled}}{\textrm{Time taken for travel}}\)

\(\textrm{So average speed }=$\dfrac{38}{6} = 6.33$ \;\textrm{miles per hour}}\\\\\)

(b) She paid $26 for 6 hours of usage
\(\textrm{So cost per hour } = \dfrac{26}{6} = \$4.33\;\textrm{per hour}\\\\\)

(c) Cost per mile, c, can be computed as follows
\(c = \dfrac{\textrm{Total Cost}}{\textrm{Miles Traveled}}\)

\(\longrightarrow \dfrac{26}{38} = \$0.68\; \textrm{per mile}\)

Answer:

True

Step-by-step explanation:

A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,

AD ≅ BC (opposite side property)

AB ≅ CD (opposite side property)

<ABC = <BCD = <CDA = <DAC = \(90^{0}\) (right angle property)

Thus,

<ABC + <BCD + <CDA + <DAC = \(360^{0}\)

AC ⊥ BD (diagonals are perpendicular to each other)

AC ≅ BD (congruent property of diagonals)

Therefore, the parallelogram is a rectangle.

Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

Total quantities of plant-produced pollutants:

\(=(10.88+15.82+0.92) \ L\\\\=27.62\ L\)

We are three medicinal plants here, Pinecrest, Macon, and Ogala. The average number of contaminants produced by plants would be

\(\to 27.62\div 3 \\\\\to \frac{27.62}{3} \\\\ \to 9.206 \ L\)

The simplification of the given expression 4x(x-a) is 4(-x²+a).

So, -4x(x-a):

Therefore, the simplification of the given expression is 4(-x²+a).

Know more about expressions here:

https://brainly.com/question/723406

#SPJ9

Given data:

The given distance is d=2100-mile.

The given speed is s=65 miles per hour.

The expression for speed is,

Substitute the given values in the above expression.

Thus, the value of time is 32.30 hours.

For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

To learn more about Parallel line visit:

https://brainly.com/question/17432060

#SPJ9

The proof of d^2y/dx^2 - 2 cot x dy/dx +3y = 0 is determined as 6cos²xsinx - 3sin³x - ​6cos²xsinx  + 3sin³x = 0

The equation is given as;

\(\frac{d^2y}{dx^2} - 2\ cotx \ \frac{dy}{dx} \ + 3y = 0 \ \ ---(1)\)

y = sin³x

y = sin³x

let u = sinx  (du/dx = cosx)

y = u³

dy/du = 3u²

\(\frac{dy}{dx} = \frac{dy}{du} \ .\ \frac{du}{dx} \\\\\)

dy/dx = 3u² x cosx

dy/dy = 3sin²xcosx

y' = 3sin²xcosx

y' = 3sin²xcosx

let u = sin²x  (du/dx = 2sinxcosx)

    v = cosx  (dv/dx = -sinx)

\(y'' = \frac{d^2y}{dx^2} = V\frac{du}{dx} + U\frac{dv}{dx}\)

y'' = 3[cosx(2sinxcosx) + sin²x(-sinx)]

y'' = 6cos²xsinx  - 3sin³x

Substitute first derivative and second derivative of y in equation (1)

\(\frac{d^2y}{dx^2} - 2\ cotx \ \frac{dy}{dx} \ + 3y \\\\(6cos^2xsinx \ - \ 3sin^3x) \ - \ 2(\frac{cosx}{sinx} )(3sin^2xcosx) \ + 3(sin^3x) \\\\6cos^2xsinx \ - \ 3sin^3x \ - 6cos^2xsinx \ + \ 3sin^3x = 0 \ \ proved\)

Learn more about differentiation here: https://brainly.com/question/25081524

The expression can be rewritten by given term as;  3^15

We need to simplify the expression below:

(3^2 x 3^3)^3

Remember that we can add these exponents, so we get:

(9 x 9)^3 = 81^3

Then we can rewrite this as:

531441

Takin the product between the exponents we will get:

(3^5)^3

Thus, the solution is 3^15

Read more about expressions at:

brainly.com/question/15775046

#SPJ1

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

First, I like to covert 2 1/3 to an improper fraction, 7/3. Then you can do Keep Change Flip. Keep the 42, change divide to multiply and flip 7/3 to 3/7. 42/1 * 3/7 = 18

Answer:

190 in²

Step-by-step explanation:

Cut the shape into simpler ones:

A=6 x 6= 36 in²

A=7x22= 154 in²

A=36 + 154= 190 in²

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

To learn more about line plot

https://brainly.com/question/16321364

#SPJ8