3. The FFA had a fundraiser by selling hot dogs for $1.50 and drinks for $2.00. Their total sales were $400.
a) Write an equation to calculate the total of $400 based on the hot dog and drink sales.
b) Graph the relationship between hot dog sales.

Part A

The yard is a quadrilateral with the following corner points

I'll label those points A through D in the order presented above.

From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.

In short: side AB is 40 feet long.

The length of side BC is not as simple. We'll need the distance formula.

[tex]B = (x_1,y_1) = (0,40) \text{ and } C = (x_2, y_2) = (40,50)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-40)^2 + (40-50)^2}\\\\d = \sqrt{(-40)^2 + (-10)^2}\\\\d = \sqrt{1600 + 100}\\\\d = \sqrt{1700}\\\\d = \sqrt{100*17}\\\\d = \sqrt{100}*\sqrt{17}\\\\d = 10\sqrt{17}\\\\d \approx 41.2311\\\\[/tex]

Segment BC is exactly [tex]10\sqrt{17}[/tex] feet long, which is about 41.2311 feet.

Use the distance formula again to find the distance from point C(40,50) to D(50,0)

[tex]C = (x_1,y_1) = (40,50) \text{ and } D = (x_2, y_2) = (50,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(40-50)^2 + (50-0)^2}\\\\d = \sqrt{(-10)^2 + (50)^2}\\\\d = \sqrt{100 + 2500}\\\\d = \sqrt{2600}\\\\d = \sqrt{100*26}\\\\d = \sqrt{100}*\sqrt{26}\\\\d = 10\sqrt{26}\\\\d \approx 50.9902\\\\[/tex]

Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.

We have these side lengths:

AB = 40

BC = 41.2311 (approximate)

CD = 50.9902 (approximate)

AD = 50

Add up those four sides and we'll get the perimeter of the quadrilateral.

AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213

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

Part B

The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).

This 15 by 20 rectangle has an area of 15*20 = 300 square feet.

The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.

The area of the trapezoid is

A = h*(b1+b2)/2

A = 15*(20+35)/2

A = 412.5

That decimal value is exact.

Add it onto the area of the rectangle

412.5+300 = 712.5

[tex]~~~5 \log 3 + \log4 \\\\=\log 3^5 + \log 4~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log(3^5 \cdot 4)~~~~~~~~~~~~~~~~~~~~~~;[\log_b(mn) = \log_b m + \log_b n]\\\\=\log(972)[/tex]

Answer:180 or halfwayStep-by-step explanation:90 is 1/4 and 360 is a full rotation so it rotated halfway all together.

Answer:

A) 2¹²

Step-by-step explanation:

Given :

Equate the equation to y :

Substituting in the expression :

Answer:

2n + 3n equals to 5n in the end, so just set n equal to literally any number :)

Step-by-step explanation:

Example:

Let n = 1000

2(1000) + 3(1000) = 5(1000)

5000 = 500

Basically, plug in the number and solve on both sides each time. You will know you've demonstrated it if it's equal on both sides

Answer:

2n + 3n equals to 5n in the end, so just set n equal to literally any number

Step-by-step explanation:

Example:

Let n = 1000

2(1000) + 3(1000) = 5(1000)

5000 = 500

Basically, plug in the number and solve on both sides each time. You will know you've demonstrated it if it's equal on both sides

Answer:

y=2/3x+4

Step-by-step explanation:

4 is y-intercept

2/3 is  the slope (rise/run)

Answer: y = [tex]\frac{2}{3}[/tex]x + 4

Step-by-step explanation:

    This is in slope-intercept form. We are missing the m and the b value. See attached for more information.

[m aka the slope]

   Starting from point (-6, 0), counting up 2 units, then right 3 units to point (-3, 2), gives us a slope of [tex]\frac{2}{3}[/tex] via rise-over-run

[b aka the y-intercept]

   The line intersects the y-axis at positive 4.

-> This value is "4"

Answer:

[tex]\boxed{\bf 7 \times 10 {}^{ - 3}} [/tex]

Step-by-step explanation:

Write 0.7 *10^-2 into scientific notation:

Hope this helps! ^^"

Answer:

[tex]7 \times 10^{-3}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}\dfrac{6.3 \times 10^{-5}}{9 \times 10^{-3}} & =\dfrac{6.3}{9} \times \dfrac{10^{-5}}{10^{-3}}\\\\& = 0.7 \times \dfrac{10^{-5}}{10^{-3}}\end{aligned}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\begin{aligned}\implies 0.7 \times \dfrac{10^{-5}}{10^{-3}} &=0.7 \times 10^{-5-(-3)}\\& = 0.7 \times 10^{-2}\end{aligned}[/tex]

[tex]\textsf{Rewrite}\:0.7\:\textsf{as}\: 7 \times 10^{-1}:[/tex]

[tex]\implies 0.7 \times 10^{-2}=7 \times 10^{-1} \times 10^{-2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \times a^c=a^{bc}:[/tex]

[tex]\implies 7 \times 10^{-1} \times 10^{-2}=7 \times 10^{-3}[/tex]

Step-by-step explanation:

Triangle MŇO is congruent to Triangle UŤS

NO=4

MN=4

MO=5.6( Which is 140% bigger than 4)

UT=10

TS=10(Therefore this also should be 10)

US=14(Which is 140% bigger than 10)

I think this is the solution but I am not 100% sure

Answer:

x=14

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Because.....

  -11 - 10 = -21

-32 - (-11) = -21

This tells us that the sequence is adding by -21, which is why the next 2 terms will be -53 and - 74 since....

-32 + -21 = -53

-53 + -21 = - 74

Hence, the answer is A.

The surface area of solid Y given the ratio of volume to surface area of solid X is 2,369.25cm²

Volume:

Surface area:

Ratio of volume to surface area of solid X and Y respectively

64 : 208 = 729 : x

64/208 = 729/x

64 × x = 208 × 729

64x = 151,632

x = 151,632 / 64

x = 2,369.25cm²

Learn more about surface area:

https://brainly.com/question/76387

#SPJ1

If the function is h(t) = - 4.9t² + 39.2t + 5. Then the maximum height will be 83.4 meters.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The function is given as

h(t) = - 4.9t² + 39.2t + 5

Then the differentiation of the function will be

h'(t) = - 9.8t + 39.2

For the maximum height, put h'(t) equals zero. Then we have

              h'(t) = 0

- 9.8t + 39.2 = 0

                  t = 4

Then the maximum height will be

h(t) = - 4.9(4)² + 39.2 x 4 + 5

h(t) = - 4.9 x 16 + 39.2 x 4 + 5

h(t) = - 78.4 + 156.8 + 5

h(t) = 83.4 meters

More about the differentiation link is given below.

https://brainly.com/question/24062595

#SPJ1

Answer:

7/2                

Step-by-step explanation:

3 hours and 30 minutes = 7/2 in improper fraction

1 hour = 60 minutes

30 minutes = 30 minutes * 1 hour/60 minutes =30/60 = 1/2 hour

3 hours and 30 minutes:

= 3 hours + 1/2 hour

= 3 1/2 hours

= [(2 * 3)+1]/2

= [6+1]/2

= 7/2

Answer:

x=14

Step-by-step explanation:

collect like terms, like so

Answer:4(x−2)−8=4+2x

Use the distributive property to multiply 4 by x−2.

4x−8−8=4+2x

Subtract 8 from −8 to get −16.

4x−16=4+2x

Subtract 2x from both sides.

4x−16−2x=4

Combine 4x and −2x to get 2x.

2x−16=4

Add 16 to both sides.

2x=4+16

Add 4 and 16 to get 20.

2x=20

Divide both sides by 2.

x=

2

20

​

Divide 20 by 2 to get 10.

x=10

Step-by-step explanation:

Answer:

potential to kinetic energy

Answer:

To the nearest 100 miles, Jessica drove about 300 miles since we haven't reached 350 miles.  If we have a number that is greater than 350 miles than we would've rounded it up to 400 but since ours is less than that we round down to the nearest hundred which is 300 miles.

The image of dilating the points by a scale factor 3.5 with centre of enlargement (4, -6) is (-7, 14), (0, 14), (-7,7) and (0, 7)

The coordinates are given as:

(2,-2) (4,-2) (2,-4) (4,-4)

The scale factor is given as:

k = 3.5

The center of enlargement is given as:

(a,b) = (4, -6)

The image of dilation is calculated using:

[tex](x,y) \to (k(x -a), k(y -b))[/tex]

So, we have:

A = (3.5(2 -4), 3.5(-2 +6))

A = (-7, 14)

B = (3.5(4 -4), 3.5(-2 +6))

B = (0, 14)

C = (3.5(2 -4), 3.5(-4 +6))

C = (-7,7)

D = (3.5(4 -4), 3.5(-4 +6))

D = (0, 7)

Hence, the image of dilating the points is (-7, 14), (0, 14), (-7,7) and (0, 7)

Read more about dilation at:

https://brainly.com/question/3457976

#SPJ1

The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%

An equation is an expression that shows the relationship between two or more numbers and variables.

The z score is given by:

z = (raw score - mean) / (standard deviation / √sample size)

Given mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages, hence, for x > 10:

z = (10 - 8.6) / (4.3 / √39) = 2.03

P(x > 10) = P(z > 2.03) = 1 - P(z < 2.03) = 1 - 0.9788 = 0.0212

The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

A. .0210

Step-by-step explanation:

I'm taking the test... could be wrong though...

Answer:

10.5 baskets

Step-by-step explanation:

The median is the middle value, but for this one just add the two in the middle and divide by 2.

4+3 = 7

Each ball is 3 baskets

7×3 = 21

21/2 = 10.5

Using an exponential function, it is found that it will take 3,252 years for the sample to degrade to 4.5kg.

It is given by:

[tex]A(t) = Pe^{-kt}[/tex]

In which:

The half-life is of 21,400 years, hence, A(21400) = 0.5P, and this is used to find k.

[tex]A(t) = Pe^{-kt}[/tex]

[tex]0.5P = Pe^{-21400k}[/tex]

[tex]e^{-21400k} = 0.5[/tex]

[tex]\ln{e^{-21400k}} = \ln{0.5}[/tex]

[tex]-21400k = \ln{0.5}[/tex]

[tex]k = -\frac{\ln{0.5}}{21400}}[/tex]

k = -0.00003239005

Hence, considering the initial mass is of P = 5 kg, the amount after t years is given by:

[tex]A(t) = 5e^{-0.00003239005t}[/tex]

The amount will be of 4.5 kg at t for which A(t) = 4.5, hence:

[tex]4.5 = 5e^{-0.00003239005t}[/tex]

[tex]e^{-0.00003239005t} = 0.9[/tex]

[tex]\ln{e^{-0.00003239005t}} = \ln{0.9}[/tex]

[tex]-0.00003239005t = \ln{0.9}[/tex]

[tex]t = -\frac{\ln{0.9}}{0.00003239005}[/tex]

t = 3252.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The correlation coefficient is 0.92

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.

In other words, it reflects how similar the measurements of two or more variables are across a dataset.

When one variable changes, the other variables change in the same direction or opposite direction.

Perfect positive correlation :When one variable changes, the other variables change in the same direction.

Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.

[tex]\rm r = \dfrac{\sum (x_{i}-x')(y_{i}-y')}{\sqrt {\sum (x_{i}-x')^{2} \sum (y_{i}-y')^{2}}}[/tex]

After calculation we get

r = 0.92

Therefore it is a Perfect positive correlation

To know more about Correlation Coefficient

https://brainly.com/question/27226153

#SPJ1

Answer:

IT IS 43./45455/.34 LIKE WHEN U ADD 10 TIMES 10 AND DIVIDED 2,000 FROM 20 U THAT ANSWER

Answer:

8 then 2 and reflection on y axes

Answer:

Here is the solution...hope it helps:)

Step-by-step explanation:

[tex]\huge{\color{black}{\fbox{\color{pink}{\colorbox{pink}{\color{red}{Answer ✨☑️}}}}}}[/tex]

The number of terms are 8. Step-by-step explanation: Given : The sum n terms of an A.P is 136 the common difference is 4 and last term is 31.

Answer:

Sn=2n{2a+(n−1)d}

a+(n−1)d=31⇒a=31−4(n−1)

∴136=2n{2[31−4(n−1)]+(n−1)d}

n[70−8n+4n−4]=272

n(66−4n)=272

4n2−66n+272=0

2n2−33n+136=0

2n(n−8)−17(n−8)=0

(2n−17)(n−8)=0

∴n=8

Answer:

The area of triangle ABC is 60 mm^2

Step-by-step explanation:

x = the area of triangle ABC

15/6 * x/24

x=60

Answer:

  (d)  150 mm²

Step-by-step explanation:

The scale factor between the triangles is the ratio of the lengths of corresponding sides. The area ratio is the square of the scale factor.

__

ΔABC is larger than ΔPRT by the factor ...

  AC/PT = 15/6 = 5/2

The area of ΔABC is the square of this factor times the area of ΔPRT:

  area ABC = (5/2)²×area PRT

  area ABC = (25/4)×(24 mm²)

  area ABC = 150 mm²

Answer:

244.93

Step-by-step explanation:

area formula for trapezoid:1/2*(b1+b2)*h

area formula for semi circles: (3.14*r^2)/2

so then we cut the figure to make a semi cirlce and trapazoid

semicircle- 14 is the full diameter, divide by 2 to make 7, 7×3.14×7)/2=76.93

trapezoid: base one is 18. base 2 is 14. 18+14=32 then times that by 10.5 which is 336 and divide that by 2 is 168

add both and you get 244.93

Answer: 48

Step-by-step explanation: 50 is the hypotenuse

14 is the opposite side - its opposite of angle Q

Answer:

[tex]\boxed{\bf \sf number : \ \frac{4}{5} }[/tex]

Explanation:

Let the number be n

According to students Condition:

[tex]\rightarrow \sf \dfrac{3}{2} \ x \ n \quad = \quad \dfrac{3n}{2}[/tex]

What He actually Did:

[tex]\rightarrow \sf n \div \dfrac{3}{2} \quad = \quad n \ x \ \dfrac{2}{3} \quad = \quad \dfrac{2n}{3}[/tex]

He got a smaller number by 2/3, so:

[tex]\rightarrow \sf \dfrac{3n}{2} - \dfrac{2n}{3} = \dfrac{2}{3}[/tex]

make the denominator's same

[tex]\rightarrow \sf \dfrac{3(3n)}{6} - \dfrac{2(2n)}{6} = \dfrac{2}{3}[/tex]

multiply the integers

[tex]\rightarrow \sf \dfrac{9n}{6} - \dfrac{4n}{6} = \dfrac{2}{3}[/tex]

Join the fractions

[tex]\rightarrow \sf \dfrac{9n-4n}{6} = \dfrac{2}{3}[/tex]

Subtract integers

[tex]\rightarrow \sf \dfrac{5n}{6} = \dfrac{2}{3}[/tex]

Cross multiply

[tex]\rightarrow \sf n = \dfrac{6 \ * \ 2}{5 \ * \ 3} \quad = \quad \dfrac{4}{5}[/tex]

Lets see

the number be x

The expression is

Answer:

[tex]12k^3 -k^2-36k-20[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex](4k + 5)(3k^2 - 4k - 4)[/tex]

[tex](4k * 3k^2)+(4k*-4k)+(4k*-4)+(5*3k^2)+(5*-4k)+(5*-4)[/tex]

[tex]12k^3-16k^2-16k+15k^2-20k-20[/tex]

Step 2:  Combine like terms

[tex]12k^3+(-16k^2+15k^2)+(-16k-20k)-20[/tex]

[tex]12k^3 -k^2-36k-20[/tex]

Answer: [tex]12k^3 -k^2-36k-20[/tex]

Answer:

The answer is attached.