Lesson 4.03
Madame Dumas has a rather extensive art collection and the overall value of her collection has been
increasing each year. Three years ago, her collection was worth $250,000. Two years ago, the value of the
collection was $525,000 and last year, the collection was valued at $1,102,500.
Assume that the rate at which Madame Dumas's art collection's value increase remains the same as it has
been for the last three years. The value of the art collection can be represented by a geochetric sequence.
The value of the collection three years ago is considered the first term in the sequence.
A) Write an explicit rule which can be used to determine the value of her art collection n years after that.
B) Use this rule to determine the value of her collection 9 years after she started tracking its worth rounded
to the nearest dollar

Answer:

y = 5x - 14

Step-by-step explanation:

*Parallel lines have the same slopes*

Rewrite your equation to slope-intercept form: y = mx + b

y = mx + b

y - 5x = 10 <== add 5x to both sides

   + 5x   + 5x

y = 5x + 10

The slope of the line that is parallel to this line is 5.

We need to find the y-intercept (b) for the parallel line using (2, -4):

y = 5x + b <== substitue 2 for x and -4 for y

-4 = 5(2) + b

-4 = 10 + b <== subtract 10 from both sides to isolate b

-10  -10

-14 = b

y = 5x + b changes to y = 5x - 14

Hope this helps!

Slope:-

Parallel lines have equal slope

Equation in point slope form

Based on the given conditions, formulate: 

34÷1 1/3

Find common denominator and write the numerators above common denominator:

34/3/3+1/3

Write the numerators over common denominator:

34/3+1/3

Calculate the sum or difference:

34/4/3

Divide a fraction by multiplying its reciprocal:34×3/4

Cross out the common factor:

17×3/2

Calculate the product or quotient:

51/2

get the result:

25.5 or 25 1/2

=25.5 or 25 1/2

Answer:

C.) 5 * 4^n-1

Step-by-step explanation:

Use the given method you use for finding the sequence with the terms.

Also K12 moment.

If it's wrong, please forgive me, I'm in the middle of the test as well.
I checked and I'm 99% sure this is the answer

Hope this helped despite being a little late!

Answer:

900 in^2

Step-by-step explanation:

Triangle area = ( b x h )/ 2

rectangle area = b x h

------------------------------------------

triangle:

30 * 40 / 2 = 600 in^2

rectangle:

30 * 20/2 = 300 in^2

---------------------------------------

600 + 300 = 900 in^2

Answer:

[tex]S_{n}=315[/tex]

Step-by-step explanation:

[tex]a_{1}=7\\a_{2}=9\\a_{n}=35\\[/tex]

d=9-7=2

no of terms n,

[tex]n=\frac{a_{n-a_{1}} }{d} +1[/tex]

[tex]n=\frac{{35}-{7}}{2} +1[/tex]

[tex]n=15[/tex]

sum of series,

[tex]S_{n}=\frac{n}{2} (a_{1}+a_{n})\\\\S_{n}=\frac{15}{2} (7+35})\\\\S_{n}=315[/tex]

Answer:

y = -2

Step-by-step explanation:

y - y₁ = m (x - x₁)

y + 2 = 0 (x + 4)

y + 2 = 0

Final simplified equation: y = -2

Hope this helps!

Answer:

x = 1.348331477 and 0.148331477

Step-by-step explanation:

TEPS USING THE QUADRATIC FORMULA2x(5x−2)+(3x−0.5)2=2x+3+10x−5+2x+3Use the distributive property to multiply 2x by 5x−2.10x2−4x+(3x−0.5)×2=2x+3+10x−5+2x+3Use the distributive property to multiply 3x−0.5 by 2.10x2−4x+6x−1=2x+3+10x−5+2x+3Combine −4x and 6x to get 2x.10x2+2x−1=2x+3+10x−5+2x+3Combine 2x and 10x to get 12x.10x2+2x−1=12x+3−5+2x+3 Subtract 5 from 3 to get −2.10x2+2x−1=12x−2+2x+3Combine 12x and 2x to get 14x.10x2+2x−1=14x−2+3Add −2 and 3 to get 1.10x2+2x−1=14x+1Subtract 14x from both sides.10x2+2x−1−14x=1Combine 2x and −14x to get −12x.10x2−12x−1=1Subtract 1 from both sides.10x2−12x−1−1=0Subtract 1 from −1 to get −2.10x2−12x−2=0This equation is in standard form: ax2+bx+c=0. Substitute 10 for a, −12 for b, and −2 for c in the quadratic formula, 2a−b±b2−4ac​​.x=2×10−(−12)±(−12)2−4×10(−2)​​Square −12.x=2×10−(−12)±144−4×10(−2)​​Multiply −4 times 10.x=2×10−(−12)±144−40(−2)​​Multiply −40 times −2.x=2×10−(−12)±144+80​​Add 144 to 80.x=2×10−(−12)±224​​Take the square root of 224.x=2×10−(−12)±414​​The opposite of −12 is 12.x=2×1012±414​​Multiply 2 times 10.x=2012±414​​Now solve the equation x=2012±414​​ when ± is plus. Add 12 to 414​.x=20414​+12​Divide 12+414​ by 20.x=514​+3​Now solve the equation x=2012±414​​ when ± is minus. Subtract 414​from 12.x=2012−414​​Divide 12−414​ by 20.x=53−14​​The equation is now solved.

x=514​+3​x=53−14​​

Answer:

$6.14.

Step-by-step explanation:

$30.70×20%

there will be after the tax and discount.

Answer:

9.99m

Step-by-step explanation:

d≈9.99m

C Circumference

31.4m

Using the formulas

C=2πr

d=2r

Solving ford

d=C

π=31.4

π≈9.99493m

Answer:

1:3, 24/8=3/1

Answer:

Empirical probability

Step-by-step explanation:

Empirical probability is data collected from experiment and real-life situation.

The "empirical probability" of an outcome is obtained by dividing the frequency of occurrence of an event by the number of trails of the experiment.

[tex]\Longrightarrow: \sf{P(E)=\dfrac{\text{number of times event occured}}{\text{number of trails}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

20

Step-by-step explanation:

2x2x5

Answer:

kate will have more money

Step-by-step explanation:

cuz Kate have 25$ × 6 weeks = 150$

in the other hand , Patty have 60$ before + ( 10$ × 6 weeks ) = 60$+ 60$ = 120$

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Volume of sphere = Volume of cubiod

↠ 4/3 πr³ = LBH

↠ 4/3 × 22/7 × r³ = 49 × 33 × 24

↠ 4/3 × 22/7 × r³ = 38808

↠ 4 × 22/7 × r³ = 38808/3

↠ r³ = 38808 × 3 × 7/4 × 22

↠ r³ = 441 × 21

↠ r³ = 9261

↠ r = 21 cm

Hence,

Answer:

21.00 cm to the nearest hundredth.

Step-by-step explanation:

The volume of the sphere will  be equal to the volume of the cuboid.

So 4/3 π r^3 =  49*33*24     where r = radius of the sphere.

r^3 = (49*33*24 ) / 4/3 π

r^3 = 38808 / 4.18879

      =  9264.728

r = ∛9264.728

  = 21.0028  cm.

Answer and explanation:

Take the area formula:

A = L * W

Then manipulate it to fit the context of which unknown you are finding:

Problem 1

[tex]\dfrac{36 = 4 * W}{4}[/tex]

[tex]9 = W[/tex]

So, the length of side c is 9 mm.

Problem 2

[tex]\dfrac{21 = W * 21}{21}[/tex]

[tex]1 = W[/tex]

So, the length of side a is 1 m.

Problem 3

[tex]\dfrac{49 = 7 * W}{7}[/tex]

[tex]7=W[/tex]

So, the length of side t is 7 cm.

Answer:

367/90

Step-by-step explanation:

As [tex]4.\bar{7}=4\frac{7}{9}[/tex], this means that [tex]0.4\bar{7}=4\frac{7}{90}=\frac{367}{90}[/tex], 1/10th of 4.7 repeated.

Step-by-step explanation:

[tex]area = l \times b[/tex]

[tex]area = \frac{3}{7} \times \frac{2}{9} [/tex]

[tex]area = \frac{6}{64} [/tex]

[tex]area = 0.09375units ^{2} [/tex]

Answer:

13.15

Step-by-step explanation:

Answer:

6a + 13

Step-by-step explanation:

2a + 4a = 6a

8 + 5 = 13

6a + 13

Answer: 6a+13

Step-by-step explanation:

2a+8+4a+5

2a+13+4a

now combine like terms:

2a+13+4a=

6a+13

To solve this problem

  ⇒ need to use the special right triangle theorem

    ⇒ 30-60-90 triangle theorem (look at diagram attached for the property)

Using the theorem:

            [tex]x\sqrt{3} =17\sqrt{3} \\x = 17[/tex]

             [tex]y = 2x = 2 * 17 =34[/tex]

Answers:

  x = 17 and y = 34

Hope that helps!

Answer:

[tex]0.41x^3-1.02xy[/tex] or [tex]0.4x^3-xy[/tex]

Step-by-step explanation:

[tex]\frac{2}{7}x(1.4x^2-3.5y) < == convert\ \frac{2}{7}\ to\ a\ decimal\\\\0.29x(1.4x^2-3.5y) < ==distribute\ 0.29x\\\\0.41x^3-1.02xy[/tex]

Can also be written as: [tex]0.4x^3-xy[/tex]

Hope this helps!

Answer: 3.75 Cups

3/4=_/20, to get that multiply the bottom number by each other, in doing so,you will get 15/20, now lets make 1/5= to 20, so we get 4/20 so therefore saying 4/20+4/20+4/20=12/20, so you can make 3 1/5 cups and you will have 3/20 (scoops? cups?) left of ice cream, so 3.75 cups

Step-by-step explanation: HOPE THIS HELPS U!!! LOV<3

The volume of a silo cylinder with radius of 8 feet and height of 36 feet is 7235 feet cube.

The volume of a cylinder can be calculated as follows;

Volume = πr²h

where

Therefore,

r = 8 ft

h = 36 ft

volume = 3.14 × 8² × 36

volume = 3.14 × 64 × 36

volume of the silo = 7234.56

Therefore, the volume of the cylindrical silo is 7235 ft³

learn more on volume here: https://brainly.com/question/27270919

The required y-intercept is (0, 7), and the horizontal asymptote y = 2. Option A is correct.

It is to detrmine the y-intercept and the horizontal asymptote of g(x) = 2x + 7.

A line can be defined as it is the shortest distance between two points on the graph called a line. Equation of the y = mx + c, where c is the y-intercept and m is the slope of the line.

The y-intercept of g(x) = 2x + 7 is the y-coordinate of a point where a line, curve, or surface intersects the y-axis i.e. (0, 7).

An asymptote of g(x) = 2x + 7 is a line that a graph approaches without touching i.e. y = 2.

Thus, The required y-intercept is (0, 7), and the horizontal asymptote y = 2. Option A is correct.

Learn more about lines here:

brainly.com/question/2696693

#SPJ2

Answer:

7 cups

Step-by-step explanation:

1 3/4 x 4 = 7

Karla will need 7 cups of sugar to serve 40 people.

Answer: Below

Step-by-step explanation:

Volume is based off of the formula (base × height/depth), with base being (width × length).

We know the three dimensions of the taller box, so:

7.75 × 2 × 12 = 186

The smaller box is 20% shorter. 12 × 0.8 gives us the 0% height, which is 9.6.

7.75 × 2 × 9.6 = 148.8

Since the problem is asking for the difference of the two volumes we do:

186 - 146.8 = 39.2

Our answer is 39.2

Answer:

KN = 11

Step-by-step explanation:

In right triangle LNM, by Pythagoras theorem:

[tex]LN=\sqrt{LM^2 -MN^2} \\ \\ \implies \: LN=\sqrt{ {(100)}^{2} -(80)^2} \\ \\ \implies \: LN=\sqrt{ 10000 -6400} \\ \\ \implies \: LN=\sqrt{ 3600} \\ \\ \implies \: LN=60[/tex]

In right triangle LNK, by Pythagoras theorem:

[tex]KN = \sqrt{LK^2-LN^2}[/tex]

[tex]\implies KN = \sqrt{(61)^2-(60)^2}[/tex]

[tex]\implies KN = \sqrt{3721-3600}[/tex]

[tex]\implies KN = \sqrt{121}[/tex]

[tex]\implies\huge{\orange{ KN =11}}[/tex]

Answer:

[tex] \: [/tex]

Step-by-step explanation:

Before, Finding the length of KN, we must have to find the length of LN. So

[tex] \: [/tex]

Here, LNM is a right angled triangle where measure of two sides are given and we are to find the measure of the third side LN(Perpendicular).

[tex] \: [/tex]

We'll find the measure of third side with the help of the Pythagorean theorem.

[tex] \\ {\longrightarrow \pmb{\sf {\qquad (Base) {}^{2} + (Perpendicular {)}^{2} = (Hypotenuse {)}^{2} }}} \\ \\[/tex]

Here,

[tex] \: [/tex]

So, substituting the values in the above formula we get :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (NM) {}^{2} + (LN {)}^{2} = ( LM{)}^{2} }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (80) {}^{2} + (LN {)}^{2} = ( 100{)}^{2} }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = ( 100{)}^{2} - (80) {}^{2}}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = 10000 - 6400}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = 3600}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad LN = \sqrt{3600} }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad LN = \frak{60}}}} \\ \\[/tex]

Therefore,

[tex] \\ [/tex]

As, we found the length of LN, now we can find the length of KN.

Where,

So, in the right angled triangle LKN, by Pythagorean theorem we get,

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} + (LN {)}^{2} = ( LK{)}^{2} }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} + {60}^{2} = ( 61{)}^{2} }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} = ( 61{)}^{2} - {(60)}^{2}}}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} =3721 - 3600}}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} = 121}}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad KN = \sqrt{121} }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad KN = \frak{11} }}} \\ \\[/tex]

Therefore,

Answer: 15 ft

Step-by-step explanation:

You basically add all the sides:

3 + 3 + 3 + 3 +3 = 15 ft

And if you have to add 12 ft then the answer should be 27 ft in total.

I hope this helped!

Answer:

83.75 yards

Step-by-step explanation:

3.75 x 67 = 251.25ft

251.25 / 3 = 83.75yards