at most how many homes can latrell roofing service build and still have 6 boxes shingles left?

The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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Answer:

 (b)  f(x) = -1/x⁹ and g(x) = -8x +4

  (d)  f(x) = x⁹ and g(x) = -1/(-8x +4) . . . . . alternate solution

Step-by-step explanation:

You want to decompose h(x) = -1/(-8x +4)⁹ into f(x) and g(x) such that h(x) = f(g(x)).

The composition h(x) = f(g(x)) means that the function g(x) will replace x in the definition of f(x).

It is often convenient to look at the order of operations when asked to decompose a function like this. Here, the parenthetical expression (-8x+4) is raised to the 9th power and its opposite reciprocal is found. This suggests that f(x) can be a function that finds the opposite reciprocal of a 9th power,  matching choice B. Thus, a reasonable choice is ...

  (b)  f(x) = -1/x⁹ and g(x) = -8x +4

We note that the reciprocal of a 9th power is also the 9th power of a reciprocal. A negative sign is preserved by the odd power. This means that another reasonable choice for the decomposition is ...

  (d)  f(x) = x⁹ and g(x) = -1/(-8x +4)

__

Additional comment

We list choice B first because that one is probably the one you're supposed to claim as the answer. However, this question has two correct decompositions among those listed. You may want to discuss this with your teacher.

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The individuals in this data set are the different apartment complexes: Grand Vistas, Maple Ridge, Old Mill, and Willow Brook.

The individuals in this data set are the different apartment complexes that Camille is comparing. The data provides information on the complex name, number of bedrooms and bathrooms, rent amount, whether rent includes heat, and the amenities offered.

Grand Vistas:

Bedrooms: 2

Bathrooms: 2

Rent: $990

Rent includes heat: No

Amenities: Fitness center, pool

Maple Ridge:

Bedrooms: 2

Bathrooms: 1.5

Rent: $685

Rent includes heat: Yes

Amenities: Fitness center, pool

Old Mill:

Bedrooms: 2

Bathrooms: 1.5

Rent: $790

Rent includes heat: No

Amenities: Pool

Willow Brook:

Bedrooms: 2

Bathrooms: 2

Rent: $885

Rent includes heat: No

Amenities: Jacuzzi

Each apartment complex is represented as an individual in the data set. Camille has collected specific details for each complex, including the number of bedrooms and bathrooms, the rent amount, whether heat is included in the rent, and the amenities provided.

This data set allows Camille to compare different apartment complexes based on these attributes. She can evaluate factors such as rent prices, included amenities, and the presence of heat in the rent. This information will assist Camille in making an informed decision about which apartment complex may be the most suitable for her needs and preferences.

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Step-by-step explanation:

hope you have a great day

The value of x will be;

⇒ x = 13.9

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now,

Since, We know that;

The sine rule is;

⇒ sin A / a = sin B / b = sin C / c

By given figure, we get;

⇒ sin 83°  / x = sin 68° / 13

⇒ sin 83° × 13 / sin 68° = x

⇒ x = 0.99 × 13 / 0.92

⇒ x = 13.9

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The laws of cosine and sine and the given parameters can be used to

calculate the measure of angles and distances.

Correct responses:

Question 1: A. m∠C = 76°, a = 7.84, b = 4.37

Question 2: C. 1 triangle

Question 3: D. 31.2 miles

Question 4: A. b = 10.799

Question 5: C. 28.9°

Question 1:

If m∠A = 72°

m∠B = 32°

c = 8

Therefore;

m∠C = 180° - 72° - 32° = 76°

\(\displaystyle \frac{a}{sin(72^{\circ})} = \mathbf{ \frac{8}{sin(76^{\circ})} }\)

\(\displaystyle a = \mathbf{\frac{8}{sin(76^{\circ})} \times sin(72^{\circ})} \approx 7.84\)

\(\displaystyle b = \frac{8}{sin(76^{\circ})} \times sin(32^{\circ}) \approx 4.37\)

The correct option is therefore;

Question 2

The given parameters are;

\(\displaystyle B = \mathbf{ \frac{\pi}{6} }\)

\(\displaystyle \frac{\pi}{6} = 30^{\circ}\)

a = 20

b = 10

Therefore,  by the law of cosine we have;

Which gives;

10² = 20² + c² - 2×20×c×cos(30°)

100 = 400 + c² - 20·c·(√3)

c² - 20·√3 ·c + 300 = 0

\(\displaystyle c = \frac{20 \cdot \sqrt{3} \pm\sqrt{1200-4 \times 1 \times 300} }{2 \times 1} = \mathbf{ 10 \cdot \sqrt{3} }\)

Therefore, given that c has only one value, the three sides of the triangle are known, and the number of triangles unique triangles by Side-Side-Side description is; C. 1 triangle

Question 3

The distance between the weather station = 24 miles

The bearing of the storm from weather station A = N17°W

The bearing of the storm from weather station B = N48°W

The angle formed at point C in ΔABC  is therefore;

108° - 42° - 107° = 31°

By sine rule, we have;

\(\displaystyle \frac{24}{sin(31^{\circ})} =\mathbf{\frac{x}{sin(42^{\circ})} }\)

Where:

x = The distance from weather station A from the storm

Which gives;

\(\displaystyle x = \frac{24}{sin(31^{\circ})} \times sin(42^{\circ}) \approx \mathbf{31.2 \ miles}\)

Question 4

∠A = 52°

∠C = 57°

Side BC = 9

Therefore;

∠B = 180° - 52° - 57° = 71°

∠B = 71°

According to the law of sines, we have;

\(\displaystyle \frac{b}{sin(71^{\circ})}= \mathbf{ \frac{9}{sin(52^{\circ})} }\)

Therefore;

\(\displaystyle b = \frac{9}{sin(52^{\circ})} \times sin(71^{\circ}) \approx \mathbf{ 10.799}\)

Question 5

Given:

Label of the vertex of the triangle formed are; The golfer, spectator, hole

Distance from the golfer to the hole = 200 yards

Distance from the golfer to the spectator = 140 yards

Vertex angle at the spectator = 110°

By using the law of sines, we have;

\(\displaystyle \frac{200}{sin(110^{\circ})} = \frac{140}{sine \ of \ the \ angle \ at \ the \ hole, \ \phi} \)

Therefore;

\(\displaystyle sin(\phi) = \mathbf{ \frac{140}{200} \times sin(110^{\circ})} = 0.7 \times sin(110^{\circ})\)

The angle at the hole, ∅ = arcsin(0.7×sin(110°)) ≈ 41.13°

Therefore;

The angle that the golfer has = 180° - 110° - 41.1° = 28.9°

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Using distributive property, the solution to the given expression is: 50v - 40w + 20

The Distributive Property is a term which is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

For example:

4(3 + 5)

According to the distributive property, you first have to multiply out the bracket to get:

4*3 + 4*5 = 12 + 20

= 32

Thus:

5(10v - 8w + 4) = (5 * 10v) - (5 * 8w) + (5 * 4)

= 50v - 40w + 20

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Answer:

75

Step-by-step explanation:

75. How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution? \ The ratio in which 30% alcohol and 60% alcohol should be mixed to get 50% alcohol is 1 : 2

Answer: Let x litres of 30% alcohol solution be added.

Then, 30% of x + 60% of 40 = 50% of (x + 40)

⇒ 30x + 60 × 40 = 50 (x + 40)

⇒ 30x + 2400 = 50x + 2000

⇒ 20x = 400

⇒ x = 20

Please brainliest please

Given the equation:

When t=1, y=3 (three percent of the ants are infected).

Replacing in the equation:

a) The equation of the line tangent to the graph is:

In t= 1.2.

The percentage of the colony infected in t=1.2 is 3.4.

b) y explicity:

integrating both sides:

The first one will be:

The second one, will be:

Substituing:

Using D=k-c

Finally:

Answer:

\(\textsf{13.} \quad(x-1)^2+(y+2)^2=9\)

       center = (1, -2)

       radius = 3

\(\textsf{14.} \quad y=5 \cdot 3^x\)

\(\textsf{15.} \quad x=\dfrac{104}{3}, \quad x=-\dfrac{88}{3}\)

Step-by-step explanation:

Equation of a circle

\((x-a)^2+(y-b)^2=r^2\)

(where (a, b) is the center and r is the radius)

Given equation:

\(x^2+y^2-2x+4y-4=0\)

To rewrite the given equation in graphing form, first add 4 to both sides of the equation and rearrange the variables:

\(\implies x^2-2x+y^2+4y=4\)

Add the square of half the coefficients of the x and y terms to both sides:

\(\implies x^2-2x+\left(\dfrac{-2}{2}\right)^2+y^2+4y+\left(\dfrac{4}{2}\right)^2=4+\left(\dfrac{-2}{2}\right)^2+\left(\dfrac{4}{2}\right)^2\)

\(\implies x^2-2x+1+y^2+4y+4=9\)

Finally, factor both trinomials:

\(\implies (x-1)^2+(y+2)^2=9\)

Now compare the equation in graphing form to the general equation of a circle to find the center and radius:

⇒ a = 1  and  b = -2  ⇒ center = (1, -2)

⇒ r² = 9  ⇒ radius = √9 = 3

General form of an exponential function:

\(y=ab^x\)

(where a and b are constants to be found)

Given points on the curve:

Substitute the given points into the general form of the equation to create two equations:

\(\textsf{Equation 1}: \quad ab^4=405\)

\(\textsf{Equation 2}: \quad ab^9=98415\)

Divide Equation 2 by Equation 1 to eliminate a, then solve for b:

\(\implies \dfrac{ab^9}{ab^4}=\dfrac{98415}{405}\)

\(\implies \dfrac{b^9}{b^4}=243\)

\(\implies b^{9-4}=243\)

\(\implies b^5=243\)

\(\implies b=\sqrt[5]{243}\)

\(\implies b=3\)

Substitute the found value of b into one of the equations and solve for a:

\(\implies a(3)^4=405\)

\(\implies 81a=405\)

\(\implies a=\dfrac{405}{81}\)

\(\implies a=5\)

Therefore, the exponential equation that passes through (4, 405) and (9, 98415) is:

\(y=5 \cdot 3^x\)

Given equation:

\(\left|\dfrac{3}{2}x-4\right|+2=50\)

Isolate the absolute value by subtracting 2 from both sides:

\(\implies \left|\dfrac{3}{2}x-4\right|=48\)

Set the contents of the absolute value to positive and negative and solve for x:

Positive absolute value:

\(\implies \dfrac{3}{2}x-4=48\)

\(\implies \dfrac{3}{2}x=52\)

\(\implies x=52 \cdot \dfrac{2}{3}\)

\(\implies x=\dfrac{104}{3}\)

Negative absolute value:

\(\implies -\left(\dfrac{3}{2}x-4\right)=48\)

\(\implies -\dfrac{3}{2}x+4=48\)

\(\implies -\dfrac{3}{2}x=44\)

\(\implies x=44 \cdot -\dfrac{2}{3}\)

\(\implies x=-\dfrac{88}{3}\)

Therefore, the solution to the equation is:

\(x=\dfrac{104}{3}, \quad x=-\dfrac{88}{3}\)

Answer + Step-by-step explanation:

13.

x² + y² - 2x + 4y - 4 = 0

(x² - 2x) + (y² + 4y )- 4 = 0

x² - 2x = (x² - 2x + 1) - 1

           = (x - 1)² - 1

y² + 4y = (y² + 4y + 4) - 4

            = (y + 2)² - 4

Then

x² + y² - 2x + 4y - 4 = 0

⇔ (x - 1)² - 1 + (y + 2)² - 4 - 4 = 0

⇔ (x - 1)² + (y + 2)² = 9

⇔ (x - 1)² + (y + 2)² = 3²

Then

The center is (1 , -2)

The radius is  3

……………………………………………

14.

(4 , 405)  ;  (9 , 98415)

y = abˣ

The graph passes through (4 , 405) ⇒ 405 = ab⁴

The graph passes through (9 , 98415) ⇒ 98415 = ab⁹

We divide:

ab⁹÷ab⁴ = 98415 ÷ 405

⇔ b⁵ = 243

⇔ b⁵ = 3⁵

⇔ b = 3

Finding a :

405 = ab⁴

⇔ 405 = a3⁴ = 81a

⇔ a = 405/81 = 5

Conclusion:

The exponential equation is :

y = 5×3ˣ

………………………………………………

15.

|3/2x - 4| + 2 = 50

Then

|3/2x - 4| = 48

Then

3/2x - 4 = 48 or 3/2x - 4 = -48

Then

3/2x = 52 or 3/2x = -44

Then

x = 104/3 or x = -88/3

Answer:

h = √(7.5² - 2.1²) = 7.2 m

Step-by-step explanation:

Pythagorean theorem

The situation in economic terms is that there is a shortage of parking space.

1. From the information, it was stated that certain university issues parking permits to allow students to park on campus and the price of the permit is set by college administrators at any price they choose.

Therefore, the situation in economic terms is that there is a shortage of parking space.

2. The price of a permit be raised to fix this situation. This will make more space available.

3. The graph of the market for parking permits would be affected by a change in price as it will help to bring about an increase in supply when the permit is increased.

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Solution

using similar triangle ABC and DEC

The value for x is 8.6 nearest tenth

Answer:

The number of black beads is going to be 42 and the number of white beads is 12

Step-by-step explanation:

You are going to divide 54 by 9. The answer is 6.

Then you will do 6x7=42

That is the number of black beads

Next you will do 6x2=12

That is the number of white beads.

42+12=54

Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

Answer:

1 and 2

Step-by-step explanation:

If y was 1: -2 x 1 + 18 = -2 + 18

= 16  This works

If y was 2: -2 x 2 + 18 = -4 + 18

= 14  This works

If y was 3: -2 x 3 + 18 = -6 + 18

= 12  This does not work since -2y + 18 has to be greater than 12.

Answer: 15x - 1500 > 0,    101 batches

Step-by-step explanation:

To begin, lets start by modeling this with a linear equation, (for sake of simplicity).

we can model this in the form y = mx + b, where y is 0, (meaning she isn't making profit OR losing money either).

Next, lets set up the parameters:

0 = mx + b. We can safely say that b, our constant, is -1500, because this is the money she "loses" every month.

Now we have 0 = mx -1500. We know she sells each batch for $20, so we also know that she makes 20x dollars for x batches. Our m = 20.

Now we have 0 = 20x - 1500. However, this equation is not completely correct, as we arent subtracting the cost for making each batch of cupcakes. The problem says that it costs her $5 to make each batch. So it will cost her 5x dollars for making x batches. If we subtract this from how much she sells each batch for, we get the profit she makes from selling each batch. So she makes a profit of (20x - 5x) = 15x dollars for x batches of cupcakes.

Out completed equation is 15x - 1500 = 0.

Solving this equation for x will give us how many batches she needs to sell to break even. To model this as an inequality for profit we simply replace the "=" sign with a ">" sign.

So our completed inequality is 15x - 1500 > 0

Solving this for x:

15x - 1500 > 0

15x > 1500

x > 100

Amanda needs to make more than 100 batches per month to make a profit. The greatest number of whole number batches over 100 is 101; so she needs to sell atleast 101 batches to make a profit every month.

Answer:

The angles are: 50.3 and 129.7

Step-by-step explanation:

The sum of supplementary angles is 180°.

Let x be one angle then the other angle will be x+79.4

Using the supplementary angle sum

\(x+x+79.4 = 180\\2x+79.4 = 180\\2x = 180-79.4\\2x = 100.6\\\frac{2x}{2} = \frac{100.6}{2}\\x = 50.3\)

For the measurement of 2nd angle

x+79.4 => 50.3+79.4 => 129.7

Hence,

The angles are: 50.3 and 129.7

9514 1404 393

Answer:

  414.5 cm³

Step-by-step explanation:

The lateral area of a cylinder is given by the formula ...

  LA = 2πrh

Then the radius is ...

  r = LA/(2πh)

The volume of the cylinder is given by ...

  V = πr²h

Using the above expression for r, this becomes ...

  V = π(LA/(2πh))²h = LA²/(4πh)

  V = (250 cm²)²/(4π·12 cm) ≈ 414.47 cm³

The volume of the cylinder is about 414.5 cm³.

Answer:

(y-4)^2/12^2 + (x-2)^2/6^2 =1​

Step-by-step explanation:

Step-by-step explanation:

The given angles are complementary

Hence sum of these are equal to 90°

X + ( 3X - 2) = 90

X + 3X - 2 = 90

4X - 2 = 90

4X = 90 + 2

4X = 92

X = 92/4

X = 23

First angle (X) = 23

Second angle ( 3X - 2 )= 3(23) - 2

= 67

Answer:

The answer is Ahope this helps

The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

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Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

Answer:

28

Step-by-step explanation:

a = b * h

a = 4 * 7 = 28

The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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Answer:

Step-by-step explanation:

At equilibrium price and quantity, the answer is 1. The quantity supplied equals the quantity demanded.

This means that the market is in a state of balance, where the quantity of a good or service that producers are willing to supply is exactly the same as the quantity that consumers are willing to buy. As a result, there is no excess supply or excess demand, and the price of the good or service is stable.

Answer:

Step-by-step explanation:

there isint enough details

SQUARE ROOT FUNCTION

Given the parent function:

Table

First, we prepare a table of easy points:

Graph

The graph of the function is attached below:

Domain and Range

As can be seen from the graph, the domain and range of the square root parent function are:

• Domain: [0, ∞)

• Range: [0, ∞)

Asymptotes

The square root parent function has NO ASYMPTOTES.