Bela's ice cream cone is 9 inches tall and 6 inches across. What volume of ice cream can fit within the cone? Show your work and draw a picture of the scenario. Type your answer as a number only. Round your answer to the nearest tenth. Volume = cubic inches

Answer:

\(y = - \frac{1}{5} x - 7\)

Step-by-step explanation:

let's rewrite the equation

\(x + 5y = 25 \\ 5y = - x + 25 \\ y = - \frac{1}{5} x + 5\)

Now let's use the given point and substitute it to find the y-intercept

\( - 6 = - \frac{1}{5} ( - 5) + b \\ - 6 = 1 + b \\ b = - 7\)

The required solution of the given equation of the line that passes through the point (-5,-6) and is parallel to the line x+5y=25 is

\(y=\frac{-1x}{5} -7\).

Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it.

Given:

The point is  (-5,-6) and is parallel to the line x+5y=25.

According to given question we have

By use of slope we get

x+5y=25

5y=25-x

Divide both sides 5 we get,

y=-1/5x+5

Where m= -1/5

Now you can find the equation of the parallel line using

\((y-y_{0} )=m(x-x_{0})\)

Put the given point as (-5,-6) we have,

\((y+6)=\frac{-1}{5} (x+5)\\\\y=\frac{-1x}{5} -1-6\\\\y=\frac{-1x}{5} -7\)

Therefore, the required solution of the given equation of the line that passes through the point (-5,-6) and is parallel to the line x+5y=25 is

\(y=\frac{-1x}{5} -7\).

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Answer:

Sue rode 1885 miles total

Step-by-step explanation:

There are 31 days in March, 30 in April, and 30 in May.

31 * 12 + 30 * 12 + 30 * 12 = 1092

There are 30 days in June and 31 in august.

30 * 13 + 31 * 13 = 793

Now we find the total:

1092 + 793 = 1885

Answer:

1)y=20-6=14

2)X=12+10=22

3)answer stated

4)n=14

5)10

6)15

7)26

8)15

9)80

10)stated

11)35

12)4

13)45

14)12

15)50

1. y + 6 = 20

subtract 6 from both sides

y = 14

2. x - 10 = 12

add 10 to both sides

x = 22

3. 12 + 2 = 15

false

4. 2 + n = 16

subtract 2 from both sides

n = 14

5. a + 4 = 14

subtract 4 from both sides

a = 10

6. m - 5 = 10

add 5 to both sides

m = 15

7. 4 + b = 30

subtract 4 from both sides

b = 26

8. 10 + c = 25

subtract 10 from both sides

c = 15

9. x - 60 = 20

add 60 to both sides

x = 80

10. 9 - 16 = 4

false

11. x - 15 = 20

add 15 to both sides

x = 35

12. w + 14 = 18

subtract 14 from both sides

w = 4

13. r - 18 = 27

add 18 to both sides

r = 45

14. 13 + k = 25

subtract 13 from both sides

k = 12

15. f - 16 = 34

add 16 to both sides

f = 50

I think you had some typos in there but I think this should get you started, you should be able to figure out the rest

The thirteenth term of this arithmetic progression a + b, 2a, 3a − b, ..... is a₁₃ = 13a - 11b.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 2a - (a + b) = 2a - a - b

Common difference, d = a - b

Substituting the given parameters into the formula, the 13th term of this arithmetic sequence is given by;

a₁₃ = (a + b) + (13 - 1)(a - b)

a₁₃ = (a + b) + (12)(a - b)

a₁₃ = a + b + 12a - 12b

a₁₃ = 13a - 11b.

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Answer:

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

The length of the line segment is the difference in y-coordinates, since x-coordinates are same:

It has dilated by a scale factor of 3.

The image is now:

Answer:

367.6

Step-by-step explanation:

Hope this helps!

Answer:

draw the diagram and multiply 5x20

Answer: The answer is -4

Step-by-step explanation: The answer is -4 because you when you substitute x for -5(2) and y for -2(3). Which then equal -10 and the -6 turns into a positive 6 which then leads to -10+6 and equals -4!

Hope this Helps :D

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Given:

Height of ladder = 13 feet

Distance from base of ladder to the house = 3 feet.

Let's find how high the ladder reaches the house.

Let's first make a sketch of this situtaion:

Now, let's apply Pythagorean Theorem:

Therefore, the ladder reaches the house at a height of 12.65 feet.

• ANSWER:

12.65 feet.

Answer:

Dear user,

Answer to your query is provided below

Scientific notation = 1.8x10^0

Step-by-step explanation:

This is usually expressed simply as 1.8 (Recall that 10^0 = 1.)

1.8×10^0

The dilation of the black figure to blue figure is a reduction with a scale factor of 0.5

A dilation is defined as a transformation that produces an image that is the same shape as the original, but is a different size.

It can either be an enlargement or a reduction.

An enlargement means a scale factor greater than 1 while a reduction is a scale factor less than 1.

Thus, this dilation is a reduction.

Coordinates of initial figure are:

(-8, 10), (10, 10), (8, -8), (2, -8)

Coordinates of dilated figure are:

(1, -4), (4, -4), (-4, 5), (5, 5)

Thus, it is clear that the scale factor is 0.5

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Graph 1 - no

Graph 2 - no

Graph 3 - yes

Graph 4 - no

Graph 5 - no

Graph 6 - yes

Good luck !!

The amount of interest he will pay on this loan$12,400.

What is  interest?

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as an annual percentage of the loan amount. The interest rate on the loan is known as this percentage.

Principal = $10,000

Rate = 8%

Time = 36 months, 1 year - 12 months

36 months - 36/12= 3 years

S.I. = PRT/100

10,000*8*3/100

240,000/100 = $2,400

A = P+I = 10,000+2,400= $12,400

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Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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3.133333333333

hope this helps :)

Answer:

192

Step-by-step explanation:

The formula for the volume of a cone is given in the problem as:

\(V=\dfrac{\pi r^2h}{3}\)

The problem instructs us to use "3" as the value for π.  (In this case, it might be helpful to think of π as a letter like "y", and we're just substituting in the value that they give us... π=3).

At the bottom of the cone, the full diameter of the circular base is given as 8 cm.  The radius (the "r" in the formula) of a circle, is half of the diameter:

r = 1/2 * d

r = 1/2 * (8cm)

r = 4cm

We're also given the height ("h" in the formula) in the diagram as 12 cm.  It is the height because it is the measurement of the distance from the vertex (top) to the base where the line segment measured forms a right angle (as indicated by the "square" where that line segment meets the base).

Substituting the known values into the formula, we get...

\(V=\dfrac{(3) (4cm)^2 (12cm)}{3}\)

Simplifying/evaluating the expression, we follow order of operations (exponents, then multiplication/division)...

\(V=\dfrac{(3) (16cm^2) (12cm)}{3}\)

\(V=\dfrac{576cm^3}{3}\)

\(V=192cm^3\)

The required, given polynomial has exactly 4 roots, which may be real or imaginary or a combination of both.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.

Here,
The fundamental theorem of algebra states that every non-constant polynomial with complex coefficients has exactly as many roots (zeros) as its degree. In this case, the degree of the polynomial is 4, so it has exactly 4 complex roots.

However, it is not clear whether any of the roots are real or imaginary, or whether they are all complex. To determine this, we would need to use methods such as the rational root theorem, synthetic division, or the quadratic formula to find the roots of the polynomial.

Without actually finding the roots, we can say that the polynomial has exactly 4 roots, which may be real or imaginary or a combination of both.

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Answer:

112 yards

Step-by-step explanation:

quarter is 1/4 right¿

28 × 4 = 112

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Given,

The points which the line passes, (x₁, y₁) = (7, 6)

Slope of the line, m = 0

We have to find the equation of the line:

We know that,

y - y₁ = m(x - x₁)

So,

y - 6 = 0(x - 7)

y - 6 = 0

y = 6

That is,

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

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Answer:

Decreasing: y, infinity

Constant: y, negative infinity

Step-by-step explanation:

You just had it backwards, the interval for infinity is based on the x-axis not the y-axis. The decreasing portion is moving toward positive infinity on the x-axis because it's moving to the right. The constant is moving to the left so it is negative infinity.

The value of the quotient expression given as negative 7.3 divided by one half is -14.6

The quotient expression is given as:

negative 7.3 divided by one half

Rewrite the above expression properly, as follows:

-7.3/0.5

Evaluate the quotient

-14.6

Hence, the value of the quotient expression given as negative 7.3 divided by one half is -14.6

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Answer:

-14.6

Step-by-step explanation:

Treat the one half as a fraction.

Then remember that when you divide by a fraction, you need to multiply by the reciprocal of the fraction, so dividing by half is the same as multiplying by 2. Also, negative times positive is negative.

-7.3 / (1/2) = -7.3 × 2/1 = -7.3 × 2 = -14.6

The value of f(3) in the function is 67

From the question, we have the following parameters that can be used in our computation:

f(a) = 4^a + 3

The function notation f(3) implies that the value of a is 3

Substitute the known values in the above equation, so, we have the following representation

f(4) = 4^3 + 3

Evaluate the exponents

f(4) = 64 + 3

So, we have

f(4) = 67

Hence, the solution is 67

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Answer:

1.7$

Step-by-step explanation:

Given

original price = $2.87

New price = $2.82

Percentage decrease = original price-New price/New price × 100

Percentage decrease = 2.87-2.82/2.87× 100

Percentage decrease = 0.05/2.87 × 100

Percentage decrease = 5/2.87

Percentage decrease = 1.7%

Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

Answer:

It is 3 15/28.

Step-by-step explanation:

To solve this problem, we first need to add the whole numbers: 2 + 1 = 3. Next, we need to add the fractions. To do this, we need to find a common denominator for the fractions 2/7 and 1/4. A common denominator for these two fractions is 28, so we can convert the fractions to equivalent fractions with a denominator of 28: 2/7 is equivalent to 8/28 and 1/4 is equivalent to 7/28. With the fractions written in this form, we can add them to get 8/28 + 7/28 = 15/28.

Finally, we need to add the whole number 3 and the fraction 15/28 to get our final answer. To do this, we need to convert the fraction 15/28 to a mixed number. We can do this by dividing 15 by 28 to get a quotient of 0 and a remainder of 15. This means that the mixed number equivalent of 15/28 is 0 + 15/28. Therefore, our final answer is 3 + 0 + 15/28 = 3 + 15/28 = 3 15/28. This is the simplest form of the mixed number, so our final answer is 3 15/28.

From the image

x is the adjacent side of the triangle while 3√2 is the hypotenuse side

Using the SOH CAH TOA notation

Cos 45 = x/3√2

x = 3√2 * Cos 45

= 3√2 * 1/√2

= 3

The probability that the three randomly selected students will have blood types A, B and AB is given as follows:

0.00164 = 0.164%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Hence the probability for this problem is calculated as follows:

41/100 x 1/10 x 1/25 = 0.00164 = 0.164%.

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Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB