Graph the quadratic function
F(x)=3x^2+6x-24

Answer:158

Step-by-step explanation:∠6 = 68 + 90 = 158°

Answer:

Step-by-step explanation:

Given that a triangle has sides 4,7 and 9

A student Gabe tried to use law of cosines to find unknown angle measure

The angle is opposite side 9 because angle across the longest side is given

He used cosine formula for triangles

[tex]a^2=b^2+c^2-2bccosA\\9^2 = 4^2+7^2-2(4)(8) cosA\\81-65 =-56 cosA\\[/tex]

But instead he adjusted -56 with 16 +49 which is wrong

Because -56 has product as cosA it is not like term as other constants

So correct step should be

81 = 65-56 Cos A

Gabe should not have subtracted 56 from  

16 + 49.

This is the correct answer

Final answer:

Options A, B, and D are geometric sequences because they have a constant ratio between successive terms. Option A has a ratio of 3, option B has a ratio of 0.5, and option D has a ratio of 2. Option C is an arithmetic sequence and not geometric.

Explanation:

The question asks which of the listed sequences are geometric sequences. A geometric sequence is characterized by a constant ratio between successive terms. Let's analyze each option:

A. 1,3,9,27,81 - Each term is multiplied by 3 to get the next term, hence it is a geometric sequence with a common ratio of 3.

B. 10,5,2.5,1.25,0.625, 0.3125 - Each term is multiplied by 0.5 (or divided by 2) to get the next term, hence it is a geometric sequence with a common ratio of 0.5.

C. 3,6,9,12,15,18 - The difference between successive terms is constant (+3), making it an arithmetic sequence, not geometric.

D. 5,10,20,40,80,160 - Each term is multiplied by 2 to get the next term, hence it is a geometric sequence with a common ratio of 2.

Therefore, options A, B, and D are geometric sequences, while option C is not.

the radius is twelve

Answer:

D. (8^2 × 3) × 3

Step-by-step explanation:

its d on plato

Answer:

Option b - The actual price is $3.89 higher than the expected price.

Step-by-step explanation:

Given : In 1983, a year-long newspaper subscription cost $12.75. Today, a year-long newspaper subscription costs $28.50. If the CPI is 193

To find : What is the relation of the actual price of a year-long newspaper subscription to the expected price, to the nearest cent?

Solution :

CPI is the consumer price index.

The formula of CPI is

[tex]\text{CPI}=\frac{\text{Cost of newspaper subscription in Given Year}}{\text{Cost of newspaper subscription in Base Year}}\times 100[/tex]

We have given CPI = 193

Cost of newspaper subscription in Base Year = $12.75

We have to find cost of newspaper subscription in Given Year

[tex]193=\frac{\text{Cost of newspaper subscription in Given Year}}{12.75}\times 100[/tex]

[tex]\text{Cost of newspaper subscription in Given Year}=\frac{193\times12.75}{100}[/tex]

[tex]\text{Cost of newspaper subscription in Given Year}=\frac{2460.75}{100}[/tex]

[tex]\text{Cost of newspaper subscription in Given Year}=24.61[/tex]

The actual price of newspaper subscription  = $28.50

The expected price of newspaper subscription = $24.61

Now, to find how much higher they expected is

$28.50 -$24.61 = $3.89

Therefore, Option b is correct.

The actual price is $3.89 higher than the expected price.

Answer:

a 1=6.9

a  an =

(an-1)(1.1)

b  an=

(6.9)

(1.1^n-1)

c

46.419  

billion

Step-by-step explanation:

Answer:

333 and 1000

Step-by-step explanation:

Answer:

Using the identity rule:

[tex](a-b)^2 = a^2-2ab+b^2[/tex]

Given the equation:

[tex]x^2-12x+36 = 90[/tex]

Rewrite the above equation as:

[tex]x^2-2 \cdot x \cdot 6+6^2 = 90[/tex]

Apply the identity rule:

[tex](x-6)^2 = 90[/tex]

Take square root to both sides we have;

[tex]x-6 = \pm \sqrt{90}[/tex]

Add 6 to both sides we have;

[tex]x = 6\pm \sqrt{90}[/tex]

or

[tex]x = 6 \pm 3\sqrt{10}[/tex]

Therefore, the value of x are:

[tex]6+3\sqrt{10}[/tex] and [tex]6-3\sqrt{10}[/tex]

Final answer:

To calculate the unit rate of rainfall in inches per hour, divide the amount of rainfall (1/2 inch) by the duration (3/4 hour), which gives 2/3 inches per hour.

Explanation:

The student is asking how to find the unit rate of rainfall in inches per hour when given that 1/2 inch of rain fell during 3/4 of an hour. To find the unit rate, divide the total amount of rainfall by the total time to get the amount of rain per one hour.

Step-by-step calculation:

Amount of rainfall: 1/2 inch

Duration of rainfall: 3/4 hour

To find inches per hour, divide the amount of rainfall by the duration:

(1/2 inch) / (3/4 hour) = (1/2) / (3/4) = (1/2) * (4/3) = 4/6 = 2/3 inches per hour.

Therefore, the unit rate of rainfall is 2/3 inches per hour.

Answer:

[tex]Volume=254[/tex] to the nearest cubic yard.

Step-by-step explanation:

The volume of a right circular cylinder can be calculated using the formula;

[tex]Volume=\pi r^2h[/tex].

The diameter of the base is given to us. We divide it into two to obtain the radius.

[tex]r=\frac{18}{2}=9yd[/tex] and also the height of the cylinder is [tex]h=3yd[/tex].

We substitute these values into the formula to obtain;

[tex]Volume=9^2\times 3\pi yd^3[/tex]

[tex]Volume=243\pi yd^3[/tex]

[tex]Volume=763.4yd^3[/tex]

Answer:

answer= 254

Step-by-step explanation:

We have been given that Paige can ride one half of a mile in 1/30 th of an hour. And we have to found the distance traveled in 1 hour if she continues to ride at the same pace.

Let d be the distance traveled in 1 hour.

In 1/30 th of an hour distance traveled is 0.5 mile

Hence, in 1 hour the distance traveled is given by

[tex]d=\frac{0.3}{1/30} \\ \\ d=0.5\times 30\\ \\ d=15[/tex]

Therefore, she will travel 15 miles.

The area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \) is \( \frac{14}{3} \)[/tex] square units, found by integrating [tex]\( x^2 + x \)[/tex] from 0 to 2.

Intersection Points: To find the area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \)[/tex] from [tex]\( x = 0 \) to \( x = 2 \)[/tex], first find their intersection points by setting [tex]\( x^2 = -x \)[/tex]. This gives [tex]\( x^2 + x = 0 \)[/tex], which factors to [tex]\( x(x + 1) = 0 \)[/tex], yielding [tex]\( x = 0 \)[/tex] and [tex]\( x = -1 \)[/tex] as the intersection points.

Limits of Integration: We are interested in the area between these curves from [tex]\( x = 0 \) to \( x = 2 \)[/tex]. Since[tex]\( x = -1 \)[/tex] lies outside this interval, we only consider [tex]\( x = 0 \)[/tex].

Integration: The area can be calculated by integrating the difference between the upper curve [tex]\( y = x^2 \)[/tex] and the lower curve [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \):[/tex]

[tex]\[ \text{Area} = \int_{0}^{2} (x^2 - (-x)) \, dx \][/tex]

Sure, here is the rewritten line:

[tex]\[ \text{The area can be found by integrating} \, x^2 + x \, \text{from} \, x = 0 \, \text{to} \, x = 2: \, \int_{0}^{2} (x^2 + x) \, dx \][/tex]

Integrating term by term:

[tex]\[ = \left[ \frac{x^3}{3} + \frac{x^2}{2} \right]_{0}^{2} \][/tex]

[tex]\[ = \left( \frac{2^3}{3} + \frac{2^2}{2} \right) - \left( \frac{0^3}{3} + \frac{0^2}{2} \right) \][/tex]

[tex]\[ = \left( \frac{8}{3} + 2 \right) - 0 \][/tex]

[tex]\[ = \frac{8}{3} + 2 \][/tex]

[tex]\[ = \frac{14}{3} \][/tex]

Complete question:

What is the area of the region between the graphs of y=x² and y=-x from x=0 to x=2?

Answer:

yur

Step-by-step explanation:

The correct answer is option B). The size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street is 42,240.

To estimate the size of the crowd, we need to calculate the total area occupied by the crowd and then divide by the area occupied by each person.

First, let's calculate the total area available for the crowd on both sides of the street:

The length of the parade route is 1 mile. Since there are 5280 feet in a mile, the length in feet is 5280.

The depth of the crowd on both sides of the street is 10 feet.

Therefore, the total area available for the crowd on both sides is:

Total area = 2 [tex]\times[/tex] (Depth of crowd) [tex]\times[/tex] (Length of parade route)

Total area = 2 [tex]\times[/tex] 10 feet [tex]\times[/tex] 5280 feet

Total area = 105,600 square feet

Next, we need to calculate how many people can fit in this area:

Each person occupies 2.5 square feet.

The number of people that can fit in the total area is:

Number of people = Total area / Area per person

Number of people = 105,600 square feet / 2.5 square feet per person

Number of people = 42,240.

The graph of the circle with the equation (x - 3)² + (y + 3)² = 36, is a circle with center (3, -3) and radius of 6 units

Please find attached the graph of the circle (x - 3)² + (y + 3)² = 36, created with MS Excel

The details of the steps used to graph of the circle are as follows;

The standard form of the equation of a circle is; (x - h)² + (y - k)² = r², where the center of the circle is (h, k)

The equation of the circle in standard form is; (x - 3)² + (y + 3)² = 36

The comparison of the above equation with the form of the general equation of a circle in standard form indicates that the center of the circle is (3, -3)

The comparison of the radius of the circle with equation (x - 3)² + (y + 3)² = 36, with the general form of the equation of a circle in standard form indicates that the radius of the circle is; √(36) = 6