Hello, I’m struggling with my geometry homework. It’s number 2

Answer is correct. Maximum vertical distance between the line y = x + 6 and the parabola y = x² for -2 ≤ x ≤ 3 is 6.25.

Follow these steps:

1. Subtract the equation of the line from the equation of the parabola to find the difference between their y-values: (x²) - (x + 6).

2. Simplify the expression: x² - x - 6.

3. Now we need to find the maximum value of this expression in the given interval. To do this, find the vertex of the parabola formed by the expression.

4. The vertex of a parabola with the form y = ax² + bx + c is given by the formula x = -b/(2a). In this case, a = 1 and b = -1, so the x-coordinate of the vertex is x = 1/2.

5. Since 1/2 is within the interval -2 ≤ x ≤ 3, the maximum vertical distance occurs at this x-coordinate.

6. Substitute x = 1/2 into the expression x² - x - 6 to find the maximum vertical distance: (1/2)² - (1/2) - 6 = 1/4 - 1/2 - 6 = -6.25.

7. Since we're looking for the maximum vertical distance, we need to consider the absolute value of the difference: |-6.25| = 6.25.

So, the maximum vertical distance between the line y = x + 6 and the parabola y = x² for -2 ≤ x ≤ 3 is 6.25.

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Answer:

1=2 5=6 6=7 8=9 is the answer

In Triangle PQR where angle Q is a right angle. QR measures 33 point 8; PQ measures 57 point 6; measure of angle P is unknown. Then the measure of ∠R = 30.4 degrees.

Measures of Angle:

An angle is formed when two lines or rays meet at a common point. Common points are called vertices.

Angles are measured using basic geometric tools such as protractors and compasses. This tool allows you to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles.

Angles are measured in three ways: degrees, radians, and revolutions. In geometry, an angular measure can be defined as the measure of the angle formed by two rays or two arms at a common vertex.

Given that:

QR = 33.8 and PQ = 57.6, and

Q is the right angle, then

tan R = opposite / adjacent

= QR / PQ = 33.8 / 57.6 = 0.586.

Therefore,

tan R = 0.586

Angle R = tan⁻¹ (0.586) = 30.4 degrees.

Complete Question:

How would you solve the following geometry problem?: ∆PQR, find the measure of ∡P. In Triangle PQR where angle Q is a right angle. QR measures 33 point 8; PQ measures 57 point 6; measure of angle P is unknown. Answers: 30.4° 35.9° 54.1° 59.6° What I did: equation: tan(x) = 33.8/57.6 tan(x)=0.56 But I know that isn't correct.

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Since the point B is between points A and C, the length BC is 22.25 units

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

Length AB = 6x - 9

Length BC = 3x + 17

Length AC = 5x + 16

The above implies that the point B is between points A and C

So, we have the following equation

AC = AB + BC

Substitute the known values in the above equation

So, we have the following equation

5x + 16 = 6x - 9 + 3x + 17

Collect the like terms

So, we have the following equation

5x - 6x - 3x = -9 + 18 - 16

Evaluate the like terms

So, we have the following equation

-4x = -7

Divide by -4

x = 7/4

Substitute x = 7/4 in the equation BC = 3x + 17

So, we have the following equation

BC = 3 x 7/4 + 17

Evaluate

BC = 22.25

Hence, the numerical length of BC is 22.25 units

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Answer:

Step-by-step explanation:

To prove ΔXYZ ~ ΔMNO using the property of SSS, we need to know that All corresponding sides of these triangles are proportional.

Similarly, If we know the length of side XZ then addition information we need to know that angle O is congruent to angle Z and length of sides YZ, MO and NO to prove ΔXYZ ~ ΔMNO by SAS property.

Angle O is the contained angle between the sides MO and NO.

Answer:

1. MN = 6 and XZ = 17.5

2. angle Z

Step-by-step explanation:

Sorry if this is a late answer but I hope this helps :)

Given, the height \($h=6$, the base $b_1=9$ and $b_2=12$.\)

The area of the trapezoid is given by the formula,

\(\[A = \frac{1}{2}h(b_1+b_2)\]\)

Substitute the given values,  

\(\[A = \frac{1}{2} \times 6 \times (9+12)\]\\\)

Simplifying the above expression,

\(\[A = 45 \text{ square feet}\]\)

Therefore, the area of the trapezoid is $45$ square feet.

The perimeter of a two-dimensional geometric shape is the entire length of the boundary or outer edge. It is the sum of the lengths of all the shape's sides or edges.

The perimeter of a square, for example, is calculated by adding the lengths of all four sides of the square.

Similarly, to find the perimeter of a rectangle, sum the lengths of two adjacent sides and then double the result because there are two pairs of adjacent sides.

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The probability that a student chosen randomly from the class passed the test or completed the homework is 20/27.

The probability that a student chosen randomly from the class passed the test or completed the homework is calculated as follows:

Let the probability that a student completed the homework be P(B).

Also, let the probability that a student passed the test be P(A)

P(A or B) = P(A) + P(B) - P(A * B)

From the data table:

The number of students who passed the test = 18

The number of students who completed the homework = 17

The number of students who both passed the test and completed the homework = 15.

Total number of students = 27

P(A) = 18/27

P(B) = 17/27

P(A*B) = 15/27

Therefore,

P(A or B) = 18/27 + 17/27 - 15/27

P(A or B) = 20/27

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The linear relationship between the total cost C and the time at the Cafe, t indicates that Ariana can use the computer for 7.5 minutes if she only has $15.75

A linear relationship is used to describe relationships between variables that form a straight line when ordered pairs are plotted as a graph on the coordinate plane.

The ordered pair of points for the linear relationship from the table are; (1, 9.9) and (7, 15.30)

The equation of a linear function is of the form, y = m·x + c

Where;

m = The slope of the function

c = the y-intercept

The slope of the function from the given pair of points is therefore;

\(m= \dfrac{15.30 - 9.90}{7 - 1} = 0.9\)

The equation of the function in point-slope form is therefore;

C - 9.9 = 0.9·(t - 1)

y = 0.9·x - 0.9 + 9.9 = 0.9·x + 9

The equation for the function in slope-intercept form is; C = 0.9·t + 9

Where;

C = The total cost the computer for t minutes

t = The duration of using the computer in minutes

When C = $15.75, we have;

15.75 = 0.9·t + 9

\(t = \dfrac{15.75-9}{0.9} = 7.5\)

The number of minutes Ariana can use the computer if she only has $15.75 is 7.5 minutes

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The solution for the system of equtaions is (57/11, 42/11)

Here we have the system of equations:

x/3 = 6 - y/3

3x/4 - 3 = 2y

We can isolate x on the first equation to get:

x = 18 - 3*y/3

x = 18 - y

Replacing that on the other equation we will get

3*(18 - y)/4 - 3 = 2y

We can solve this for y.

3*(18 - y)/4 = 2y + 3

54 - 3y = 4*(2y + 3) = 8y + 12

54 - 12 = 8y + 3y

42 = 11y

42/11 =y

And the value of x will be:

x = 9 - 42/11

x  = 99/11 - 42/11 = 57/11

That is the solution of the system.

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Answer:

\(3x^2-3x\left(x-2\right)-12=0\)

\(3x^2-3x\left(x-2\right)-12+12=0+12 \longleftarrow (\mathrm{Add\:}12\mathrm{\:to\:both\:sides})\)

\(3x^2-3x\left(x-2\right)=12\)

\(-3x\left(x-2\right)=-3xx-\left(-3x\right)\cdot \:2\)

\(=-3xx+3\cdot \:2x\)

\(-3xx+3x^{2}\)

\(=3x^{1+1}\)

\(=3x^2\)

\(3\cdot \:2x=6x\)

\(=-3x^2+6x\)

\(3x^2-3x^2+6x=12\Longleftarrow Add\:similar\:elements\)

\(6x=12\)

\(\frac{6x}{6}=\frac{12}{6} \Longleftarrow Divide\)

\(x=2\)

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Answer:

There isnt a diagram

Step-by-step explanation:

Answer: 46, 57, 68

Step-by-step explanation:

If you look at the sequence, you see that every time, it goes up by 11, so just add 11 three more times after the last number

A permit is a legal document that enables a person or a business to utilize a specific area for a project or other activity.

To obtain permission to use a specific location for a project, you may need to submit a request in writing or fill out a permission form. The exact document that you need to obtain permission will depend on the specific location and the requirements of the owner or manager of the location.

You may also need to provide information about your project, including the purpose, duration, and any potential impact on the location. Depending on the location and the nature of your project, you may also need to obtain other approvals or permits, such as building permits or environmental permits.

It is a good idea to research the requirements for using the specific location that you are interested in and to contact the appropriate authorities or individuals to find out what documents you need to obtain permission.

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Answer:

The common ratio is 1/2

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

8/16 = 1/2

We can check by the third term by the second term

4/8 = 1/2

Answer:

1/2 for APX

Step-by-step explanation:

Answer:

domain (-4,8,9,1)

range. (4,-1,-9,2,8)

Step-by-step explanation:

The areas of the composite figures are, respectively:

Case A: A = 104 m²

Case B: A = 174 m²

Case C: A = 321.461 cm²

Case D: A = 20 m²

In this problem we need to determine four case of composite figures, the area of each composite figure is the result of adding or subtracting the areas of different figures. The area formulas to be used below are introduced below:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Quarter of a circle

A = 0.25π · r²

Where:

Finally we determine the area of the composite figures:

Case A

A = (10 m) · (8 m) + 0.5 · (8 m) · (6 m)

A = 80 m² + 24 m²

A = 104 m²

Case B

A = (12 m)² + 0.5 · (12 m) · √[(13 m)² - (12 m)²]

A = 174 m²

Case C

A = (20 cm)² - 0.25π · (10 cm)²

A = 321.461 cm²

Case D

A = (4 m) · (6 m) - 0.5 · (4 m) · (2 m)

A = 24 m² - 4 m²

A = 20 m²

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The range is ( 290, 230).

In statistics, the standard deviation is a measure of the amount of variation. The low standard deviation indicates that the values tend to be close to the expected value of the set, while a high standard deviation indicates that the values are spread out over a wide range.

According to the question,

The middle 50% of the pregnancies are within two standard deviations of the mean: 260 ± 2*15

               = ( 260 + 2*15 , 260 - 2*15)

               = ( 260 + 30, 260-30)

               = ( 290, 230)

Hence the range is ( 290, 230).

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With a monthly payment of $350 and a maximum repayment period of 4 years, and interest rate of 6.2% per year compounded monthly, Henna can afford to spend approximately $16,324.20 on buying her car.

To calculate the maximum amount Henna can spend on buying her car, we can use the present value formula for a loan or annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r],

where PV is the present value or the maximum amount Henna can spend on the car, PMT is the monthly payment, r is the monthly interest rate (converted from the annual interest rate), and n is the total number of months for the repayment period.

First, we need to convert the annual interest rate of 6.2% to a monthly interest rate. Dividing 6.2% by 12, we get 0.062/12 = 0.00517, which is the monthly interest rate.

Next, we substitute the values into the formula:

PV = $350 * [(1 - (1 + 0.00517)^(-48)) / 0.00517],

where 48 months (4 years * 12 months) is the total number of months for the repayment period.

Evaluating the formula, we find:

PV ≈ $350 * [(1 - (1.00517)^(-48)) / 0.00517]

≈ $350 * [(1 - 0.70370) / 0.00517]

≈ $350 * [0.29630 / 0.00517]

≈ $350 * 57.27813

≈ $16,324.20.

Therefore, the most Henna can spend on buying her car today, considering her monthly payment limit and the best available interest rate, is approximately $16,324.20.

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Joint Distribution of x and y is 25.

Joint Distribution is based on joint probability, which can be simply defined as the probability of two events happening together.

We know the formula for joint distribution

F(x,y) = P(X ≤ x and Y ≤ y) = ∑∑p(xi,yi)

Here x is the number of aces and y is the number of kings in a poker hand.

That means x can take values from 0 to 4 and y can take values from 0 to 4.

∴ F(x,y) = P(X ≤ 4 and Y ≤ 4)

⇒ F(x,y) = p(0,0) + p(0,1) + p(0,2) + p(0,3) + p(0,4) + p(1,0) + p(1,1) + p(1,2) + p(1,3) + p(1,4) + p(2,0) + p(2,1) + p(2,2) + p(2,3) + p(2,4) + p(3,0) + p(3,1) + p(3,2) + p(3,3) + p(3,4) + p(4,0) + p(4,1) + p(4,2) + p(4,3) + p(4,4).

To find all these values we will construct a table as follows;

P(x,y)           Y=0      Y=1         Y=2      Y=3    Y=4

X=0              0          1/4          1/2        3/4       1      

X=1               1/4        1/2        3/4         1        5/4

X=2             1/2         3/4         1            5/4     3/2

X=3             3/4          1          5/4         3/2      7/4      

X=4               1          5/4         3/2       7/4       2

Now the joint distribution will become,

F(x,y) = 0 + 1/4 + 1/2 + 3/4 + 1 + 1/4 + 1/2 + 3/4 +1  + 5/4 + 1/2 + 3/4 + 1 + 5/4 + 3/2 + 3/4 + 1 + 5/4 + 3/2 + 7/4 + 1 + 5/4 + 3/2 + 7/4 + 2

F(x,y) = 25

Therefore the joint distribution of x and y is 25.

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The function rule for this question is d = 90t.

The rate of the cheetah is given as 90 feet per second. The distance travelled by the cheetah is a function of seconds travelled. Let the distance be denoted as d and the time be denoted as t. The function is therefore a linear function of the form y = mx + b.

The equation can be expressed as d = 90t + b. The constant b is the initial distance travelled at time zero since the rate is constant. Therefore, b is zero when the time is zero. The final equation is given as follows: d = 90t, where d is the distance travelled, t is the time and 90 is the rate or speed of the cheetah.

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Answer:

Secθ = 11 / 9.22 or sec33°

Sinθ = 6 / 11 or Sin33°

Tanθ = 6 / 9.22 or Tan33°

θ = 33°

Step-by-step explanation:

Given:

Hypotenuse = 11 unit

Perpendicular = 6 unit

Find:

Secθ

Sinθ

Tanθ

Computation:

Base = √Hypotenuse² - Perpendicular²

Base = √11² - 6²

Base = √121 - 36

Base = √85

Base = 9.22 unit (Approx.)

Secθ = Hypotenuse / Base

Secθ = 11 / 9.22 or sec33°

Sinθ = Perpendicular / Hypotenuse

Sinθ = 6 / 11 or Sin33°

Tanθ = Perpendicular / Base

Tanθ = 6 / 9.22 or Tan33°

So value of θ = 33°

Answer

Area = 21 Sq units

Step-by-step explanation:

Area= 1/2[(x1y2 + x2y3 + x3y1) - (x2y1 + x3y2 + x1y3)]

Area = 1/2[(-5×5 +-3×-2+1×-2) - (-3×-2+1×5+-5×-2)]

Area = 1/2(-42)

Area = -21 sq units

Area = 21 sq units (The area is negative because it is below the x-axis.)

Answer:

k = 146

m= 106

Kirchoff has $146

Maxi has $106

Step-by-step explanation:

For the purpose of the equations, I’ll call Kirchoff and Maxi a and b respectively.

a - 20 = b + 20 (equation 1)

2(b - 22) = a + 22 (equation 2)

We can juggle those around for

a = b +40 (equation 1r (re-arranged)) and

2b - 44 = a + 22 so 2b - 66 = a (equation 2r (rearranged))

The equations are now:

a = b + 40 (new equation 1) and

a = 2b - 66 (new equation 2)

Substitute from new equation 1 to new equation 2:

b + 40 = 2b - 66 so 40 = b - 66 making b = 106.

Plug b = 106 into new equations 1 and 2 for:

a = 106 + 40 (new equation 1) and

a = 212 - 66 (new equation 2)

This gives a = 146 and b = 106

TEST: There’s a gap of $40, so giving $20 from a to b makes them equal.

SECOND TEST: Subtracting $22 from b makes it $84 and giving that sum to a makes it $168, twice as much. The tests work.

Kirchoff has $146 and Maxi has $106.

Answer:

Step-by-step explanation:

To the 4th power means that all the items in the parenthesis is mulitplied 4 times

(9m)⁴

=9*9*9*9*m*m*m*m*m  or

= (9m)(9m)(9m)(9m)

She uses 1/2 cup in each batch.

So, if she has 3 1/4 cups in total, we have to divide this total by 1/2 to know how many batchs she can make:

She can make 6 1/2 batches.