Use the diameter (d) or the radius (r) to find the area

The given quadrilaterals, 1 and 2,  are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.

3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.

4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.

3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:

Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:

AB = √((7 - 0)² + (1 - 0)²) = √50

BC = √((5 - 7)² + (6 - 1)²) = √29

CD = √((-2 - 5)² + (5 - 6)²) =√50

DA = √((0 - (-2))² + (0 - 5)²) = √29

We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.

Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:

Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:

Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5

Slope of RS = (4 - 3) / (4 - (-1)) = 1/5

Slope of QR = (4 - 1) / (4 - 3) = 3

Slope of SP = (3 - 0) / (-1 - (-2)) = 3

The lengths of opposite sides can be calculated using the distance formula:

PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26

RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3

QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10

SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10

We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.

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Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

Answer:

A Beginner's Guide to Teaching with Algebra Tiles

explanation: hope it helps

The overall free throw success rate in the entire game is 25%

A rate is a ratio that compares two different quantities which have different units.

Success rate of free = number of free throw made ÷ total number of free throws × 100

In the first half,

represent the total free throw by x

40 = 2/x × 100

40x = 200

x = 200/20

x = 5

In the second half;

20 = 3/x × 100

20x = 300

x = 300/20

x = 15

Therefore the total success rate of free throw = total number of free throw made ÷ total number of free throws × 100

= (3+2)/(15+5)

= 5/20 × 100

= 25%

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Answer:

I believe it's 7 cups.

Step-by-step explanation:

I did 3/2 times 4 + 1/4 times 4 which gave me 7.  

Please let me know if this works for you. Double check first.

Another way you could do this is by adding both fractions 3/2 + 1/4

to get 7/4 and multiply 7/4 by 4.        so,   3/2 + 1/4= 7/4       7/4  x   4   =   7

As a result, the volume of R1 around AB is 8π/15.

As per the question given,  

For ℛ1 about AB, we can use the method of cylindrical shells to find the volume. We integrate the area of each cylindrical shell from x=0 to x=1 and then sum them up. The radius of each cylindrical shell is the distance from the line y=4x to the point on the curve y=4∜x with the same x-coordinate, which is 4x - 4∜x. The height of each cylindrical shell is dx. Therefore, the volume is given by:

V = ∫[0,1] 2π(4x - 4∜x)x dx

= 2π ∫[0,1] (4x^(2) - 4x^(3/2)) dx

= 2π [4/3 x^(3) - 8/5 x^(5/2)] from x=0 to x=1

= 2π (4/3 - 8/5)

= 8π/15

Therefore, the volume of ℛ1 about AB is 8π/15.

For ℛ2 about BC, we can again use the method of cylindrical shells. We integrate the area of each cylindrical shell from x=1 to x=4 and then sum them up. The radius of each cylindrical shell is the distance from the curve y=2∜x to the point on the line y=2x with the same x-coordinate, which is 2∜x - 2x. The height of each cylindrical shell is dx. Therefore, the volume is given by:

V = ∫[1,4] 2π(2∜x - 2x)x dx

= 4π ∫[1,4] (√x - x) x dx

= 4π [1/3 x^(5/2) - 1/2 x^(3)] from x=1 to x=4

= 4π (32/15 - 21/2)

= -44π/15

Note that the negative sign indicates that the volume is below the x-axis. Therefore, the volume of ℛ2 about BC is 44π/15 (in cubic units).

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Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.

Answer:

The radius is 1 unit.

Step-by-step explanation:

The radius of a circle is half of its diameter. 2/2=1 unit

The sec 132 degrees 15 minutes in degrees is approximately -1.638 degrees.

The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).

In other words,

sec(x) = 1 / cos(x)

The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.

To convert sec(132 degrees 15 minutes) to degrees, we first need to convert the angle to decimal degrees.

We know that 1 degree is equal to 60 minutes, so 15 minutes is equal to 15/60 = 0.25 degrees.

Therefore, the angle 132 degrees 15 minutes is equal to 132 + 0.25 = 132.25 degrees.

Now we can find the secant of this angle:

sec(132.25 degrees) = 1/cos(132.25 degrees) ≈ -1.638

So the answer is approximately -1.638 degrees.

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The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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the answer to the equation is -280

Answer:

Step-by-step explanation:

The general equation of the circle is:

(x-h)²+(y-k)²=r²

(h, k)=(-3,-5)  are the coordinates of the center of the circle.

r=6  is the radius

The equation of the circle is:

(x+3)²+(y+5)² = 36

Answer:

326

Step-by-step explanation:

The value of the given expression is 326.

Given:

The given expression 2 hundreds + 12 tens + 6 ones.

To find:

The value of the given expression.

Explanation:

The numeric form of given expression is:

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

Therefore, the value of the given expression is 326.

Answer:

°This is the graph of a nonlinear function.

°The y-intercept of the graph is the function value y=-6.

°The x-intercepts of the graph are located at x=2 and x=6.

°The greatest value of y is y=2, and it occurs when x=4.

°For x between x=2 and x=6, the function value y>0.

Step-by-step explanation:

I had the same question as you, I didn't get it right but i though i would answer this for you!

Answer:

C

Step-by-step explanation:

you are multiplying 7 by its self 5 times

Answer:

c. 7x7x7x7x7

Step-by-step explanation:

\(7^{5}\) = 16807

7x5= 35. wrong

5x5x5x5x5x5x5= 78125 wrong

7x7x7x7x7= 16807 correct

\(5^{7}\)= 78125 wrong

Answer:

-6, 1

Step-by-step explanation:

For the things to equal 0 one of them must equal 0. (x+6)(-x+1)=0 in the first brackets x must equal -6. The other case where x=0 is when x=1 because

1-x=0

Thus from least to greatest the answers are -6, 1

Answer:

625

Step-by-step explanation:

i dont know why people keeps on deleting my answers that are right, but yeah this IS CORRECT STOP DELETING MY ANSWERS THAT ARE RIGHT....please

You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.

Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.

For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.

Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.

The correct answer is C.

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Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.

We're given:

\(\dfrac{3240\hspace{4}feet}{hour}\)

We also know that:

\(\dfrac{hour}{60\hspace{4}minutes}\)

Multiply the two to cancel out the hour:

\(\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}\)

Simplify:

\(=\dfrac{54\hspace{4}feet}{minute}\)

\(\dfrac{54\hspace{4}feet}{minute}\)

Answer:

Diameter is 10 units

Step-by-step explanation:

Convert standard form to general form by completing the square:

\(x^2+y^2-8x+2y-8=0\)

\(x^2-8x+y^2+2y-8=0\)

\(x^2-8x+y^2+2y=8\)

\(x^2-8x+16+y^2+2y+1=8+16+1\)

\((x-4)^2+(y+1)^2=25\)

\((x-4)^2+(y+1)^2=5^2\)

So, since the radius of the circle is 5 units, then the diameter is twice the radius, which is 10 units.

Answer:

50

Step-by-step explanation:

x2 + y2 - 8x + 2y - 8 = 0

first we find the radius with the equation.

write the equation in standard form.

x2 + y2 - 8x + 2y - 8 = 0

(x-4)^2 + (y+1)^2 = 25

(x-h)² + (y-k)² = r²

this means 25 is the radius and the diameter is two times the radius so,

25 x 2 = 50

Answer:

The point of intersection is \(\left[\begin{array}{c}4&-17&3\end{array}\right]\)

Step-by-step explanation:

In order to find the intersection point we will need to find the vector equation of the line.

The plane equation is \(y=-17\)

Now to find the line that is perpendicular to this plane, we can do the following reasoning :

The plane and the line will be perpendicular between each other if and only if the direction vector of the line is a scalar multiple from the normal vector of the plane.

The plane equation is \(y=-17\). Then any vector with the following form :

\(\left[\begin{array}{c}0&a&0\end{array}\right]\)

With \(a\) ∈ IR , \(a\neq 0\) will be perpendicular to the plane.

Let's choose \(a=1\) to simplify the calculations.

The normal vector of the plane is \(\left[\begin{array}{c}0&1&0\end{array}\right]\)

Now the direction vector of the line must be a scalar multiple of this vector ⇒ \(V=b\left[\begin{array}{c}0&1&0\end{array}\right]\)    , \(b\) ∈ IR

Let's also choose \(b=1\) in order to simplify the calculations.

The vectorial equation of the line is :

\(\left[\begin{array}{c}x&y&z\end{array}\right]=\alpha V+P\)      with \(\alpha\) ∈ IR

Where \(V\) is the direction vector and \(P\) is any point where the line passes through.

Using the data from the question we complete our equation with :

\(IL=\left[\begin{array}{c}x&y&z\end{array}\right]=\alpha\left[\begin{array}{c}0&1&0\end{array}\right]+\left[\begin{array}{c}4&8&3\end{array}\right]\)     with \(\alpha\) ∈ IR

Now let's find the intersection point between the plane \(y=-17\) and the line \(IL\)

This intersection point must belong to the line and also to the plane.

In order to belong to the plane its second component must be \(-17\)

Knowing this and using the vector equation of the line we obtain this equation :

\(\alpha +8=-17\) ⇒ \(\alpha =-25\)

Using \(\alpha =-25\) in the vector equation of the line we find that the point is

\(\left[\begin{array}{c}4&-17&3\end{array}\right]\)

This point belongs to the plane (because its second component is \(-17\)) and also to the line (because it can be obtained using the vector line equation with \(\alpha =-25\)).

Answer:

BD ≅ BD                              Reflexive Property of Congruence

∠ADB ≅ ∠CDB                    Definition of Angle Bisector

I'm taking Geometry this year actually. Hope this helps!

Answer:

The statement is triangle BAD ≅ triangle BCD. The reason is SSS or side-side-side

Answer:

7

Step-by-step explanation:

(x = increase each week)

(6=weeks)

(42= total Grade Change)

Linear equation:

42=6x

Solved:

x=7

Answer:

\(x=-\frac{4}{5}\)

Step-by-step explanation:

\(6=\frac{3}{4}(10x+16)\\\mathrm{or,\ }6\times 4=3(10x+16)\\\\\mathrm{or,\ }24=30x+48\\\\\mathrm{or,\ }-24=30x\\\\\mathrm{\therefore}\ x=-\frac{4}{5}\)

The Equation is 10 + x= 30 and 20 actors are from third grade.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

There are 30 actors in a school play.

There are 10 actors from second grade.

The rest are from third grade.

let the actors in third grade is x.

Equation is:

Actors from second grade + Actors from third grade = Total actors

10 + x= 30

Now, solving

Subtract 10 from both side

10 +x - 10 = 30 - 10

x = 20

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Answer:

2/10 or 1/5 gold, 3/10 blue and 5/10 or 2/5 white

Step-by-step explanation:

2+3+5=10

since you do this 5 times and get 5 marbles it can be:

2/10 or 1/5 gold, 3/10 blue and 5/10 or 2/5 white

The probability of choosing 1 gold marble, 1 blue marble and 3 white marbles is 2/5

Probability is the likelihood or chance that an event will occur.

If there are 2 gold marbles, 3 blue marbles and 5 white marble in the bowl, the total number of marbles will be 10 marbles.

Pr(1 gold marble) = 2/10 = 1/5

Pr(1 blue marble) = 3/10

Pr(3 white marble) = \(\frac{3}{5C_3} = \frac{3}{10}\)

Add all the probability;

Pr(hoosing 1 gold marble, 1 blue marble and 3 white marbles) = 1/5 +3/10 + 3/10 = 8/10 = 2/5

Hence the probability of choosing 1 gold marble, 1 blue marble and 3 white marbles is 2/5

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True. Summarizing allows you to focus on the important information by finding the introduction, topic sentence and conclusion.

Summarizing is a technique that helps to distill the main points of a text by identifying the introduction, topic sentence, and conclusion. It involves condensing the information to focus on the most important aspects and omitting unnecessary details.

This process enables the reader to grasp the core message of the text quickly and efficiently.

By summarizing, one can communicate the key ideas in a concise and clear manner, making it easier for others to understand and engage with the information presented.

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