Determine the average rate of change of f(x) = x² - 10x + 5 over the interval [-4, 4].

The normal distribution is a probability curve that describes a data set that follows a symmetrical pattern. In this case, the normal distribution applies because the reading level of the students in the elementary school is normally distributed.

The mean for the reading level is 85 words per minute and the standard deviation is 22 words per minute.

The child's reading level of 44.2 words per minute falls at the 16th percentile. This means that 16% of the students have a lower reading level than the child, and 84% have a higher reading level.  

The normal distribution graph (attached below) illustrates this concept, with the mean of 85 words per minute and the student's reading level marked at the 16th percentile.

The percentile of the student's reading level emphasizes the gravity of the situation. The graph demonstrates that the student is below average in reading level and is in need of remediation.

A suggested course of action is to provide the student with extra help in reading, such as one-on-one tutoring or extra reading material. Additionally, the student should be encouraged to practice and hone their reading skills in order to reach their reading potential.

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Pizza is therefore consumed in the following sequence, from best to worst: J. Antonio, Marcus, and Joe

A sequence in mathematics is a group of numbers that are organized in a particular order and that adhere to a particular pattern or formula. Sequences can be endless or finite and have a variety of uses in many disciplines, including probability theory, analysis, and number theory. Sequences can be defined recursively, where each term is defined in terms of the terms that came before it, or they can be defined using a formula that produces each term of the sequence. For instance, using the equation a = 2n, where n is a positive integer and a1 = 2 is the first term, one can determine the sequence of even numbers. If n is greater than 1, it can also be defined recursively as a1 = 2, and a = an-1 Plus 2.

given

Half of Joe's pie was consumed.

The result of multiplying the numerator and denominator by 3/8 is as follows:

5/8 × 3/3 = 15/24 = 5/8

We must change 3/4 into a comparable fraction with a denominator of 24 in order to compare this fraction to Joe and Marcus' fractions (the least common multiple of 3 and 8).

The result of multiplying the numerator and divisor by 6/6 is as follows:

3/4 × 6/6 = 18/24

Joe: 2/3

Marcus, 5/8 equals 15/24.

Thomas: 18/24

We can transform the fractions to decimals and arrange them in ascending order:

Joe: 2/3 = 0.666...

Marcus, 15/24 equals 0.625

Anthony: 18/24 equals 0.75

Pizza is therefore consumed in the following sequence, from best to worst: J. Antonio, Marcus, and Joe .

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The expression (3*6)+(4*12) is equal to 108.

The expression (3*6)+(4*12) can be written mathematically as 3x6+4x12=108. This can be solved by using the distributive property of multiplication over addition, which states that a*(b+c)=a*b+a*c. This can be applied to the expression in the following way: 3x6+4x12=(3x6)+(4x12)=3x(6+12)+4x(6+12)=3x18+4x18=54+72=108. Therefore, the expression (3*6)+(4*12)=108.

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Therefore, the probability that st > 0 is 9/24 or 3/8, which is approximately 0.375 or 37.5%.

Probability is a measure of how likely an event is to occur. It is a number between 0 and 1, with 0 suggesting that an occurrence is impossible and 1 indicating that an event is unavoidable. A given event's probability is computed by dividing the number of positive outcomes by the total number of potential possibilities.

Here,

To find the probability that st > 0, we need to consider all possible pairs of values (s, t) such that their product is positive.

We can start by considering the possible pairs of values for s and t separately.

For s, there are three possible values that are negative: -4, -3, and -1. There are also three possible values that are positive or zero: 0, 2, and 8.

For t, there are two possible values that are negative: -7 and 1. There are also two possible values that are positive: 4 and 6.

We can now list all possible pairs of values (s, t) and determine whether their product is positive:

(-4, -7): Negative

(-4, 1): Negative

(-4, 4): Negative

(-4, 6): Negative

(-3, -7): Positive

(-3, 1): Negative

(-3, 4): Negative

(-3, 6): Negative

(-1, -7): Positive

(-1, 1): Negative

(-1, 4): Negative

(-1, 6): Negative

(0, -7): Negative

(0, 1): Zero

(0, 4): Zero

(0, 6): Zero

(2, -7): Negative

(2, 1): Positive

(2, 4): Positive

(2, 6): Positive

(8, -7): Negative

(8, 1): Positive

(8, 4): Positive

(8, 6): Positive

Out of the 24 possible pairs, there are 9 pairs whose product is positive.

P=9/24

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Answer:

B) 7.4

C) 3.7

Step-by-step explanation:

B) The opposite of squaring is to square root. Therefore we do the square root of 55.11 to find the radius. (√55.11)

This is 7.4 (to one decimal place)

C) The diameter is half of the radius.

We divide the value in our calculator by 2

We get 3.7 (to one decimal place)

Sorry hon, just saw the comment on the last answer!

B. Approximately 7.4m

   To get to the answer... the equation was 55.11= r^2, so you would just find the square root of 55.11 to eliminate r.

C. Approximately 14.8m

  To get to the answer... diameter is just from one end of the circle to the opposite.  This being said, it is just double the radius.

The additional information that would be needed to prove that △WYZ and △XZY are congruent is (B) WY ≅ ZX.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

According to the ASA congruence rule, two triangles are congruent when their two included sides and two included angles are equivalent to each other.

So, we know that:

In △WYZ and △XZY:

ZY = ZY (Common)

∠Z = ∠Y (90°)

Then, additional information could be:

WY ≅ ZX

Therefore, the additional information that would be needed to prove that △WYZ and △XZY are congruent is (B) WY ≅ ZX.

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By using the graphs above, a graph that represent h(x), given that function h(x) = f(x) + g(x) include the following: A. graph A.

In Mathematics, the general form of a quadratic function is modeled by the following mathematical expression;

y = ax² + bx + c

Where:

Next, we would write quadratic functions that represent both f(x) and g(x) in standard form and with a leading coefficient of 1 as follows;

f(x) = (x + 3)(x + 1)

f(x) = x² + 3x + x + 3

f(x) = x² + 4x + 3

For the function g(x), we have the following:

g(x) = -(x - 3)(x - 1)

g(x) = -(x² - 3x - x + 3)

g(x) = -x² + 4x - 3

Therefore, a function that represent h(x) can be calculated as follows;

h(x) = f(x) + g(x)

h(x) = x² + 4x + 3 -x² + 4x - 3

h(x) = (x² - x²) + (4x + 4x) + (- 3 + 3)

h(x) = 8x

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We would need 4 pattern block triangles to create 2 trapezoids.

A trapezoid is a four-sided polygon (or quadrilateral) with at least one pair of parallel sides. The parallel sides of a trapezoid are called the bases, and the non-parallel sides are called the legs. The height (or altitude) of a trapezoid is the perpendicular distance between the two bases

To answer this question, we need to know the number of triangles that make up one trapezoid using pattern blocks.

One trapezoid made up of pattern blocks would have the following shapes:

2 trapezoids

2 triangles

1 parallelogram

So, one trapezoid would require 2 triangles.

If we want to create 2 trapezoids, we would need:

2 trapezoids x 2 triangles per trapezoid = 4 triangles

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High order thinking:

PART A:

If each friend buys 11 more action figures, then each will have x + 11 action figures. Since the total action figures is 120, we can write the equation:

[tex]5(x+11)=120[/tex]

PART B:

Solve for x. Divide both sides by 5.

[tex]x+11=24[/tex]

Substract 11 from both sides:

[tex]x=13\\[/tex]

Each friend originally had 13 action figures each.

Assessment practice:

11: Let Kevin Earns X amount

So, Jason earns = 2x - 32.50

= 212.50

2x = 2120 x 50 +32.40 = 245.00/2

= 122.5

Answer: Kevin Earns $122.50

12: Subtract 6. Then multiply by 2.

[tex]\frac{1}{2} x+6=18\\\\\frac{1}{2}x = 18-6\\\frac{1}{2}x=12\\\frac{1}{2}x*2=12*2\\x=24[/tex]

Thanks,
Eddie E.

Answer:

10)

a) 5x + 5(11) = 120

b) x = 13

11) $392.50

12) Letter D

Step-by-step explanation:

10:

5x + 5(11) = 120

5x + 55 = 120  Subtract 55 from both sides

5x + 55 - 55 = 120 - 55

5x = 65  Divide both sides by 5

[tex]\frac{5x}{5}[/tex] = [tex]\frac{65}{5}[/tex]

x = 13

11:

Let j = Jason's earnings

Let k = Kevin's earnings

j = 212.50

k = 2j - 32.50

substitute 212.50 for j in the second equation and solve for k

k = 2(212.50)- 32.50

k = 425 - 32.50

k = 392.50

Kevin earned $392.50.

12:

18 = [tex]\frac{1}{2}[/tex] x + 6   Subtract 6 from both sides

18 - 6 = [tex]\frac{1}{2}[/tex] x + 6 - 6

12 = [tex]\frac{1}{2}[/tex] x  Multiply both sides by 2

12(2) = [tex]\frac{1}{2}[/tex] x ([tex]\frac{2}{1}[/tex])   ([tex]\frac{2}{1}[/tex] is another name for 2)

24 = x

To solve we subtract 6 first and then multiply by 2.  Letter D.

Helping in the name of Jesus.

Answer:

40°

Step-by-step explanation:

The angles of a triangle will always sum to 180°.

Therefore, we can say that

[tex](x) + (x+6) + (2x+14) = 180\\4x + 20 = 180\\4x = 160\\x = 40[/tex]

The value of x° = 40°.

Given function, f(x) = x^6 - 12x^5 + 45x^4 - 405x^2 + 972x - 729; 3 (mult. 5).

Zeroes of f(x) are the values of x for which f(x) = 0. So, f(x) is factorable if and only if we can find zeroes of f(x).

Let's solve f(x) = 0 using x = 3 as the initial guess. Then, f(3) = 3^6 - 12(3^5) + 45(3^4) - 405(3^2) + 972(3) - 729 = 0. So, x = 3 is a zero of f(x) of the given multiplicity, which is 5.

Since x = 3 is a zero of f(x) of multiplicity 5, we can represent f(x) as follows:

$$f(x) = (x-3)^5 p(x)$$

where p(x) = EXPRESSF[X] and EXPRESSF[X] is a polynomial expression in x.

Now, we have to find the polynomial expression p(x) so that we can express f(x) as a product of linear factors.

The best way to find p(x) is by polynomial division:

$$\begin{array}{r|rrrrrr} &x^5&-5x^4&30x^3&-90x^2&180x&-243\\hline x-3&x^6&-12x^5&45x^4&-405x^2&972x&-729\\hline &x^6&-3x^5&+18x^4&-45x^3&135x^2&-243x\ & & & &360x^3&-1080x^2&648x\ & & & &360x^3&-1080x^2&648x\ & & & & &1260x^2&-891x\ & & & & &1260x^2&-3780x\ & & & & & &2889x\\end{array}$$

So, p(x) = x^5 - 3x^4 + 18x^3 - 45x^2 + 135x - 243.

Therefore, we can express f(x) as a product of linear factors as follows:

$$\begin{aligned}f(x) &= (x-3)^5 p(x)\ &= (x-3)^5 (x^5 - 3x^4 + 18x^3 - 45x^2 + 135x - 243)\ &= (x-3)^5 (x-3) (x^4 + 2x^3 + 12x^2 + 36x + 81)\ &= (x-3)^6 (x^4 + 2x^3 + 12x^2 + 36x + 81)\ \end{aligned}$$

Therefore, f(x) is a product of linear factors.

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Molly is correct in stating that the formula for finding the area of a parallelogram and a rectangle is the same.

A parallelogram is a four-sided polygon with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles of a parallelogram are also equal in measure. The area of a parallelogram can be found by multiplying the base of the parallelogram by its height, where the height is the perpendicular distance between the parallel sides. Some common examples of parallelograms include rectangles, squares, and rhombuses. Parallelograms are used in various areas of mathematics, physics, and engineering, and are commonly encountered in geometry problems and applications.

A rectangle is a four-sided polygon with two pairs of parallel sides and four right angles. The opposite sides of a rectangle are equal in length, and the adjacent sides are perpendicular to each other

Both a parallelogram and a rectangle are types of quadrilaterals (four-sided polygons). The formula for finding the area of any quadrilateral is to multiply the base of the shape by its height. In the case of a parallelogram, the base and height are not necessarily the same as the sides of the shape are not perpendicular to each other. However, in the case of a rectangle, the base and height are the same as the sides are perpendicular to each other.

Therefore, the formula for finding the area of a parallelogram is:

Area = base x height

And the formula for finding the area of a rectangle is also:

Area = base x height

Since the formulas are the same, Molly is correct in stating that the formula for finding the area of a parallelogram and a rectangle is the same.

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There are 15 true/false questions on the test and 5 multiple choice questions on the test.

Equations can be written in many forms, but they all have the same basic structure: an expression on the left-hand side of the equals sign, and an expression on the right-hand side of the equals sign, with the equals sign itself indicating that the two expressions are equal.

Let the number of true/false questions be x and the number of multiple choice questions be y. We know that:

x + y = 20 (since there are 20 questions in total)

3x + 11y = 100 (since the test is worth 100 points)

We can solve this system of equations by substitution or elimination. Here, we'll use substitution:

x + y = 20 -> x = 20 - y

Substitute x = 20 - y into the second equation:

3x + 11y = 100

3(20 - y) + 11y = 100

60 - 3y + 11y = 100

8y = 40

y = 5

So there are 5 multiple choice questions on the test. To find the number of true/false questions, we can substitute y = 5 back into x + y = 20:

x + y = 20

x + 5 = 20

x = 15

Therefore, there are 15 true/false questions on the test and 5 multiple choice questions on the test.

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The probability that between 44% and 54% of the sampled adults work during summer vacation is approximately 1.

The most important continuous probability distribution in probability theory and statistics is the normal distribution, often known as the gaussian distribution. It is also known as a bell curve sometimes. In every physical field and in economics, the normal distribution accurately or nearly represents a huge number of random variables. Moreover, it may be used to approximate different probability distributions, supporting the employment of the name "normal" as in reference to the most common distribution.

Given that, adults that work during summer vacation is:

p=0.49

The mean is:

μ = np = (300)(0.49) = 147

The standard deviation is given by:

σ = sqrt(npq) = sqrt((300)(0.49)(0.51)) ≈ 8.24.

Now, the probability that between 44% and 54%:

z1 = (0.44 - 0.49) / 0.00824 ≈ -6.07

z2 = (0.54 - 0.49) / 0.00824 ≈ 6.07

The area under this curve using the z-table is 1.

Thus, probability that between 44% and 54% of the sampled adults work during summer vacation is approximately 1.

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The probability οf getting 6 and 2 = [tex]\frac{1}{18}[/tex]

There are 216 ways to roll 3 dice.

Prοbability is a way of calculating how likely something is to happen. It is difficult to prοvide a complete prediction for many events. Using it, we can οnly forecast the probability, or likelihood, of an event occurring. The prοbability might be between 0 and 1, where 0 denotes an impοsibility and 1 denotes a certainty.

Here  that dice has been rοlled twice. So, there could be 1 number on the top side each time.

I also assume that the numbers may οr may not appear in given sequence.

Prοbability of getting 6 or 2 on first time = [tex]\frac{2}{6}[/tex]

Now since we have gοt either of six or two we need the other one now.

Examples are better for explaining. Sο, consider that two appeared on top now we need 6.

Prοbability of getting 6 = [tex]\frac{1}{6}[/tex]

Then prοbability of rοlling 6 and 2 = [tex]\frac{2}{6}\times\frac{1}{6}[/tex] = [tex]\frac{1}{18}[/tex]

When a dice is rolled, there are six possible outcomes.

So, the tοtal number of outcomes when three dice are rolled is

=> [tex]6\times6\times6=6^3=216.[/tex]

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Answer:

0.1

Step-by-step explanation:

100 x 10 = 1000. Essentially, you just add a zero to 100. so you take a zero out of .01. SO your answer is 0.1.

Answer: 0.1 fluid ounce

explanation:

since 100 drops of a liquid have 0.01 fluid ounces

1 drop of a liquid has (0.01/100)× 1 fluid ounces = 0.0001 ounces

so 1000 drops of a liquid have (1000×0.0001)= 0.1 fluid ounce

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=x^2-1\implies y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+0}x\stackrel{\stackrel{c}{\downarrow }}{-1} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 0}{2(1)}~~~~ ,~~~~ -1-\cfrac{ (0)^2}{4(1)}\right) \implies \left( - \cfrac{ 0 }{ 2 }~~,~~-1 - \cfrac{ 0 }{ 4 } \right) \\\\\\ \left( 0 ~~~~ ,~~~~ -1 +0 \right)\implies (0~~,~-1)[/tex]

The range of values of x that satisfy sec(x) = -√(2) and π/2 is:

x = 3π/4, 5π/4, 0.453, 5.829.

The range of values of x is calculated as follows;

Since sec(x) = 1/cos(x), we can use the identity cos^2(x) + sin^2(x) = 1 to solve for cos(x).

First, we consider the case where sec(x) = -√(2).

We know that sec(x) = 1/cos(x), so we can write:

1/cos(x) = -√(2)

Multiplying both sides by cos(x) gives:

1 = -√(2)cos(x)

Dividing both sides by -√(2) gives:

-1/√(2) = cos(x)

So, x is an angle whose cosine is -1/√(2). This occurs in the second quadrant, where cosine is negative. We can find the reference angle for this value of cosine by taking the arccosine of its absolute value:

arccos(|-1/√(2)|) = π/4

Therefore, x is either:

x = π - π/4 = 3π/4

or

x = π + π/4 = 5π/4

Next, we consider the case where sec(x) = π/2. We know that sec(x) = 1/cos(x), so we can write:

1/cos(x) = π/2

Multiplying both sides by cos(x) gives:

1 = π/2 cos(x)

Dividing both sides by π/2 gives:

2/π = cos(x)

So, x is an angle whose cosine is 2/π. This occurs in the first quadrant, where cosine is positive. We can find the reference angle for this value of cosine by taking the arccosine:

arccos(2/π)

Using a calculator, we find that:

arccos(2/π) ≈ 0.453

Therefore, x is either:

x = 0.453

or

x = 2π - 0.453 ≈ 5.829

So the range of values of x that satisfy sec(x) = -√(2) and π/2 is:

x = 3π/4, 5π/4, 0.453, 5.829

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The complete question is below:

If sec(x) = -√(2) and π/2, find the range of values of x

The measures of angles 1 and 2 are m∠1 = 50° m∠2 = 130 °

Given that the chord intercepted arc RQ = 53° and the chord intercepted arc ST = 47°, we must determine the angle 1 and angle 2 measurements.

The measure of the angle formed by two chords that intersect within the circle is equal to half the sum of the chord's intercepted arcs, as determined by the geometric property.

Measurement of angle 1 = (53° + 47°)/2 = 100°/2

m∠1 = 50°

m∠2 = 180°

m∠2 = 180° - 50°

m∠2 = 130°

Consequently, m1 = 50° and m2 = 130°.

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Complete Question:

What are the measures of angles 1 and 2? m∠1 = ° m∠2 = °

Answer:

-0.11

Step-by-step explanation:

Using a standard normal distribution table or calculator, we can find that the closest z-value to 0.48 in the table is -0.11.

This means that approximately 48% of the area under the standard normal distribution is to the left of -0.11.

Answer:

Below

Step-by-step explanation:

See image below

The expression 4x^2 + 14x + 10 can be completely factored into 2(2x + 5)(x + 1).

We can begin by factoring out the biggest common factor of the three components, which is 2, in order to factor 4x2 + 14x + 10 completely:

4x^2 + 14x + 10 = 2(2x^2 + 7x + 5)

The quadratic expression 2x2 + 7x + 5 must now be factored. Finding two binomials whose product is equal to 2x2 + 7x + 5 will help us achieve this.

Choose two integers that sum up to 7 and multiply by 2*5 to factor the expression. These are the digits 2 and 5. Hence, we can write:

2x^2 + 7x + 5 = 2x^2 + 2x + 5x + 5

= 2x(x + 1) + 5(x + 1)

= (2x + 5)(x + 1)

Adding this to our initial expression yields the following:

4x^2 + 14x + 10 = 2(2x + 5)

(x + 1)

As a result, the phrase 2(2x + 5)(x + 1) may completely factor the expression 4x2 + 14x + 10.

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[tex]2x^{2} - 22x - 52 = 2(x^{2} - 11x - 26) = 2(x^{2} + 2x - 13x - 26) = 2[x(x + 2) - 13(x - 2)]\\[/tex]

[tex]= \bf 2(x + 2)(x - 13)[/tex]

Answer:

-1

Step-by-step explanation:

if x<0 then the value of x must be a negative number

If we substitute the value of -1 for x in the equality equation, we get.

[tex]1 < 1[/tex]

Which does not satisfy the inequality.

Hope this helps!

Brainliest is much appreciated!

Answer:

-1 because -1 + 2 < 1
1 < 1 which is false therefor not satisfying the inequality.

Answer:

£155.55

Step-by-step explanation:

To determine the number of British pounds Brian will receive for R2100, begin by calculating the total commission he must pay an agent by multiplying the amount being exchanged (R2100) by the commission rate of 1.5%:

⇒ Commission = R2100 × 0.015 = R31.50

Subtract the commission from the total amount being exchanged to get the net amount:

⇒ Net amount = R2100 - R31.50 = R2068.50

Given R1 is worth 0.075199 British pounds, convert the net amount from South African rand to British pounds by multiplying by the exchange rate:

⇒ British pounds = 2068.50 × 0.075199

⇒ British pounds = £155.55 (2 d.p.)

Therefore, Brian will receive £155.55 for R2100 after paying a commission of R31.50.

Brian will get 155.5501 pounds for 2100 South African rand after paying an agent commission of 1.5%.

To calculate how many pounds Brian will get for 2100 South African rand, we can use the following steps:

Calculate the total amount of pounds that Brian would receive if there were no commission.

To do this, we can multiply the amount of South African rand (2100) by the exchange rate (0.075199):

2100 × 0.075199 = 157.9189 pounds

So without commission, Brian would receive 157.9189 pounds.

Calculate the commission that the agent will charge.

The commission is 1.5% of the total amount, so we can calculate it as:

0.015 × 157.9189 = 2.3688 pounds

So the agent will charge Brian a commission of 2.3688 pounds.

Calculate the final amount of pounds that Brian will receive.

To calculate the final amount of pounds, we can subtract the commission from the total amount of pounds:

157.9189 - 2.3688 = 155.5501 pounds

So Brian will receive 155.5501 pounds after paying the agent commission.

Therefore, Brian will get 155.5501 pounds for 2100 South African rand after paying an agent commission of 1.5%.

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An equation of the line that passes through the points (2, -9) and (-1, 1) is y + 9 = -10/3(x - 2).

In Mathematics, the point-slope form of any straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (2, -9), an equation of this line can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-9) = (1 - (-9))/(-1 - 2)(x - 2)

y + 9 = -10/3(x - 2)

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Answer:

A.

Two A's: 11.5 × 4 = 46   (since there are 2 A's, double that)   92 m

Two B's:   3.8 × 4 = 15.2   (since there are 2 B's, double that)   30.4 m

Two C's:   11.5 × 3.8 = 43.7   (since there are 2 C's, double that)   87.4 m

B.

Add the three totals.

The total surface area is 209.8 m².

Step-by-step explanation:

We can model the areas of rectangles B and C using the formula:

A = l × w,

where l is the shape's length, and w is its width.

So, the area of one rectangle B is:

3.8 × 4 = 15.2,

and the area of two of those is:

15.2 × 2 = 30.4

And, the area of one rectangle C is:

11.5 × 3.8 = 43.7.

So, the area of two of those is:

43.7 × 2 = 87.4.

The surface area of the figure is the sum of 2 A's, 2 B's and 2 C's:

92 m + 30.4 m + 87.4 m = 209.8 m

A) To the nearest 0.1°, [tex]$\angle ABC\approx63.8\textdegree$[/tex] and B) AC is approximately 4.2 units long, correct to 1 decimal place.

A) We can use the law of cosines to solve for the angles of triangle ABC and then use the fact that opposite angles in a cyclic quadrilateral are supplementary to find angle ADC. Finally, we can use the law of cosines again to find AC.

Let angle ABC be x. Then, applying the law of cosines to triangle ABC, we have:

[tex]$AC^2=AB^2+BC^2-(2AB* BC*\cos(x))$[/tex]

Substituting the given values, we get:

[tex]$AC^2=5^2+4.5^2-2\cdot5\cdot4.5\cdot\cos(x)$[/tex]

Simplifying and solving for AC, we get:

[tex]$AC=\sqrt{3.125+11.25\cos(x)-10\cos^2(x)}$[/tex]

Next, applying the law of cosines to triangle BCD, we have:

[tex]$\cos(ADC)=\frac{3.4^2+4.5^2-(2*3.4*4.5*\cos(x))}{3.4*4.5}$[/tex]

Simplifying, we get:

[tex]$\cos(ADC)=\frac{29.15-15.3\cos(x)}{15.3}$[/tex]

Since ABCD is a cyclic quadrilateral, we have:

[tex]$\angle ADC=180\textdegree-\angle ABC=180\textdegree-x$[/tex]

Substituting this into the above equation and solving for [tex]$\cos(x)$[/tex], we get:

[tex]$\cos(x)=\frac{7.2}{15.3}$[/tex]

Using a calculator, we find that

[tex]$x\approx63.8\textdegree$[/tex].

Therefore, [tex]$\angle ADC\approx116.2\textdegree$[/tex].

B) Finally, substituting [tex]$x\approx63.8\textdegree$[/tex] into the expression for AC, we get:

[tex]$AC=\sqrt{3.125+11.25\cos(63.8\textdegree)-10\cos^2(63.8\textdegree)}$[/tex]

[tex]$AC\approx4.2$[/tex]

Find out more about cyclic quadrilateral

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Question:

ABCD is a cyclic quadrilateral with AB=5.6cm,BC=4.5cm,CD=3.4cm and AD=2.5cm.Calculate

a)B in ABC

b)AC?

Answer:

-3x + 3z = 0

Step-by-step explanation:

To find an equation of the plane that contains the curve with the vector equation R(t) = (t, t^3, t), we can use the fact that a plane can be defined by a point and a normal vector to the plane. We can choose any point on the curve as a point on the plane, say (0, 0, 0), and find a normal vector to the plane by taking the cross product of the tangent vectors to the curve at two different points.

To find the tangent vector to the curve at a point (t, t^3, t), we can take the derivative of the vector equation with respect to t:

R'(t) = (1, 3t^2, 1)

So, the tangent vector to the curve at (t, t^3, t) is (1, 3t^2, 1).

Now, we can find the normal vector to the plane by taking the cross product of the tangent vectors at two different points on the curve. Let's choose the points (0, 0, 0) and (1, 1, 1) on the curve:

Tangent vector at (0, 0, 0): R'(0) = (1, 0, 1)

Tangent vector at (1, 1, 1): R'(1) = (1, 3, 1)

The normal vector to the plane is the cross product of these two tangent vectors:

N = R'(0) x R'(1) = (-3, 0, 3)

Now, we can use the point-normal form of the equation of a plane to find the equation of the plane that contains the curve:

N · (r - P) = 0, where N is the normal vector to the plane, P is a point on the plane, and r is a point on the plane.

Substituting in the values we have, we get:

(-3, 0, 3) · (r - (0, 0, 0)) = 0

Simplifying this equation gives us:

-3x + 3z = 0

Therefore, the equation of the plane that contains the curve with the vector equation R(t) = (t, t^3, t) is -3x + 3z = 0.

Answer:

$0.20 : 1 ounce

The nuts cost 20 cents per ounce.

Step-by-step explanation:

First, set up the ratio

$3.20 : 16 ounces [cost : weight]

Next, to find the price per ounce, divide each side by 16

$3.20 / 16: 16 ounces / 16

$0.20 : 1 ounce