2.2 2.1.4 a Given that A and B are complementary angles and 7 cos A-3 = 0. Determine WITHOUT the use of a calculator, the value of: 7 cos B-3 tan A. (4)​

Answer:

  40°, 60°, 80°

Step-by-step explanation:

You want the measures of the three angles of a triangle if the larger angles are 20° and 40° greater than the smallest.

The largest angle is 20° more than the middle angle, and the smallest is 20° less. Then the sum of the three angles is 3 times the middle angle, which must be 180°/3 = 60°.

The three angles are 40°, 60°, 80°.

__

Additional comment

If you need equations, you can designate the angles a, b, c, smallest to largest. Then c=a+40, and b=a+20. The sum is ...

  (a) +(a +20) +(a +40) = 3a +60 = 180

Dividing by 3 tells you ...

  a +20 = 60 . . . . . matches the value of b

  a = 60 -20 = 40

  c = 40 +40 = 80

If we were to write the equations in terms of b, we would have ...

  (b -20) +b +(b +20) = 180

  3b = 180

  b = 60

This version gives a 1-step equation to solve instead of a 2-step equation, easier to do mentally.

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The measure of the Angles in the triangle are: the smallest angle is 40 degrees, the largest angle is 80 degrees, and the remaining angle is 60 degrees.

The measure of the smallest angle as x.

According to the given information, the largest angle is 40 degrees more than the smallest angle. Therefore, the measure of the largest angle is x + 40.

Similarly, the remaining angle is 20 degrees more than the smallest angle. So, the measure of the remaining angle is x + 20.

The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:

x + (x + 40) + (x + 20) = 180.

Simplifying the equation, we have:

3x + 60 = 180.

Subtracting 60 from both sides of the equation:

3x = 120.

Dividing both sides by 3:

x = 40.

Therefore, the measure of the smallest angle is 40 degrees.

Using this value, we can find the measures of the other two angles:

The largest angle is x + 40 = 40 + 40 = 80 degrees.

The remaining angle is x + 20 = 40 + 20 = 60 degrees.

the measure of the angles in the triangle are: the smallest angle is 40 degrees, the largest angle is 80 degrees, and the remaining angle is 60 degrees.

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The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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

x + y > 3

x - 3y < 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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The four numbers are 1, 5, 11, and 23.

Four numbers have a mean of 10 and the median is 8. Two of the numbers are 1 and 5. The other two numbers must be 11 and 23.

The mean of a set of numbers is calculated by adding all of the numbers and dividing by the number of numbers. In this case, the mean is 10, so the sum of the four numbers is 40. We already know that two of the numbers are 1 and 5, so the other two numbers must add up to 34.

The median of a set of numbers is the middle number when the numbers are arranged in ascending order. In this case, the median is 8, so the third number must be 8. This leaves the fourth number to be either 11 or 23.

If the fourth number is 11, then the mean of the four numbers will be 9.5, which is not correct. Therefore, the fourth number must be 23.

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Using the fact that ∠A is congruent to ∠B and ∠C is a complement of ∠A, we determined that the measure of ∠B is 65° based on the given measure of ∠C as 25°.

If ∠A is congruent (≅) to ∠B and ∠C is a complement of ∠A, we can use the properties of complementary angles to find the measure of ∠B.

Given that m∠C = 25° and ∠C is a complement of ∠A, we know that ∠A + ∠C = 90°.

Since ∠A is congruent to ∠B, we can replace ∠A with ∠B in the equation:

∠B + ∠C = 90°.

Substituting the given value, we have:

∠B + 25° = 90°.

To isolate ∠B, we subtract 25° from both sides of the equation:

∠B = 90° - 25°.

Simplifying, we get:

∠B = 65°.

Therefore, the measure of ∠B is 65°.

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The slope of line WX is 2.Since the slope of RK is -1/2, the slope of WX will be the negative reciprocal of -1/2, which means we flip the fraction and change its sign:

slope of WX = -1 / (-1/2) = 2.

a) To find the slope of the line RK, we can use the formula:

slope = (change in y) / (change in x)

Given the points R(6, 9) and K(-6, 15), we can calculate the change in y and change in x:

change in y = 15 - 9 = 6

change in x = -6 - 6 = -12

Plugging these values into the slope formula:

slope = (6) / (-12) = -1/2

Therefore, the slope of line RK is -1/2.

b) Since line VB is parallel to line RK, it will have the same slope as RK. Therefore, the slope of line VB is also -1/2.

c) To find the slope of line WX, which is perpendicular to RK, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. Since the slope of RK is -1/2, the slope of WX will be the negative reciprocal of -1/2, which is 2.

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Answer:

F(4) = -256

Step-by-step explanation:

f(1)=4

f(2)= -4* f(1) = -4 *4 = -16             F(2 ) = -16

f(3) = -4* f(2) = -4* (-16) = 64       F(3) = 64  

f(4) = -4* f(3)  = -4* 64 = -256     F(4) = -256

Answer:

f(4) = -256

Step-by-step explanation:

A recursive formula defines the nth term of a sequence based on the values of earlier terms.

To find the value of f(4) using the given recursive formula, we can work our way up from f(1) using the formula repeatedly.

Given recursive rule:

[tex]\begin{cases}f(1)=4\\f(n)=-4f(n-1)\end{cases}[/tex]

To find f(2):

[tex]\begin{aligned}f(2)&=-4f(2-1)\\&=-4f(1)\\&=-4 \cdot 4\\&=-16\end{aligned}[/tex]

To find f(3):

[tex]\begin{aligned}f(3)&=-4f(3-1)\\&=-4f(2)\\&=-4 \cdot -16\\&=64\end{aligned}[/tex]

To find f(4):

[tex]\begin{aligned}f(4)&=-4f(4-1)\\&=-4f(3)\\&=-4 \cdot 64\\&=-256\end{aligned}[/tex]

Therefore, the value of f(4) is -256.

The reason that best supports Statement 2 in the given proof is

C. Linear Pair Postulate

The Linear Pair Postulate, also known as the Linear Pair Axiom, is a fundamental concept in geometry related to angles and their relationships. It states the following:

If two angles form a linear pair, then they are supplementary.

In the proof the angles are linear pair hence their sum id supplementary

∠ 1 + ∠ 2 = 180 degrees

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The Probability of guessing the right combination in one try is approximately 0.0007716, or 0.07716%.This probability is extremely low, indicating that it is highly unlikely to guess the correct combination by chance in a single attempt.

The probability of guessing the right combination in one try, we need to calculate the total number of possible combinations and the number of successful outcomes.

In this case, we have 4 dials, each with 6 letters. Since each dial can be set to one of the 6 letters, the number of possible combinations for each dial is 6.

To calculate the total number of possible combinations for the lock, we need to multiply the number of options for each dial. In this case, since we have 4 dials, the total number of combinations is:

6 * 6 * 6 * 6 = 6^4 = 1,296

So, there are 1,296 possible combinations in total.

Now, to calculate the probability of guessing the right combination in one try, we divide the number of successful outcomes (which is 1, as there is only one correct combination) by the total number of possible outcomes:

Probability = Number of successful outcomes / Total number of possible outcomes

Probability = 1 / 1,296

Simplifying this fraction, we get:

Probability = 1 / 1,296 ≈ 0.0007716

Therefore, the probability of guessing the right combination in one try is approximately 0.0007716, or 0.07716%.

This probability is extremely low, indicating that it is highly unlikely to guess the correct combination by chance in a single attempt. Locks with multiple dials and options are designed to provide a high level of security by creating a vast number of possible combinations, making it difficult to guess the correct one.

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[tex]\Huge \boxed{\Florin f(x) = 2x^{3} - 8x^{2} + 6x}[/tex]

The given zeros are 0, 1, and 3.

Since the zeros are the values of [tex]\bold{x}[/tex] that make the polynomial equal to zero, we can write the factors corresponding to each zero as [tex](x - 0)[/tex], [tex](x - 1)[/tex], and [tex](x - 3)[/tex].

Simplifying the first factor, we get [tex](x)[/tex], [tex](x - 1)[/tex], and [tex](x - 3)[/tex].

Now, multiply the factors together to form the polynomial:

                             [tex]\Large \boxed{(x)(x - 1)(x - 3)}[/tex]

Expanding this expression, we get:

                             [tex]\Large \boxed{x^{3} - 4x^{2} + 3x }[/tex]

The leading coefficient is 2, so we need to multiply the entire polynomial by 2:

                           [tex]\Large \boxed{2(x^{3} - 4x^{2} + 3x)}[/tex]

Expanding this expression, we get:

                          [tex]\Large \boxed{2x^{3} - 8x^{2} + 6x}[/tex]

So, the polynomial function in standard form with a leading coefficient of 2 and zeros at 0, 1, and 3 is:

                        [tex]\large \boxed{\Florin f(x) = 2x^{3} - 8x^{2} + 6x}[/tex]

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The value of the expression [tex]\sqrt[4]{a}^3[/tex] when evaluated is [tex]a^\frac34[/tex]

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

[tex]\sqrt[4]{a}^3[/tex]

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

[tex]\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}[/tex]

Apply the exponent rule of indices

[tex]\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14[/tex]

Apply the power rule of indices

[tex]\sqrt[4]{a}^3 = a^\frac34[/tex]

Hence, the expression [tex]\sqrt[4]{a}^3[/tex] when evaluated is [tex]a^\frac34[/tex]

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Answer:

19.2

Step-by-step explanation:

(32) 3/5

= 32 multiple 3/5

= 96/5 [ explanation: 32 multiple 3 = 96 ]

= 19.2 [ explanation: 96 divided by 5 = 19.2 ]

The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

The area of the sector is approximately 36.0 ft²

To find the area of the sector formed by a central angle of 260° in a circle with a radius of 4 ft, you can use the formula:

Area of sector = (θ/360°) * π * r²

where θ is the central angle in degrees, π is the value of pi, and r is the radius.

Plugging in the values:

θ = 260°

r = 4 ft

π = 3.14

Area of sector = (260/360) * 3.14 * 4²

Area of sector = (0.7222) * 3.14 * 16 = 36.3 square feet

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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: The function rule is f(x) = 5(10)^x. Using this rule, we can find f(0) by substituting x with 0: f(0) = 5(10)^0 = 5 * 1 = 5. So f(0) = 5.

Here are the steps to find f(0) using the function rule f(x) = 5(10)^x:

1. Substitute x with 0 in the function rule: f(0) = 5(10)^0

2. Any non-zero number raised to the power of 0 is equal to 1: f(0) = 5 * 1

3. Multiply 5 by 1: f(0) = 5

4. So f(0) = 5.

Answer:

f(0) = 5

Step-by-step explanation:

The given function is:

[tex]f(x)=5(10)^x[/tex]

To find f(0), substitute x = 0 into the given function:

[tex]f(0)=5(10)^0[/tex]

According to the zero exponent property, any non-zero number raised to the power of zero is equal to 1. Therefore, 10⁰ = 1:

[tex]f(0)=5 \cdot 1[/tex]

According to the multiplicative identity property, when any number is multiplied by 1, the result is equal to the original number. Therefore:

[tex]f(0)=5[/tex]

The converse of the parallelogram angle theorem is proved.

The term parallelogram is defined as a quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle and then the quadrilateral.

Here we are given that  LM ≅ ON and  LO ≅ MN

Here we have also know that ∠LNO and ∠NLM are alternative and interior angles

Then according to the reflexive property, it can be written as

=> LN ≅ LN

Then as per the SSS similarity the given triangle is written as,

ΔLNO ≅ ΔNLM

Here we have also it can be written as ∠OLN ≅ ∠MNL and  ∠LNO ≅ ∠NLM

Then it can be written as LM || ON and  LO || MN

Then the LMNO is a parallelogram

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Answer:

Question 3) c.

Question 4) d.

Step-by-step explanation:

For the first question, it would be c., x is greater than and equal to -5. On the graph, there is a point at, (-5, -4). This restricts the graph from being all real numbers and the x value can't be less than -5. Since the point is a closed circle, it includes the point, so the domain will be -5, and everything greater than that value, making it C.

For the next question its asking for the range of the given graph. The range is based on y values. Domain is based on x values. There is a point at (-5, -4). Restrict the values of y to not be anything less than -4. And since the function continues and increases to positive infinity, the range would have to be y is greater than and equal to -4, making it d.

The equation of the line in slope-intercept form is y = (3/4)x.

To write the equation of a line in slope-intercept form, we need to use the slope-intercept form equation: y = mx + b,

where m is the slope and b is the y-intercept.

Given that the line passes through the point (-8, 5) and has a slope of 3/4, we can substitute the values into the equation to find the y-intercept (b).

First, let's find the value of b using the point-slope form equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Using (-8, 5) as the point and 3/4 as the slope, we have:

5 - 5 = (3/4)(-8 - x)

0 = (3/4)(-8 - x)

0 = (-3/4)(8 + x)

0 = -6 - (3/4)x

Next, we can solve for x:

(3/4)x = -6

x = -6 [tex]\times[/tex] (4/3)

x = -8

Now that we have the value of x, we can substitute it back into the equation to find the value of b:

0 = -6 - (3/4)(-8)

0 = -6 + 6

0 = 0

So, the value of b is 0.

Finally, we can write the equation of the line in slope-intercept form:

y = (3/4)x + 0

y = (3/4)x.

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The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

The correct ordered pairs represented in the table are (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).

The given table represents a function f(c) where c represents the quantity of furniture and f(c) represents the per unit cost in hundreds of dollars. We need to determine the correct ordered pairs based on the given information.

From the table, we can see that the values of c increase by 1 each time, starting from 1 and going up to 5. Similarly, the values of f(c) represent the square of the corresponding value of c. For example, f(1) = 1, f(2) = 4, f(3) = 9, and so on.

Based on this pattern, we can determine the correct ordered pairs:

(1, 1) corresponds to c = 1 and f(c) = 1

(2, 4) corresponds to c = 2 and f(c) = 4

(3, 9) corresponds to c = 3 and f(c) = 9

(4, 16) corresponds to c = 4 and f(c) = 16

(5, 25) corresponds to c = 5 and f(c) = 25

Therefore, the correct ordered pairs represented in the table are (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).

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19. The calculated value of x in the triangles is 5

21. The calculated value of x in the triangles is 4

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

The similar figures

The value of x can then be calculated using the following ratio

x : 4 = 15 : 12

Express the ratio as fraction

So, we have

x/4 = 15/12

Solving for x, we have

x = 4 * 15/12

Evaluate

x = 5

Hence, the value of x is 5

For the second pair of triangles, we have the following ratio

x : 2 = 12 : 6

Express the ratio as fraction

So, we have

x/2 = 12/6

Solving for x, we have

x = 2 * 12/6

Evaluate

x = 4

Hence, the value of x is 4

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If a pattern is observed in a residual plot, such as non-linearity, heteroscedasticity, outliers, or systematic deviations, it indicates that a linear model may not be a good fit for the data.

A residual plot is a graphical representation that shows the difference between the observed values of the dependent variable and the predicted values by a linear regression model. It is useful for assessing the goodness of fit of the model to the data.

When examining a residual plot, if a clear pattern or structure is observed, it suggests that the linear model may not be an appropriate fit for the data. Here's why:

In summary, It suggests the need for alternative models or adjustments to better capture the underlying relationships in the dataset.

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Answer:

The cross-over diagram is correct. The number of flies of each sex with red eyes will depend on the genotype of the parents.If a red-eyed male mates with a white-eyed female, all of the offspring will be female and have red eyes (XRXr).If a red-eyed male mates with a red-eyed female, half of the offspring will be male and have red eyes (XRY) and half will be female and have red eyes (XRXr).If a white-eyed male mates with a white-eyed female, all of the offspring will be white-eyed (XrXr).Therefore, if there are 100 males and 200 females, the number of flies of each sex with red eyes will be:Males: 50Females: 150I hope this helps!

The set B is the set of integers between -1 and 1, which includes -1, 0, and 1.

The set B can be defined as follows:

B = {x: x is an integer between -1 and 1}

This means that B is a set that contains all the integers x that satisfy the condition of being between -1 and 1. In other words, B includes the integers -1, 0, and 1. These are the only integers that fall within the specified range.

To represent this set in roster notation, we can write:

B = {-1, 0, 1}

In set-builder notation, we can express B as:

B = {x | x ∈ ℤ, -1 ≤ x ≤ 1}

This notation indicates that B consists of all the integers x such that x belongs to the set of integers (ℤ) and x is greater than or equal to -1 and less than or equal to 1.

In summary, the set B is the set of integers between -1 and 1, which includes -1, 0, and 1.

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Answer:

[tex]6[/tex]

Step-by-step explanation:

[tex]\mathrm{Solution: }\\\\\mathrm{sin30^o=\frac{p}{h}=\frac{a}{12}}\\\\\mathrm{or,\ \frac{1}{2}=\frac{a}{12}}\\\\\mathrm{or,\ 2a=12}\\\\\mathrm{\therefore a=6}[/tex]

Answer:

[tex]\$17181.86[/tex]

Step-by-step explanation:

[tex]A=P(1+r)^t\\A=10000(1+0.07)^8\\A=10000(1.07)^8\\A\approx\$17181.86[/tex]

Answer: $17182.

This is an example of an exponential growth function, which looks like f(x)=a(1+r)^x, where r is the growth rate, a is the initial value, and x is the time. 10000 is the initial value, 7% is the growth rate, and 8 years is the time. 7% can become 0.07. f(x)=10000(1+0.07)^8. f(x)=10000(1.07)^8. First simplify the exponent. f(x)=10000(1.71818618). f(x)≈17182.