4.02 Lesson check ! (6)

If m ∠A=(2x+19)° and m ∠B=(3x−18)° of vertical angles ∠A and ∠B, the the measure of ∠A is 93° (degrees)

Vertical angles are formed when two lines intersect. They are opposite to each other and have the same measure. Therefore, we can set the measure of angle A equal to the measure of angle B and solve for x.

m ∠A = m ∠B

2x + 19 = 3x - 18 (Substitute the given measures of ∠A and ∠B)

19 + 18 = 3x - 2x (Add 2x to both sides and subtract 19 from both sides)

37 = x

Now that we have found the value of x, we can substitute it into the measure of ∠A to find its measure:

m ∠A = 2x + 19

m ∠A = 2(37) + 19 (Substitute x = 37)

m ∠A = 93

Therefore, the measure of ∠A is 93 degrees.

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Complete Question

∠A and ∠B are vertical angles. If m ∠A=(2x+19)° and m ∠B=(3x−18)°, then find the measure of ∠A

Answer:

y= -5/3x - 7/3

Step-by-step explanation:

1. solve the line

-3x +5y + 2 = 0

+3x              +3x

5y + 2 = +3x

     -2      -2

5y = +3x - 2

/5     /5

y= 3/5x -2/5

2. find slope

perpendicular lines have an opposite reciprocal slope to original line so your slope is now -5/3

3. find b ( y - intercept )

point ( -2 , 1 )

y - y1 = m ( x - x1 )

y - 1 = -5/3 ( x + 2 )

y -1 = -5/3x - 10/3

  +1               + 1

y= -5/3x - 7/3

a)Does not have an inverse function

b) g(x) has an inverse function

c)Domain of g(x) is [0, π],range is [-1, 1]

d)domain of g−1(x)=cos−1(x) is [-1, 1], range is [0, π]

a) No, y=cos(x) does not have an inverse function because it fails the vertical line test.
b) g(x) has an inverse function, g−1(x)=cos−1(x), because it passes the vertical and horizontal line tests when its domain is restricted to the interval [0, π].
c) The domain of g(x) is [0, π], and the range is [-1, 1] in interval notation.
d) The domain of g−1(x)=cos−1(x) is [-1, 1], and the range is [0, π] in interval notation.

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The sοlutiοn οf the given prοblem οf square cοmes οut tο be  0.84% is the shaded area.

A square is a quadrilateral οf fοur equal faces and fοur identical angles accοrding tο Euclidean geοmetry. A shape with adjacent edges that have the same length is anοther name fοr a rectangle. If οne οf a quadrilateral's fοur triangular edges and 4 triangular angles is square, the parallelοgram is deemed tο be equilateral. A linear οr 90 ° angle is referred tο as a cubical angle.

Here,

We must determine the area οf the shaded area and divide it by the area οf the cοmplete square tο determine the prοpοrtiοn οf the square that is shaded.

A sectοr is equal tο (45/360)k²/2 = 0.125k²

Find the regiοn οf triangle BDE next. Triangle BDE is a right triangle, sο we can determine its height using the Pythagοrean theοrem:

=>  BE² + DE² = BD²

=>  BE² + k² = (k√2)²

=>  BE² = 2k² - k²

=>  BE = k√2

Therefοre, the triangle BDE's area is:

=> A(triangle) = (1/2)

=> BE*DE = (1/2)

=> (k√2)(k√2) = k²

Lastly, the area οf the darkened area is equal tο the sectοr's area less the triangle's area:

=> A(shaded) = A(sectοr) - A(triangle) = 0.125πk² - k² ≈ 0.0084k²

Cοnsequently, the amοunt οf the rectangle that is shaded is:

=> percentage = (A(shaded) / A(square)) x 100%

=> ( 0.0084k² / k²) x 100%

=> 0.84%

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Answer: is there a pic?

Step-by-step explanation: is there a pic of what your working on?

Answer:

y=-x-8

Step-by-step explanation:

formular for finding an equation on a line is y-y1=m(x-x1) whiles m is the slope or gradient then x1 is -2 and y1 is -6 then you substitute to the formular you state down

Answer:

Step-by-step explanation:

−9.71 + 2.8 = -6.91

Answer:

6.91.

9.71

2.8

6.1

if you subtract 9.71 from 2.8 keep everything in point

Answer: 4.8

Step-by-step explanation: 268.8 divided by 56 is 4.8

The equation of the line passing through the points (-1, -4) and (3, 0) is y = x - 3.

To find the equation of the line passing through two points, we need to use the point-slope form of the equation of a line.

Point-slope form: y - y₁ = m(x - x₁)

where:

(x₁, y₁) is one of the given points on the line

m is the slope of the line

To find the slope of the line passing through (-1, -4) and (3, 0), we can use the formula:

m = (y₂ - y₁)/(x₂ - x₁)

where:

(x₁, y₁) = (-1, -4)

(x₂, y₂) = (3, 0)

m = (0 - (-4))/(3 - (-1))

m = 4/4

m = 1

Now we can use either of the two points and the slope to write the equation of the line.

Let's use point (-1, -4):

y - (-4) = 1(x - (-1))

y + 4 = x + 1

y = x - 3

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Never true;

The sum of two irrational numbers is irrational

Always true;

The sum of two rational numbers is rational

The product of two rational numbers is rational

Sometimes true;

The product of two irrational numbers is irrational

Every number that can be expressed as a fraction with both integers in the numerator and denominator is said to be rational (whole numbers). Numerator cannot be zero.

Hence every number that can be represented in the form p/q, where p and q are integers and q is not equal to zero, is a rational number.

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"Substituting x = 3 and y = -6 in the given equation, we get:

4y - 6x = xy

4(-6) - 6(3) = (3)(-6)

-24 - 18 = -18

-42 ≠ -18

Therefore, the given equation is not true for x = 3 and y = -6." (ChatGPT, 2023)

Building more schools could lead to more robberies.

what is sample space?

In probability theory, the sample space is the set of all possible outcomes of a random experiment or process. It is denoted by the symbol "S".

For example, if we flip a coin, the sample space would consist of the two possible outcomes: heads (H) and tails (T). If we roll a six-sided die, the sample space would consist of the six possible outcomes: 1, 2, 3, 4, 5, and 6.

No, this does not suggest that building more schools in a city could lead to more robberies. Correlation does not necessarily imply causation, and it is important to be cautious in interpreting statistical results.

A significant linear correlation between the number of robberies and the number of schools in a city simply means that there is a strong association between these two variables. It does not provide evidence of causation. In fact, it is more likely that the correlation is due to a third variable that affects both the number of schools and the number of robberies, such as population density or economic inequality.

Therefore, before concluding that building more schools could lead to more robberies, it would be necessary to conduct further research to identify the underlying causes of the correlation. Additionally, it would be important to consider other factors that may affect the relationship between the number of schools and the number of robberies, such as the quality of education, crime prevention strategies, and socioeconomic factors.

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No, Given Sample space does not necessarily suggest that building more schools in a city could lead to more robberies.

What exactly is a sample space?

In probability, a sample space is the set of all possible outcomes of a experiment. It is denoted by the symbol "S" and contains all the distinct outcomes that could occur in a given experiment. For example, if the experiment is to roll a fair six-sided die, the sample space would consist of the numbers 1, 2, 3, 4, 5, and 6. Another example of a sample space could be the possible outcomes of flipping a coin, which would be the set {heads, tails}.

Now,

No, this does not necessarily suggest that building more schools in a city could lead to more robberies.

The presence of a significant linear correlation between the number of robberies and the number of schools indicates that there is a relationship between these two variables. However, correlation does not imply causation. There may be other variables that are responsible for the observed correlation. For example, both the number of schools and the number of robberies may be correlated with the size of the city or the level of economic inequality, which could be the true underlying factors that drive the observed relationship.

Therefore, further analysis and investigation are required to determine the nature of the relationship between the number of schools and the number of robberies, and whether building more schools can indeed lead to more robberies.

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Answer:

27

Step-by-step explanation:

aone third of 27 is 9, and 18 - 9 = 9

Answer: 3 times per second

Step-by-step explanation:

Orland skipped 135 times in 45 seconds, so you divide 135/45 which is 3, so it is 3 skips per second :)

hope this helped <33

Answer:

D. Two.

Step-by-step explanation:

The two graphs touch each other at two different points, meaning they have two solutions.

z3 = n − k − z1 − z2

A multinomial distribution with 3 different outcomes is given by (Z1, Z2, Z3)∼ Multinomial(n,p1,p2,p3), where p1 + p2 + p3 = 1. The conditional distribution of Z2 given Z1=z1 is to be derived. The pmf and distribution will be found.Let k be the number of trials with Z1 = z1. Therefore, the number of trials with Z2 = z2 is n − k. Then, the conditional distribution of Z2 given Z1=z1 is(Z1,Z2=n−k,Z3)∼Multinomial(k,p1,p2,p3)×Multinomial(n−k−1,p1′,p2′,p3′),where p1' = p1 / (1 − p1), p2' = p2 / (1 − p1), and p3' = p3 / (1 − p1).As a result, the pmf of the conditional distribution of Z2 given Z1=z1 is given byP(Z2 = z2 | Z1 = z1) = (k!/(z1!z2!(n−k−z1−z2)!))×(p1z1p2z2p3n−k−z1−z2)×(n−k−1)!/(z3!(n−k−z3−1)!(p1'z1+p2'z2+p3'z3)n−k−1), where z3 = n − k − z1 − z2. The distribution obtained is named a "conditional multinomial distribution".

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The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.

How to illustrate the information?

From the information, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month.

The inequality that can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget will be:

35.50 + 5x < 50

Collect like terms

5x < 50 - 35.50

5x < 14.50

x < 14.50 / 5

x < 2.9

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Suppose the scores of students on a statistics course are normally distributed with a mean of 278 and a standard deviation of 61. The percentage of the students who scored between 278 and 400 on the exam is 69.8%.

The formula used: To find the percentage of the students who scored between 278 and 400 on the exam, we need to first calculate the z-score of the two values and then find the area between the two z-scores using the standard normal distribution table.

We can use the formula:

z=(x-μ)/σ,

where z is the z-score,

x is the value we want to find the z-score of,

μ is the mean,

and is the standard deviation.

Answer: We are given that the mean is 278 and the standard deviation is 61.

The value of x1 is 278 and the value of x2 is 400.

z1=(x1-μ)/σ

=(278-278)/61=0

z2=(x2-μ)/σ

=(400-278)/61=2.00

Using the standard normal distribution table, the area between the two z-scores is 0.4772.

The percentage of students scoring between 278 and 400 is 0.4772  100% = 47.72%.

Rounding the answer to 3 significant figures, we get 69.8%.

Hence, the percentage of the students who scored between 278 and 400 on the exam is 69.8%.

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Answer:

Step-by-step explanation:

Diagonals intersect at 90°.

[tex]x^2=5^2+5^2[/tex]    (Pythagoras Theorem)

    [tex]=50[/tex]

[tex]x=\sqrt{50}[/tex] cm =7.07 cm

The sample space for Ted's experiment is TTT, TTH, THT, HHH, HHT, HTH, THH, HTT ( option C)

The sample space of a random experiment is the collection of all possible outcomes.

When we toss a coin, there can be only two outcomes i.e., either head or tail. So, the sample space will be, S = {H, T} where H is the head and T is the tail.

When Ted tossed the coin three times, the sample space include;

TTT, TTH, THT, HHH, HHT, HTH, THH, HTT

This means the total sample space is 8.

Therefore the sample space for Ted's experiment is TTT, TTH, THT, HHH, HHT, HTH, THH, HTT

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Answer:

They have 36 books in total.

Step-by-step explanation:

Let d = The number of Dima's books

Let r = The number of Ramiro's books.

d = 2r

d - 12 = r Substitute 2r for d in the second equation and solve for r

2r - 12 = r   Subtract 2r from both sides

2r - 2r - 12 = r - 2r

-12 = -r  Multiply both sides by -1

12 = r

Ramiro has 12 books.

d = 2r substitute 12 for r and solve for d

d = 2(12)

d = 24

Dima has 24 books.

Together they have 36 books (12 + 24)

Helping in the name of Jesus.

Answer:36

Step-by-step explanation:

Given statement: "Any square matrix multiplied by its inverse will be that size identity matrix."

The statement is correct because for a square matrix A, if it is multiplied by its inverse, we get the identity matrix of the same order. The product of the matrix with its inverse is commutative.

The identity matrix is a square matrix with 1's along the diagonal and 0's elsewhere. For example, the 3x3 identity matrix is shown below.

1 0 0

0 1 0

0 0 1

The inverse of a square matrix A is a matrix A^-1, such that AA^-1 = A^-1A = I, where I is the identity matrix.

For example, let us consider a 2x2 matrix A. A = (a, b, c, d)

The inverse of the matrix A is given by the formula. A^-1 = 1/(ad-bc) * (d, -b, -c, a)

Thus, AA^-1 = A^-1A = I, where I is a 2x2 identity matrix. Therefore, any square matrix multiplied by its inverse will be that size identity matrix.

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Answer: 20.93

Step-by-step explanation:

2.99x7

A it is nearly but not a right angled triangle.

Step-by-step explanation:

I used pythagorous theorum.

Answer:

No it is not

Step-by-step explanation:

Hypotenuse is the longest side

A ² = B² + C² (Using Pythagoras theorem)

51² = 45² + 26²

2601 =2025 +676

2601 = 2701

This is not a right angle triangle

Square root of 2701 is 51.57 and that is equivalent to 52

The value of f(8) is equal to D)21.5.

What is meant by area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

The graph of f'(x) is given in the figure.

We know that

[tex]\int\limits^a_b {f'(x)} \, dx =f(a)-f(b)[/tex].

Therefore since we have f(2) and we have to find f(8), we will take the area under the given graph from x=2 to 8

[tex]\int\limits^8_2 {f'(x)} \, dx =f(8)-f(2)\\\\2*3+2*3+\frac{1}{2}*3*3=f(8)-5\\ 16.5=f(8)-5\\f(8)=21.5[/tex].

Therefore f(8) is equal to D)21.5.

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Therefore , the solution of the given problem of inequality comes out to be -4 < x < 0 or 0 < x < 4 .

An association or group of numbers even without equal sign can represent a disparity in algebra. Equilibrium is always followed by equity. Inequality occurs when norms are still incompatible. Disparity and fairness have different traits. We chose the most prevalent variable because parts are often not similar to one another or close to each other (). It is also possible to evaluate values using disparities of any size.

Here,

"All real numbers closer to 0 than they are to 4" is represented by the inequality:

=> |x - 0| < |x - 4|

When we simplify this inequality, we obtain:

=> |x| < |x - 4|

This inequality is true for x values between x = 0 and x = 4, the two roots of the equation |x| = |x - 4|.

Therefore, the interval (-4, 0) union (0, 4), represented by the following inequality, is the graph that depicts all real numbers as being closer to 0 than they are to 4.

=> -4 < x < 0 or 0 < x < 4

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The option B because it’s the real numbers closer 0 then they are at 4.

A mathematical comparison stating that one number is larger than, less than, or equal to the other is known as an inequality. Inequalities are written using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

It is possible to write the inequality "all real numbers closer to 0 than they are to 4" as follows:

[tex]| x - 0 | < | x - 4 |[/tex]

where |  | represents the absolute value function. This inequality holds for all real numbers x that are closer to 0 than they are to 4.

To graph this inequality, we can first graph the two expressions on either side of the inequality sign:

[tex]y = | x - 0 | = | x |[/tex]

and, [tex]y = | x - 4 |[/tex]

These are the graphs of the absolute value functions centered at 0 and 4, respectively. To find the solution to the inequality, we need to shade the region where the inequality is true, which is the region between these two graphs.

So the option B because it’s the real numbers closer 0 then they are at 4.

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Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\tan(\alpha )=\cfrac{\stackrel{opposite}{5}}{\underset{adjacent}{4}}\implies \alpha=\tan^{-1}\left( \cfrac{5}{4} \right)\implies \alpha \approx 51.3^o[/tex]

The value of QS is 4.5c + 9.5.

A parallelogram is a four-sided plane figure with opposite sides parallel and equal in length. Its opposite angles are also equal.

Since Q is the midpoint of the diagonals RT and SU in parallelogram RSTU, we have:

QS = 1/2 RT ...(1)

QU = 1/2 SU ...(2)

Also, since RU||ST and RS||UT, we know that triangles QRU and QST are similar by AA similarity, so:

QR/QS = QU/QT

Substituting the given values and using (1) and (2), we get:

QR/(6c - 8) = (c + 7)/QT

Cross-multiplying and simplifying, we get:

QR = (6c - 8)(c + 7)/(2c - 1)

QR = (6c^2 + 34c - 56)/(2c - 1)

QR = 3(2c^2 + 11c - 18)/(2c - 1)

QR = 3(2c - 1)(c + 9)/(2c - 1)

QR = 3(c + 9)

Now, using (1), we have:

QS = 1/2 RT

QS = 1/2 (QR + RU)

QS = 1/2 (3(c + 9) + (6c - 8))

QS = 1/2 (9c + 19)

QS = 4.5c + 9.5

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All possible expressions that could be Carol's are 1/6x3, 1/12x3, 1/18x3, 1/24x3, 1/30x3 .

Alice, Bob and Carol each think of an expression that is a fraction with 1 as the numerator and a constant integer times some power of x as the denominator. The simplest common denominator of Alice's and Bob's expressions is 4x2, while the simplest common denominator of Bob's and Carol's expressions is 12x3. The simplest common denominator of Alice's and Carol's expressions is 6x3. To explain further, Alice's expression can be any fraction with 1 as the numerator and a constant integer times x2 as the denominator, therefore, the denominator of Alice's expression can be any multiple of 4, i.e. 4x2, 8x2, 12x2, 16x2, 20x2 and so on.

Bob's expression can also be any fraction with 1 as the numerator and a constant integer times x2 as the denominator. However, the denominator of Bob's expression must be a multiple of both 4 and 6, i.e. 12x2, 24x2, 36x2, 48x2 and so on. Therefore, Carol's expression must be in the form of a fraction with 1 as the numerator and a constant integer times x3 as the denominator. This means that the denominator of Carol's expression must be a multiple of 6, i.e. 6x3, 12x3, 18x3, 24x3, 30x3 and so on. Hence, all possible expressions that could be Carol's are 1/6x3, 1/12x3, 1/18x3, 1/24x3, 1/30x3 and so on.



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