If the groub A= {-3} then IAI equals?

a)The value of  ∠b=64°.

b)The values of angles q, r, s, t are ∠q= 65°, ∠r=65°, ∠s=50°, ∠t=65°.

c)The value of  ∠B=72 degrees.

The same-side interior angles are additional if a transversal connects two parallel lines. Alternate interior angles are equivalent if a transversal connects two parallel lines. Corresponding angles are equal.

a) Given line PQ is parallel to ST.

   One of the theorems of parallel lines is, Corresponding angles are equal.

Here the corresponding angles are ∠a, ∠b.

so, ∠a=∠b

∴∠b=64°

b) It is given that lines B and C are parallel, according to one of the theorems of parallel lines, vertically opposite angles are equal. So, the angle opposite to 65° is also equal to 65°. Sum of the angles suspended by a line on another line is 180°. Therefore the other angle in the triangle is 180°-130°=50°.

Since the sum of interior angles in a triangle is 180°, the angle q will be:

   ∠q= 180°-(65°+50°)

    ∠q= 65°.

Vertically opposite angles are equal, therefore ∠q=∠r=65°.

∠s=180°-(65°+65°)

∠s=50°.

Corresponding angles are equal, therefore

130°=65°+∠t

∠t=65°.

c) Given lines A, and B are parallel. We know that the Corresponding angles are equal, therefore

3m=4m-24

⇒m=24

Therefore ∠B=4(24)-24

∠B=72 degrees.

To learn more about parallel lines properties refer to the link below:

https://brainly.com/question/29549295

#SPJ1

Answer:

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

Step-by-step explanation:

To find the quadratic equation that passes through these points, we can start by using the standard form of a quadratic equation:

y = ax^2 + bx + c

We know that the graph passes through the point (-2,2), so we can substitute these values into the equation:

2 = a(-2)^2 + b(-2) + c

Simplifying this equation, we get:

4a - 2b + c = 2

We also know that the graph has x-intercepts at (-1,0) and (6,0). This means that when x = -1 and x = 6, the value of y (i.e., the height of the graph) is 0. We can use these two points to write two more equations:

0 = a(-1)^2 + b(-1) + c

0 = a(6)^2 + b(6) + c

Simplifying these equations, we get:

a - b + c = 0

36a + 6b + c = 0

Now we have a system of three equations:

4a - 2b + c = 2

a - b + c = 0

36a + 6b + c = 0

We can solve for a, b, and c using any method of solving systems of equations. One way is to use substitution:

From the second equation, we get:

c = b - a

Substituting this into the other two equations, we get:

4a - 2b + (b - a) = 2

36a + 6b + (b - a) = 0

Simplifying these equations, we get:

3a - b = 1

35a + 7b = -b

Multiplying the first equation by 7 and adding it to the second equation, we eliminate b:

21a = -7

a = -1/3

Substituting this value of a into the first equation, we can solve for b:

4(-1/3) - 2b + (b - (-1/3)) = 2

-4/3 - b + b + 1/3 = 2

b = -2

Finally, we can use either of the first two equations to solve for c:

c = a - b = (-1/3) - (-2) = 5/3

So the quadratic equation in standard form is:

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

The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589

See table for sum of values.

The regression equation is:

y=α+βx

β = \(\frac{Sxx}{Syy}\)=6995-97799779\(\frac{6995-9\times\frac{779}{9}\times\frac{77}{9}}{68613-9(\frac{779}{9} )2}\)= 0.449

α=y-βx= 779-(0.449)7799 = =-30.27

The equation is y=-30.27+0.449x

Where y = predicted variable; x = independent variable = 0.449; - 30.27 = intercept/ slope

Constructing a 91% prediction interval for y:

x = 910

Inputting x = 91 into the regression equation : y = 0.449(91) - 30.27

y = 40.859 - 30.27 = 10.589

Prediction interval = y pm error margin

To save computing time, error margin (E) can be obtained using the online error margin calculator.

Obtained error margin (E) value = 2.3398

(10.589- 2.3398, 10.589+ 2.3398)

(8.2492, 12.9288)

(8, 13)

The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589

Know more about equation of regression: https://brainly.com/question/14852545

#SPJ4

The equation y = 4x-1 matches the graph, which has a slope of 4 and a y-intercept of -1. This is because the coefficient of x is 4 (slope) and the constant term is -1 (y-intercept).

A line's slope is a measure of how steeply it rises or falls as it goes from left to right on a coordinate plane. It is defined as the shift in vertical coordinate (y) to horizontal coordinate (x) between any two locations on a line. The slope (m) may be written symbolically as:

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

Positive, negative, zero, or undefined slopes are all possible. A horizontal line has a slope of zero, while a vertical line has an indeterminate slope.

Based on the given options, the equation that matches the graph is:

b. y = 4x-1

This is because the graph has a slope of 4 (meaning it increases by 4 units in the y-direction for every 1 unit in the x-direction), and a y-intercept of -1 (meaning the line crosses the y-axis at -1). This matches the equation y = 4x-1, where the coefficient of x is 4 (slope) and the constant term is -1 (y-intercept).

To know more about slope, visit

brainly.com/question/14511992

#SPJ1

Answer:

I believe the answer is 1.36

Given that;

Danielle picks a card at random. Without putting the first card back, she picks a second card at random.

We want to determine whether the two events above are dependent or independent.

Since after Danielle picks the first card at random, she did not put the card back before picking the second. So, the result of the second pick would be dependent on the result of the first pick.

Therefore, the two events are dependent.

The number of hours that James have to work each week will be 25 hours.

The word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge.

In this case, James has a job moving lawns during the summer. Suppose the formula for calculating the number of hours he will have to work each week is five times the difference of thirty-eight and three times the difference of fifteen and four hours.

The number of hours that James have to work each week will be:

= 5(38) - 3(15 - 4)

= 5(38) - 3(11)

= 5(38 - 33)

= 5 × 5

= 25 hours

Learn more about word problem on:

brainly.com/question/21405634

#SPJ1

Answer:

8n³ + 3n² + 8

Step-by-step explanation:

To find the sum of the two polynomials, we can simply add the corresponding terms:

(-5n^4 + 8) + (5n^4 + 8n³ + 3n²)

Combine the like terms:

(-5n^4 + 5n^4) + 8n³ + 3n² + 8

The -5n^4 and 5n^4 terms cancel each other out:

0 + 8n³ + 3n² + 8

So the expanded polynomial in standard form is:

8n³ + 3n² + 8

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

The percentage of companies with revenue between 73 million and 87 million dollars is; 0.30

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

Population mean; μ = 80 million

Population standard deviation; σ = 18 million

The percentage of companies with revenue between 73 million and 87 million dollars is expressed as;

P(73 < X < 87)

z₁ = (73 - 80)/18

z₁  = -0.389

z₂ = (87 - 80)/18

z₂ = 0.389

Using probability between two z-scores, we have;

P(-0.389 < Z < 0.389) ≈ 0.30

Read more about probability from z-score at; https://brainly.com/question/25638875

#SPJ1

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

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

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

The correct option regarding the mean of X + Y is given as follows:

a. MX+MY.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

Hence, when two variables are added, we can add their means, as we add all the observations and divide by the number of observations, considering the two variables.

This means that the correct option is given by option A.

More can be learned about the mean of a data-set at brainly.com/question/1156334

#SPJ1

Answer:

20.25

Step-by-step explanation:

Since 4/6 is the same as 0.25 and 20 doesn't need to be changed, 20 4/16 is equal to 20.25 in decimal form
Hope this helps :)

Answer:

20.25

Step-by-step explanation:

\(\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}\)

\(20\frac{4}{16}=\frac{20\cdot 16+4}{16}=\frac{324}{16}\)

\(\mathrm{Write\:the\:problem\:in\:long\:division\:format}\)

\(16\overline{|\smallspace324}\:\)

\(\mathrm{Divide\;32\;by\;16\;to \;get\;2}\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\emptyspace2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 16\overline{|\smallspace324}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace3\emptyspace2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace0\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\mathrm{Divide\;4\;by\;16\;to \;get\;0}\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\emptyspace2\emptyspace0.\:\:\:\:\:\:\:\:\:\:\:\\ 16\overline{|\smallspace324.0}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace3\emptyspace2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace0\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace0\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\mathrm{Divide\;80\;by\;16\;to \;get\;5}\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\emptyspace2\emptyspace0.\emptyspace2\emptyspace5\:\:\:\\ 16\overline{|\smallspace324.0\cdot \:0}\:\:\:\:\:\:\:\\ \underline{\emptyspace3\emptyspace2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \emptyspace0\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\\ \underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \emptyspace4\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \underline{\emptyspace3\emptyspace2}\:\:\:\:\:\/\\\emptyspace8\emptyspace0\:\\ \underline{\emptyspace8\emptyspace0}\:\\\ \emptyspace0\end{matrix}\)

\(\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{324}{16}\:\mathrm{is}\:20.25\)

~Lenvy~

The polygon does not belong to the group as it is created by a finite number of line segments and the concept of the radius of curvature is not applicable.

In this problem we have three shapes related to circle-like and ellipse-like arcs (circle, semicircle, ellipse) and a regular polygon.

Circles are closed figures created by a arc whose radius of curvature is the same at every point and ellipses are closed figures created  by a arc whose radius of curvature varies in the following interval: a ≤ r ≤ b, where a, b are the lengths of the semiaxes.

Polygons are closed figures created by a finite number of line segments and therefore the concept of radius of curvature is not applicable.

Therefore, the polygon does not belong to the group as it is created by a finite number of line segments and the concept of the radius of curvature is not applicable.

To learn more on polygons: https://brainly.com/question/17756657

#SPJ1

A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

Learn more about vertex at https://brainly.com/question/1217219

#SPJ1

The translation rule is T<5, 2> and the image of U' is (0,3)

Translation.

The transformation of a shape in a plane that preserves length, which means that the object is transformed without getting its dimensions affected. i.e., it may just be shifted to left/right/up/down is referred as translation.

Given,

The vertices of a rectangle are R(-5, -5), S(-1,-5), T(-1, 1), and U(-5, 1). A translation maps R to the point (0, -3).

Here we need to find the translation rule and the image of U

Here we know the given the vertices of rectangle which are  R(–5, –5), S(–1, –5), T(–1, 1), and  U(–5, 1).

And it is also given that the translation maps R(-5,-5) to the point (0, -3). we have to find the translation rule and the image of U.

In order to find the translation rule,

First we have to identify the Horizontal shift for the given point

That is calculated as,

=> 0 - (-5) = 5 unit

Which means R is shifted to 5 units horizontally.

Now, the Vertical shift is calculated as,

=> -3 - (-5) = 2 units

Which means R is shifted to 2 units vertically.

Therefore, the translation rule is < 5, 2 >  

So, the image of U(-5, 1) is calculated as,

=> -5 + 5 = 0

=> 1 + 2 = 3

Therefore, the point of the image U' is (0, 3)

To know more about Translation rule here.

https://brainly.com/question/19007400

#SPJ1

Answer:

18 hours. For 1 hour you packed 10 boxes.

Step-by-step explanation:

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

to know more about unitary method

https://brainly.com/question/28276953

Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

-14/3

Step-by-step explanation:

if a = -4, then replace your a with -4, making it -4 to the second power. b = 2, so replace b with 2 and solve with "pemdas."

(If you don't know what pemdas is, it the order of operation which goes parentheses, exponents, multiplication, division, addition, and subtraction.

First solve your exponent, which is -4 to the second power. A negative time a positive would be a negative, and -4 to the second power is -16.

-16 + 2 = -14, leaving you with -14/3

Answer = -14/3

Answer:

4.625

Step-by-step explanation:

5/8 = 0.625 add 4 =

4.625

Answer: x=2

Step-by-step explanation:

−3x+4=2x−6

Subtract 2x from both sides.

−3x+4−2x=−6

Combine −3x and −2x to get −5x.

−5x+4=−6

Subtract 4 from both sides.

−5x=−6−4

Subtract 4 from −6 to get −10.

−5x=−10

Divide both sides by −5.x=−5−10

​Divide −10 by −5 to get 2

x=2

Answer:

-8/15 this is the answer to you question

You have the following expressions for the area and the width of a rectangle:

Area: A = x² - 2x - 15

width: w = x - 5

consider that the area of a rectangle is given by:

A = w·l

where l is the length and w the width. In order to calculate l, you have:

l = A/w

Then, divide the expressions for A and w via division standard fomr, as follow:

x² - 2x - 15 | x - 5

-x² + 5x x + 3

3x - 15

-3x + 15

0

Hence, the result is x + 3

Hence. the missing length is given by the expression (x + 3)

Answer:

The cost of the roses are $53.10

Celebration! Hope this helps ^_^

Answer:

-12≥x

Step-by-step explanation:

-10≥2x+14

-24≥2x

-12≥x