In triangle ABC, the measure of angle B is 21 less than four times the measure of angle A and the measure of angle C is more than five times the measure of angle A. Find the measure, in degrees, of each angle of triangle ABC.

Answer:

i think its done like this

Answer:

12

Step-by-step explanation:

[tex] area = \frac{1}{2} \times \: base \times \: height \\ \frac{1}{2} \times 6 \times height \: = 36 \\ height \: = \frac{36}{3} \\ = 12 \: feet[/tex]

The value of expression is ,

10) 6

11) 18

12) 2

13) 4

14) [tex]\frac{1}{4}[/tex]

15) [tex]\frac{1}{3}[/tex]

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression

10) 7+x+(-3)

Put x=2 then

=> 7+2-3

=> 7-1 = 6

11) 4[tex]x^2[/tex]+2

put x=2 then

=> [tex]4*2^2+2[/tex]

=> 4*4+2

=> 16+2=18

12) Ix+10I

put x=-12 then

=> I-12+10I

=> I-2I = 2

13) |2x + 1|

put x= 3/2 then

=> I2*[tex]\frac{3}{2}[/tex]+1I

=> I3+1I

=> I4I = 4

14)(x - 3)/4

put x=4 then

=> [tex]\frac{4-3}{4}[/tex]

=> [tex]\frac{1}{4}[/tex]

15) (5 - x)/6

put x=3 then

=> [tex]\frac{5-3}{6}[/tex]

=> [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

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Answer:

b. Considering your answer to part (a) and the possible outcomes listed above, how much total revenue (i.e., regular and premium) can be expected from ticket sales?

Answer: 9n-7

Step-by-step explanation:

9n-7 because there are no like terms

Answer:

Step-by-step explanation:

Answer: We can write an inequality to show how many hours of television Julia can still watch this week by using the following information:

Julia is allowed to watch no more than 6 hours of television a week.

So far this week, she has watched 2.5 hours.

We can use the inequality x + 2.5 <= 6, where x is the number of hours Julia can still watch this week.

This inequality represents the total number of hours watched (x + 2.5) being less than or equal to the maximum number of hours allowed (6).

To solve this inequality, we can subtract 2.5 from both sides:

x <= 6 - 2.5

x <= 3.5

So, Julia can still watch 3.5 hours of television this week.

Step-by-step explanation:

Answer:

The remaining hours of TV Julia can watch this week can be expressed as

[tex]x \leq 3.5hours[/tex]

Step-by-step explanation:

since Julia is allowed not to watch not more than 6 hours of television a week and she has watched 2.5 hours already

the remaining time (X)  would be expressed as

[tex]x \leq (6 - 2.5)[/tex]

[tex]x \leq 3.5[/tex]

Answer:

maximum value = 2

Step-by-step explanation:

the maximum value of the function is the y- coordinate of its vertex

given a quadratic function in standard form

y = ax² + bx + c (a ≠ 0 )

then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = - x² + 2x + 1 ← is in standard form

with a = - 1 and b = 2 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{2}{-2}[/tex] = 1

to find the y- coordinate of the vertex, substitute x = 1 into y

y = - 1² + 2(1) + 1 = - 1 + 2 + 1 = 2

then maximum value of the function is 2

Therefore , the solution of the given problem of scatter plot comes out to be Line 3 to the right of the graph is best fit line.

Line of best fit refers to a line through a scatter plot of data points that best expression the relationship between those points.The graphs that show the association between two variables in a data set are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.

Here,

In the xy plane, a scatter plot is displayed. The x-axis has values from 0 to 9 with 1 increments, while the y-axis has values from 0 to 9 with 1 increments.

On the x-axis, data points range from 0 to 3; on the y-axis, they range from 0 to 8.5. There are three lines marked Line 1, Line 2, and Line 3. Line 1 connects the points in a way that places the majority of the points on the left of the line,

Line 2 connects the points in a way that places the majority of the points on both sides of the line, and Line 3 connects the points in a way that places the majority of the points on the right of the line.

Line 3 to the right of the graph is best fit line

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Answer:

$1850×4÷100×8=$592 as interest

A unit vector u in the direction opposite of ⟨−9,−2,−8⟩  is  ⟨-9/√(149) , -2/√(149) , -8/√(149) ⟩

What are vector equations ?

Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.

Let unit vector u be = k⟨−9,−2,−8⟩.

√(81k^2 + 4k^2 + 64k^2) = 1

SO k = 1/√(149)

So a unit vector u in the direction opposite of v=⟨−9,−2,−8⟩ = (-9/√(149) , -2/√(149) , -8/√(149))

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Answer:

A 10

Step-by-step explanation:

a proportional relationship is defined as

y = kx

k is the constant of proportionality, because it is constant for this function for any value of x.

it is usually called the slope of the line or rate of change.

these are special lines : lines that go through the origin (0, 0).

and for these lines people often call k the constant of proportionality.

as we can see right in the given equation, this constant of proportionality is 10.

The diameter of the wheel of the truck is 3.33 feet.

A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.

The distance around the wheel of a truck is 10.45 feet.

Let the diameter of the wheel = d feet.

Circumference of the wheel

= Distance around the wheel,

πd = 10.45 feet.

d = (10.45/π) feet.

Here, we take the π = 3.14.

So,

d = 3.326

d = 3.33

Therefore, the diameter is 3.33 feet.

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Answer:

y=1/6x+2 is the slope formula.

The equation of a line passing through the point (0,2) and having slope 1/6 is: x-6y+12=0

Step-by-step explanation:

Equation of a line passing through a point (x1,y1) and having slope m is: [tex]y-y_{1} =m(x-x_{1} )[/tex]

where m= slope of the line

Given point (x1 , y1)= (0 , 2)

So, the Equation of a line: [tex]=y-y_{1} =m(x-x_{1} )[/tex]

[tex]y-2 =(\frac{1}{6} )(x-0 )[/tex]

[tex]y-2 =(\frac{1}{6} )(x)[/tex]

[tex]6*(y-2) =(x)[/tex]

[tex]6y-12=x[/tex]

[tex]6y-12-x=0[/tex]

[tex]-x+6y-12=0[/tex]  OR [tex]x-6y+12=0[/tex]

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Answer:

[tex]\boxed{x^2 - x - 6}[/tex]

Step-by-step explanation:

If a is the root of a polynomial then x-a is a factor of that polynomial

Since - 2 is a root, x -(-2) = x + 2 is a factor

Since 3 is a root, x - 3 is a factor

Multiplying the factors of a polynomial gives you the polynomial equation

So the polynomial equation is

[tex](x + 2)(x-3)[/tex]

Apply FOIL method:
[tex](x + 2)(x-3) \\\\= x\cdot x+ x\left(-3\right)+2x+2\left(-3\right)\\\\= x^2 -3x + 2x -6\\\\x^2 - x - 6\\\\Answer: \boxed{x^2 - x - 6}[/tex]

Answer:

456.17

Step-by-step explanation:

Rounding to the nearest hundredths' is asking is the number given 456.173 closer to 146.170 or 146.171.   You can see that the number is closer to 146.170 which is the same number as 146.17

Rule

Look at the digit in the thousandths' place.  In this case 3.  If this number is 5 or greater round up, if this number is 4 or smaller round down.  We will round down.

456.17

Answer:456.17

Step-by-step explanation:

If the thousandth place is 5-9, for example 456.178, the answer rounded to hundredth place will be 456.18.

But if the thousandth place is 1-4, the answer rounded to hundredth will be 456.17.

So the answer is 456.17.

Answer:

  DE = 9

Step-by-step explanation:

Given quadrilateral DEFG with DG≅EF, ∠FDG≅∠DFE, and markings EF=(6x+4), DG=(4x+8), and FG=(4x+1), you want the measure of DE.

The given congruences mean that the figure DEFG is a parallelogram. Opposite sides are the same length.

  EF = DG

  6x +4 = 4x +8

  2x = 4 . . . . . . . . subtract (4x+4)

  x = 2 . . . . . . . . divide by 2

Now, we can find FG.

  FG = 4x+1 = 4(2) +1 = 9

Opposite side DE is the same length:

  DE = 9

__

Additional comment

You can prove ΔEFD ≅ ΔGDF using SAS. Then CPCTC tells you corresponding parts of the triangles are congruent: DE≅FG.

Answer:

[ 5, ∞ )

Step-by-step explanation:

brackets on the ends of the interval indicate x can equal the value inside the bracket

parenthesis on the ends of the interval indicate x cannot equal the value inside the parenthesis.

x ≥ 5

expressed in interval notation as

[ 5, ∞ )

The given relation {(-1, 1), (1, 1), (-2, 4), (2, 4)} is a function because: A. yes each input has exactly one output.

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two (2) or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).

In this context, we can reasonably infer and logically deduce that given relation is a function because each input variable (domain) has exactly an output variable (range) as illustrated below;

x      F(x)

-1       1

1        1

-2      2

2       4

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The simplified form of the univariate monomial expression as requested in the task content is; 1.6 y⁴.

It follows from the task content that the simplified form of the univariate monomial expression is to be determined.

Since the given expression is;

32 y⁶ / 20 y²

The expression can be simplified as follows;

( 32 / 20 ) • y⁶ / y²

= 8/5 • y⁴

= 1.6 y⁴.

On this note, it can be inferred that the simplified form of the expression is; 1.6 y⁴.

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The equation perpendicular to the line is y= −1/2 x. Therefore, option B is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

In the given graph, the coordinates are (2, 3) and (0, -1)

Slope m=(-1-3)/(0-2)

= -4/(-2)

m=2

Substitute m=2 and (x, y)=(2, 3) in y=mx+c, we get

3=2(2)+c

c=-1

Substitute m=2 and c=-1 in y=mx+c, we get

y=2x-1

Find any equation perpendicular to the line.

y= −1/2 x

Therefore, option B is the correct answer.

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Answer:

The bus journey takes 25 minutes (5 minutes per stop x 5 stops). The bus leaves the Railway Station every 10 minutes (the wait time between circuits).

The first departure is at 09:15, so the bus will arrive back at the Railway Station at:

09:15 + 25 minutes = 09:40

Bart will drive the bus for 4 circuits, so the bus will arrive back at the Railway Station for the final time at:

09:40 + (4 x 25 minutes + 4 x 10 minutes) = 09:40 + 130 minutes =

11:50.

So the final arrival time will be D 11:55.

Answer:

Step-by-step explanation:

Each circuit takes 25 minutes (5 destinations times 5 minutes) plus the 10 minute wait at the Railway Station.  So the entire circuit is 35 minutes with the wait.  Bart drives 4 circuits - 4 times 35 minutes is 140 minutes.

140 minutes equals 2 hours and 20 minutes.

Add 2 hrs and 20 minutes to 9:15 and the sum = 11:35

The answer is B -  11:35

Answer:

third option

Step-by-step explanation:

Instead of having a constant rate of change, the third option does not as it goes up by 1 then 3 then 5

Answer:

if it is bracket than see explanation

darw a table with

x 3 5 -4

y 0 2 -7

taking x as 3 so

y= (3-1)-2

= 0

so like this do by 5 also and -4 too

and after solving plot in in the graph

The expression is 18/a

An algebraic expression can be described as mathematical expressions consisting of variables, coefficients, terms, factors and constants.

They are also made up of arithmetic operations, such as;

A quotient can be defined as a quantity determined  by the division of two numbers.

From the information given, we have that;

the quotient of 18 and a number a

This is represented as;

18/a

Hence, the representation is 18/a

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Answer:

Yes.

(2, 23) is a solution for the equation y = 9x + 5

Step-by-step explanation:

(2, 23) means that for an x value of 2, the y value should be 23

The equation is y = 9x + 5

Substitute x = 2 on the right side

y = 9(2) + 5 = 18 + 5 = 23

Since this matches the given value of y =23, we can conclude that

(2, 23) is a solution for y = 9x + 5

Answer:

Let's call the two numbers x and y. We know that:

y = x + 14 (because one number is 14 more than the other)

x + y + 7 = 83 (because the sum of the two numbers plus 7 is 83)

We can substitute the first equation into the second equation:

x + (x + 14) + 7 = 83

Simplifying this equation:

x + x + 14 + 7 = 83

2x + 21 = 83

2x = 62

x = 31

So one number is 31 and the other number is 45 (since one is 14 more than the other).

A model rocket is launched from the roof of a building. It's flight path is modeled by -5t^2 + 30t + 10 and the Distance from ground = 10 + height after 3 sec

Where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds.

Ans as h = -5t2+30t+10

at t=0, H = 10, which is height of the building from the ground

at t= 2 sec

h= -5.4+30.2+10

= -20+60 +10 = 50 m

For max height dh/dt = 0

-10t+30 = 0

t=3 sec

Therefore, the Distance from ground = 10 + height after 3 sec

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The y - intercept of the function f(x) = (3x + 4)⁴(x - 5)⁵ is (0, -800,000)

When an equation's graph crosses the y-axis, that location is known as the y-intercept. When x = 0, it is y's value.

A linear equation's constant term serves as a representation for the y-intercept. The y-intercept of the equation y = 2x + 3 is 3, for instance. This indicates that the coordinate plane point (0, 3) is at y = 3 when x = 0.

y= mx + b, where m is the slope and b is the y-intercept, is another way to express a linear equation.

For instance, the equation y = -2x + 5 can be written as y = -2x + 5, and since the y-intercept is 5, the point (0, 5) is on the graph of the equation.

The y-intercept of an equation, or the value of y when x = 0, is the point at which the graph of the equation crosses the y-axis. It can be represented by b in the slope-intercept form of a linear equation as well as by the constant term in the equation.

In the function given;

f(x) = (3x + 4)⁴(x - 5)⁵

Substitute the value of 0 for x and solve to find the y - intercept.

f(0) = (3(0) + 4)⁴(0 - 5)⁵

f(0) = -800000

The value of y - intercept(s) is (0, -800000)

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The y-intercept of the function f(x) = (3x + 4)^4(x - 5)^5 is given as follows:

-800,000.

The function for this problem is defined as follows:

f(x) = (3x + 4)^4(x - 5)^5

Graphically, the y-intercept of a function represents the value of y assumed by the function when the graph of the function crosses the y-axis.

Hence, algebraically, the y-intercept of a function is given by the numeric value of the function when the input x assumes a value of zero.

The numeric value of the function at x = 0 is calculated replacing the two instances of x in the function by zero, hence the y-intercept of the function is defined as follows:

f(0) = (3(0) + 4)^4(0 - 5)^5

f(0) = 4^4 x (-5)^5

f(0) = -800,000.

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Hope it helps.

If you have any query, feel free to ask.

The graph shows that the x-values increase as the y-values increase, which is consistent with the inequality x+4y ≤ 15. The y-values are all greater than or equal to 0, which is consistent with the inequality y ≥ 0.

Inequality is the unequal distribution of resources or opportunities among different individuals, groups, or social classes. It is a situation in which some individuals or groups have significantly more resources or opportunities than other individuals or groups. Inequality can be seen in terms of income, wealth, social class, access to education and health care, political power, or other factors. Inequality can be caused by systemic oppression and discrimination, or by the unequal distribution of resources within a society. It can have a negative impact on the ability of individuals and groups to meet their basic needs and achieve their full potential.

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