For the figure below, suppose
∠3 = 30°
and
∠7 = 97°.


Find the measures (in degrees) of the other angles.
∠1 =
°
∠2 =
°
∠4 =
°
∠5 =
°
∠6 =
°
∠8 =
°

The z values are-

Obtain the  z values from the t-distribution table for 0.86 and  0.78 confidence interval.

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The values of the two original numbers are 7 and 9.

Two numbers when multiplied equal 63 if one number is x and the other number is greater than x by 2.

As per the given phrase, the information given in equation form is as

x × (x + 2) = 63

It expresses as a quadratic equation:

x² + 2x - 63 = 0

Solve the quadratic equation to find possible values of x

x² + 9x - 7x - 63 = 0

x(x + 9) - 7(x + 9) = 0

(x + 9)(x - 7) = 0

(x + 9) = 0 and (x - 7) = 0

x = -9 and x = 7

Since we were told that the two numbers are positive numbers so take x = 7.

Thus, the values of the two original numbers are 7 and 9.

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Answer:

y = -3x + 10

Step-by-step explanation:

slope of perpendicular line = -3

y-1 = -3(x-3)

y-1 = -3x + 9

y = -3x + 9 + 1

y = -3x + 10

average speed = 3 3/4 km/h

In order to find how many kilometers the hiker will walk in 5 hours, you'll need to multiply the average speed by the hiker's hours.

[tex]3\dfrac{3}{4} \times5[/tex]

[tex]=\fbox{18.75 km}[/tex]

Relations on the set (1,2,3,4), decide whether it is reflexive, whether it is symmetric, whether it is anti symmetric, and whether it is transitive.

Given :

a )

=  { ( 2, 2 ),( 2, 3 ),( 2, 4 ),( 3, 2 ),( 3, 3 ) ,( 3, 4 ) }

Not reflexive because we do not have (1, 1), (3, 3), and (4, 4).

Not symmetric because while we we have (3, 4), we do not have (4, 3).

Not anti symmetric because we have both (2, 3) and (3, 2).

Transitive because if we have (a, b) in this relation, then a will be either 2 or 3. Then (2, c)

b )

{(1, 1),(1, 2),(2, 1),(2, 2),(3, 3),(4, 4)}

Reflexive because (a, a) is in the relation for all a = 1, 2, 3, 4.

Symmetric because for every (a, b), we have a (b, a).

Not antisymmetric because we have (1, 2) and (2, 1).

Transitive because while we have (1, 2) and (2, 1), we also have (1, 1) and (2, 2) in the relation.

c )

{(2, 4),(4, 2)}

Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.

Symmetric because for every (a, b), we have a (b, a).

Not antisymmetric because we have both (2, 4) and (4, 2).

Not transitive because we are missing (2, 2) and (4, 4)

d )

{(1, 2),(2, 3),(3, 4)}

Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.

Not symmetric because we do not have (2, 1),(3, 2), and (4, 3).

Antisymmetric because for every (a, b), we do not have a (b, a).

Not transitive because we do not have (1, 3) for (1, 2) and (2, 3)

e )

{(1, 1),(2, 2),(3, 3),(4, 4)}

Reflexive because we have (a, a) for every a = 1, 2, 3, 4.

Symmetric because we do not have a case where (a, b) and a 6= b.

Antisymmetric because we do not have a case where (a, b) and a 6= b.

Transitive because we can satisfy (a, b) and (b, c) when a = b = c.

f )

{(1, 3),(1, 4),(2, 3),(2, 4),(3, 1),(3, 4)}

Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.

Not symmetric because the relation does not contain (4, 1), (3, 2), (4, 2), and (4, 3).

Not antisymmetric because we have (1, 3) and (3, 1).

Not transitive because we do not have (2, 1) for (2, 3) and (3, 1).

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The value of the piecewise function h(x) at x = 2 is (b) -1

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

Part 1:

h(x) = x cubed for x less than negative 3

Part 2:

h(x) = 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4,

Part 3

h(x) = 5 times x plus 4, for x greater than or equal to 4

When the above statements are represented properly, we have the following equations

Part 1: h(x) = x³ for x < -3

Part 2: h(x) = 2x² - 9 for -3 ≤ x < 4

Part 3: h(x) = 5x + 4, for x ≥ 4

To calculate the function h(2), we use the domain -3 ≤ x < 4

So, we have the following function

h(x) = 2x² - 9

Substitute the known values in the above equation, so, we have the following representation

h(2) = 2(2)² - 9

Evaluate the expression

h(2) = -1

Hence, the value is (b) -1

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Complete question

The piecewise function h(x) is shown on the graph.

the function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4

What is the value of h(2)?

Answer:

27x^6y^12

Step-by-step explanation:

3^3×x^2(3)×y^4(3)

=27^6y^12

The values of the functions g[f(0)]b) f(-5), f[h(3)], h°f(x) and h⁻¹(x) are 9.5, -2, 16, (4x+22)/x and 6/(x-2) respectively

A function is a relationship between inputs where each input is related to exactly one output

Given:  f(x)= 2x+8, g(x)= 5x-2/4 and h(x)= 2x+6/x

(a) g[f(0)]

Substitute x = 0 into  f(x)= 2x+8 to get f(0)

f(0) = 2(0)+8 =8

g[f(0)] =  g(8)

Substitute x = 8 into g(x)= 5x-2/4 to get g[f(0)]

g[f(0)] =  g(8)

g[f(0)]  = 5x-2/4

g[f(0)]  = 5(8)-2/4 = 9.5

b) f(-5)

Substitute x = -5 into  f(x)= 2x+8 to get f(-5)

 f(x)= 2x+8

f(-5)= 2(-5)+8 = -2

c) f[h(3)]

h(x)= 2x+6/x

h(3) = 2(3)+6/3 = 4

f[h(3)] = f[4]

f[4] = 2(4)+8 = 16

f[h(3)]  = 16

d) h°f(x)

h°f(x)  = h(2x+8)  

Since h(x)= 2x+6/x

h°f(x) = 2(2x+8) +6/x

h°f(x) = 4x+16+6/x = (4x+22)/x

e) h⁻¹(x)

h(x)= 2x+6/x

Let y = 2x+6/x

x = 6/(y-2)

x = h⁻¹(y)

h⁻¹(x) = 6/(x-2)

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The value of m in the equation m=-(4+m)+2 is -1.

How are linear equations solved step-by-step?

One of the easiest methods for resolving a system of linear equations is graphing. Simply plot each equation as a line on a graph and identify the point or points where the lines converge to find the value. These equations are simple to graph because they are already expressed in slope-intercept form.

m = -(4+m)+2

m = -4 -m + 2

m = -2 - m

m + m = -2

2m = -2

m = -1

Hence, the value of m in equation m=-(4+m)+2 is -1.

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[tex]\textit{arc's length}\\\\ x = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =\frac{\pi }{3} \end{cases}\implies x=10\cdot \cfrac{\pi }{3}\implies x\approx 10.47[/tex]

Solution set of the equation is -3,-1, and 2 by simplifying the equation we get m³+2m²-5m-6 = 0

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Mathematical algebraic equations typically have one or more variables.

Given equation is: (6/m)+2 = (m+3)(m-1)

multiply with m both sides,

⇒6+2m = m(m²+2m-3)    

⇒m³+2m²-3m = 6+2m

So we get,

m³+2m²-5m-6 = 0

Solving we get, m = -3, m = -1, m = 2 as solution of given equation.

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The equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.

What is two point equation form?

The equation of the line passing through two points is

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

Here, (x₁,y₁) ∈ (7, -2)

(x₂, y₂) ∈ (5, 3).

y - (-2) / 3 -(-2) = x - 7/ 5 - 7

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

-2y - 4 = 5x - 35

5x + 2y - 31 = 0

Hence, the equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.

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The triangles ΔSTU and ΔRQV are congruent triangles

Two triangles are congruent if the three sides of one triangle are congruent to the three sides of the other triangle.

The parameters from the diagram includes;

Side [tex]\overline{TU}[/tex] in triangle ΔSTU is congruent to side [tex]\overline{QV}[/tex] in triangle ΔRQV

Segment [tex]\overline{UV}[/tex] is congruent to segment [tex]\overline{RS}[/tex]

[tex]\overline{UV}[/tex] ≅ [tex]\overline{RS}[/tex]

[tex]\overline{UV}[/tex] = [tex]\overline{RS}[/tex] By definition of congruency

Side [tex]\overline{ST}[/tex] in triangle ΔSTU is congruent to side [tex]\overline{QR}[/tex] in triangle ΔRQV

Segment [tex]\overline{RU}[/tex] is congruent to segment [tex]\overline{UR}[/tex], by reflexive property

[tex]\overline{RV}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{UV}[/tex] by segment addition postulate

Similarly, [tex]\overline{SU}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{RS}[/tex]

Therefore; [tex]\overline{SU}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{UV}[/tex] (by substitution property)

[tex]\overline{RV}[/tex] = [tex]\overline{SU}[/tex] by substitution property

[tex]\overline{RV}[/tex] ≅ [tex]\overline{SU}[/tex] by definition of congruency

The three sides of the triangle ΔSTU are congruent to the three sides of the triangle ΔRQV, therefore;

The triangles ΔSTU and ΔRQV are congruent by Side-Side-Side, SSS, congruency postulate

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Answer:

m1= 35

m2= 65

m3= 29

m4= 115

m5=65

The distance between the points C = (-9, 7) and Q = (-1, 3)  in the coordinate plane will be;

⇒ D = 10

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

Two points on the coordinate plane are C = (-9, 7) and Q = (-1, 3).

Now,

Since, Two points on the coordinate plane are C = (-9, 7) and Q = (-1, 3).

Hence, The distance between the points C = (-9, 7) and Q = (-1, 3)  in the coordinate plane will be;

⇒ D = √(3 - 7)² + (- 1 - (-9))²

⇒ D = √ (-4)² + (8)²

⇒ D = √36 + 64

⇒ D = √100

⇒ D = 10

Thus, The distance = 10

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Answer:

cosU = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

cosU = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{TU}{ST}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

the center of the circle is at (5, 1) and the radius is approximately 5.48 units.

Why it is and what is perimeter of a circle?

The standard equation of a circle with center (a,b) and radius r is:

(x - a)²2 + (y - b)²2 = r²2

Comparing this equation to the given equation, we can see that the center of the circle is (5, 1) and the radius is the square root of 30. Therefore, the center of the circle is at (5, 1) and the radius is approximately 5.48 units.

The perimeter of a circle is also known as its circumference, and it can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.

Alternatively, you can also use the formula:

C = πd

where d is the diameter of the circle.

So if you know the radius or diameter of a circle, you can use either of these formulas to calculate its circumference (perimeter).

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The equation to express the total cost, c, to use the Internet at the coffeehouse for t hours is c = rt.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the coffeehouse charges a flat rate, r, for each hour a customer wants to use the Internet. An equation to express the total cost, c, to use the Internet at the coffeehouse for t hours.

The equation will be:

c = r(t)

c = rt

where c = cost

t = number of hours

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Python is a dynamic, high-level, free open source, and interpreted programming language.

#definition of "median" function

def median(list):

#checking median condition to make sure the list returns zero if empty

if len(list) == 0:

return 0

#sort the list

list.sort()

#find middle element

mid = len(list) / 2

#check the condition

if len(list) % 2 == 1:

return list[mid]

else:

return (list[mid] + list[mid - 1]) / 2

#definition of "mean" function

def mean(list):

#checking mean condition to make sure the list returns zero if empty

if len(list) == 0:

return 0

#sort the list

list.sort()

#set the value

total = 0

#initiate a for loop

for num in list:

#then we calculate the total

total += num

#return the value

return total/ len(list)

#definition of "mode" function

def mode(list):

#checking mode condition to make sure the list returns zero if empty

if len(list) == 0:

return 0

#declare the variable

num_Dictionary = {}

#check the condition

for digit in list:

num = num_Dictionary.get(digit, None)

if num == None:

num_Dictionary[digit] = 1

else:

num_Dictionary[digit] = num + 1

#getting the maximum value

max_Value = max(num_Dictionary.values())

mode_List = []

for k in num_Dictionary:

if num_Dictionary[k] == max_Value:

mode_List.append(k)

return mode_List

#definition of main function

def main():

#set the list

num_list = [7, 4, 8, 10, 9]

#call the "mean" function with a parameter

print ("Mean of the given list: ", mean(num_list))

#call the "mode" function with a parameter

print ("Mode of the given list:", mode(num_list))

#call the "median" function with a parameter

print ("Median of the given list:", median(num_list))

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Answer:

Below

Step-by-step explanation:

See image below:

Answer:

The first one, due to the x being raised to the power of 2

Step-by-step explanation:

The Onion publishes a satirical, comedic story making fun of President Trump. Nothing in the story is remotely true

False information is presented as fake news. This is bogus news since the onion published a satirical fictional report about President Trumb. GSU fabricates false, deceptive information, often known as false news. False news is not defined as news that has factual inaccuracies.

GSU intentionally produces and disseminates a phony but plausible-looking news item touting the excellent parking situation on campus in an effort to boost applicants.

The term "fake news" describes news sources that pose as authentic while actually being false. It frequently aims to make money from advertising or to harm someone's or an organisation's reputation.

By purposefully fabricating and spreading a bogus but plausible-looking news article claiming how excellent the parking situation is on campus, GSU hopes to increase the number of applications. Which is false information that will cause people to come forward with job applications.

The Onion publishes a satirical, comedic story making fun of President Trump. Nothing in the story is remotely true

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Answer:

Let x be the number of free throws Jason made, and y be the number of two point shots he made.

The system of equations will be

x+ 2y = 20x+2y=20

x + y = 13x+y=13

Solving these using elimination method we get,

x + 2y = 20x+2y=20

----------------------------

y = 7y=7

x = 6⇒x=6

The number of free throws Jason made are 6, and the number of two point shots he made are 7.

Answer:

-0.3

Step-by-step explanation:

just sum -0.66x and 0.36x

Answer: -21

Step-by-step explanation:

To begin, we can combine like terms, -0.66 and 0.36 are coefficients with the same variable.

This gives us -0.66x+0.36x= -0.30x, and the equation becomes -0.30x=6.3.

Next, we can simply solve for x by dividing 6.3 by -0.30, and that gives us x=-21.

Answer:

9/12

Step-by-step explanation:

The easiest way to do this would to multiply the numerator and the denominator.

We need to find out how to get the numerator (3) to 9.

We can do this equation.

3 × 3 = 9

Now that we have multiplied the numerator by 3, we now need to multiply the denominator by 3.

4 × 3 = 12

The new fraction is 9/12.

Answer:

2((2x+2)+3x)=124 units

Step-by-step explanation:

We know that the formula for perimeter is 2(b+h) and since we know this, we just substitute the values for this and solve.

The equation of a line that represents the table is y = 6x - 5.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

To obtain the linear equation first we need slope(m) = (y₂ - y₁)/(x₂ - x₁)

= (1 + 11)/(1 + 1) = 12/2 = 6.

Now, we'll take any one of these coordinate points and construct an equation in slope-intercept form,

- 11 = 6(-1) + b.

- 11 = - 6 + b.

b = - 5.

∴ y = 6x - 5 is our equation.

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Sasha's balance after 12 years, if she makes no other deposits or withdrawals would be $ 4, 598. 07

Sasha's balance after 12 years will be the future value of her savings after 12 years at a rate of 2. 3% per year.

This future value can be found by the formula :

Amount after 12 years = Amount deposited by Sasha x ( 1 + annual compound interest ) ^ number of years

= 3, 500 x ( 1 + 2 .3 % ) ¹²

= 3, 500 x 1.3137344983996021269289886802331

= $ 4, 598. 07

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