Answers
Answer:
z = 54
Step-by-step explanation:
The sum of all interior angles in a polygon is given by the formula :
(n-2) × 180 (Where n is the number of sides) .
There are 5 sides so the sum of all interior angles will be :
(5-2) × 180 = 540°
So :
108 + 130 + 140 + 2z + z = 540
Simplify :
378 + 3z = 540
Subtract 378 from both sides :
3z = 540 - 378
3z = 162
Divide both sides by 3 :
z = 162 ÷ 3
z = 54
Hope this helped and have a good day
Related Questions
Look at this angle:
What is the vertex?
Answers
Answer:
T. The vertex is where the angle is measured. It is often associated as the vertex angle.
Step-by-step explanation:
Hope it helps! =D
Answer:
T is the vertex
Step-by-step explanation:
the point where the angle lies , is the vertex, in this case T
using the letters forming the angle , with the vertex T placed in the middle
∠ STU or ∠ UTS
Divide. Express your answer in scientific notation.
7.2x 10-4
3x10-3
7.2x10-4
3x10^-3
(Use scientific notation. Use the multiplication symbol in the math palette as needed.
Answers
The value of 7.2 × 10^-4 divided by 3 × 10^-3 when expressed in scientific notation is 2.4 × 10^-7.
What is scientific notation?It should be noted that scientific notation is simply used to illustrate the numbers that are either too large or too small. It is denoted as a × 10ⁿ.
It should be noted that the exponents will be added. Therefore, 7.2 × 10^-4 divided by 3 × 10^-3 will be:
= 7.2 × 10^-4 / 3 × 10^-3
= 2.4 × 10^-7.
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Determine the length of the missing side in the triangle shown.
right triangle with one leg labeled 13 and hypotenuse labeled 16
square root of 425
square root of 3
square root of 29
square root of 87
Answers
hypotenuse = 16
perpendicular = 13
base= ?
By using pythogoras theroem :
H² = P² + B²
16² = 13² + B²
256 = 169 + B²
B² = 256 -169
=87
B² = 87
B = √87
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Answer: The correct answer is D - square root of 87
Step-by-step explanation: I took the test and I got it right.
Have a good day/night :)
Jenna is making knit hats for Christmas presents.
Each hat requires her to use 1 1/3 yards of yarn. If she has 30 yards of yarn, how many hats can she make?
This problem is asking me to determine?
Write the equation you will be using to solve.
Answers
Answer:
22 hats
Step-by-step explanation:
30÷1 1/3=22.5
The question is implying how many completed hats she can make, and since half a hat is not completed, she can only make 22 completed hats.
Line E passes through the points (-3, 4) and (2, 7). What is the slope of a line perpendicular to line E?
Answers
The slope of a line perpendicular to line E is -(5/3).
How do you calculate slope of a perpendicular line?By taking the negative reciprocal of the slope of the provided line, one can determine the slope of a perpendicular line from that line. We obtain m₂ = -1/m₁ if the slope of the provided line is m₁ and the slope of a perpendicular line is m₂.Given:
Line E passes through the points (-3, 4) and (2, 7).
Slope of line E = [tex]\frac{y_{2}-x_{1} }{x_{2}-x_{1} }[/tex]
= [tex]\frac{7-4}{2-(-3)}[/tex]
= [tex]\frac{3}{5}[/tex]
So, the slope of a line perpendicular to line E will be the negative reciprocal of the slope of line E i.e. -(5/3).
Therefore, the slope of a line perpendicular to line E is -(5/3).
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Mr. Lou teaches 7 reading groups. Each reading group has 5 students. Find how many total
students Mr. Lou teaches today if 3 students are absent.
Which expression correctly represents the problem?
7x (5-3)
(7x5)-3
KC
7-(5 x 3)
D
(7-5) x 3
11
Answers
Based on the number of reading groups, and the number of absent students, the expression for the problem is (7 x 5) - 3.
How to find the expression?Every reading group taught by Mr. Lou has 5 students. There are also 7 reading groups. This means that the total number of students under Mr. Lou is:
= Number of reading groups x Number of students per group
= 7 x 5
Then out of this total number, 3 students are absent. The expression then becomes:
= Number of students - Number o absent students
= (7 x 5) - 3
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ing Equations Practice
CONCEPT: Multi-Step Equations
C Level:
What is the value of x? Show your work and explain how you found the answer.
-4x-43 = -95
Answers
Answer:
X:15
Step-by-step explanation:
only a genius can explain i can ask my colic to help
Which of the following functions is graphed below?
Answers
The functions that are shown on the graph are:
Square function.Linear function.What is square function and linear function?General equation of square function is :
f(x) = x2
It's called a parabola.It is symmetric around the y-axis (like a mirror image).Domain : R (Real numbers).It has a range of Non-Negative Real Numbers: [0, +∞)General equation of linear function is :f(x) = mx + b
where 'm' and 'b' are real numbers.
It is an algebraic functionThe domain is entirely made up of real numbers. A function's range is the set of all possible output values.To learn more about type of functions refer to :
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The formula for the volume of a cylinder with a base radius equal to 3 inches (in) is shown below. v ≈28.3h where v=volume and h=height What is the closest estimate of the height of the cylinder if the volume is 200 in ³?
Answers
Answer:
7 inches
Step-by-step explanation:
π * 3^2 *7 = 197.920337
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
Answers
An inequality which best models the situation described above is: D. 52 + 3w ≥ 90.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Less than or equal to (≤).Less than (<).Greater than or equal to (≥).Greater than (>).In order to solve this word problem, we would assign a variable to the number of weeks and then translate the word problem into algebraic equation as follows:
Let w represent the number of weeks.
Translating the word problem into an algebraic equation, we have;
Volunteering hours = 52 hours.Remainder of her volunteer hours = 3w hours.Total time to graduate (at least) = 90 volunteer hours.Next, we would combine the above parameters to form an algebraic equation as follows:
52 + 3w ≥ 90
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Complete Question:
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
answer choices
A. 52w + 30w ≥ 90
B. 52w + 30w ≤ 90
C. 52 + 3w ≤ 90
D. 52 + 3w ≥ 90
Find system of equations algebraically. d = f; 2d + 4e - 3f = 1; - 3d + 2e + 4f = 5
Answers
The solution of the system of equation is [tex]e=1 , d= 3[/tex] [tex],f=3[/tex]
How do you solve algebra?The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.
The solution is written as below:
Given: d= f
2d + 4e - 3f = 1 --------------1
and - 3d + 2e + 4f = 5----------------------2
Put the value of f as d because it is given,
thus equation becomes; 2d+ 4e - 3d= 1 ⇒ 4e- d= 1 ----3
-3d+2e +4d= 5 ⇒ 2e+ d=5 ----4
Thus on solving 3 and 4 we get;
[tex]4e-d=1\\+2e+d=5\\[/tex]
We get 6e= 6 which implies e= 1
And putting this value of e in equation 3 we get,
4X1 -d=1
-d= 1-4 ⇒ -d= -3
thus d = 3
Thus [tex]e=1 , d= 3[/tex]
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Solve the inequality 1/4 (x-20)<-6 or -6x+5≤-1. Write your solution in algebraic form, interval notation, and graphed on a number line.
Answers
The solution of the given inequality is:
x ≥ 1.
And the graph on the number line can be seen in the image at the end.
How to solve and graph the inequality?
The inequality we want to solve and graph is:
-6x + 5 ≤-1
To solve this, we need to start by isolating the variable x in one of the sides, we will get:
-6x + 5 ≤-1
-6x ≤-1 - 5
-6x ≤ -6
Now we can divide both sides by -6 to get:
x ≥ 1.
Then the graph will be like the one below. You need to have a closed dot on x = 1 (because that is a solution to the inequality) and then shade all the region to the right of x = 1, because x also can be larger than 1.
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Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
Answers
The value of her investment at compound interest after 4 years will be £8934.34.
What is compound interest?
Compound interest is the adding of interest to the principle sum of a loan or deposit, or interest on interest plus interest. It is the outcome of making an investment interest, or adding it to the lent assets, rather than repaying it out or requesting return from the borrower, so that interest is received on the principle sum plus previously accrued interest in the next month. In finance and economics, compound interest is the norm. Compound interest differs from simple interest in that previously accrued interest is not added to the main amount of the current month, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods per year.
Given,
Principal (P) = £8000
Rate of interest (r) = 2.8% compound interest p.a.
Time (n) = 4 years
Then, according to compound interest compounded annually,
Amount = P(1+r/100)ⁿ
= 8000(1+2.8/100)⁴
= 8000(102.8/100)⁴
= 8934.34
Hence, the value of her investment at compound interest after 4 years will be £8934.34.
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A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the
unit cost is given by the function C(x)=0.5x²-180x+25,885. What is the minimum unit cost?
Do not round your answer.
Answers
Answe(0.5x²-180x+25,885= 47,925.25
Step-by-step explanation:
x=1
six tickets to a movie cost 76.50 what constant of proportional relates the number of tickets and total cost
Answers
Based on the number of movies, $12.75 is the constant of proportionality per movie
How to determine the constant of proportionality?The given parameters are
Number of the movie tickets = 6
Cost of the movie tickets = 76.50
The constant of proportionality of the movie tickets is calculated as
Constant of proportionality = Cost of the movie tickets/Number of the movie tickets
Substitute the known values in the above equation
So, we have
Constant of proportionality = 76.50/6
Evaluate the quotient
So, we have
Constant of proportionality = 12.75
Hence, the constant of proportionality per movie is $12.75
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Answer:
Step-by-step explanation:
$12.75
Why is the variable x called x?
Answers
Have an AWESOME day! :)
You have a $25 calling card. Calls made using the card within the United States cost $.10 per minute while calls made from the US to France cost $.25 per minute. a. Write an inequality that relates the number of minutes ‘x’ you can use for calls within the U.S. and the number of minutes ‘y’ you can use for calls from the U.S. to France.
Answers
The inequality that represents the number of minutes of calls made in the United States and in France, can be presented as follows:
The inequality that represents the duration of calls that can be made in the United States: 0 ≤ x ≤ 250The inequality that represents the number of minutes of calls that can be made in France using the calling card is: 0 ≤ y ≤ 100What is an inequality in mathematics?An inequality expresses the relationship between two or more values that are not equal.
The value of the calling card = $25
The cost of calls made in the United States = $0.10
Cost of calls made in France = $0.25
The number of minutes that can be used for calls in the U.S. = x
The number of minutes that can be used for making calls in France = y
The duration of calls that can be made in the United states is therefore:
[tex]x_{max} = \dfrac{\$25}{\$0.10} = 250[/tex]
The inequality that represents the number of calls that can be made in the United States is therefore: 0 ≤ x ≤ 250
The duration of calls that can be made in France with the $25 calling card is therefore: [tex]y_{max}=\dfrac{\$25}{\$0.25} = 100[/tex]
The inequality that represents the number of minutes the calling card can be used in making calls in France is: 0 ≤ y ≤ 100
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Mrs. [Name] has 56 pencils and 42 erasers. If she wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers, what is the greatest number of students she can have in her class so there are none left over? How many pencils and erasers will each student have
Answers
The pencils and erasers that each student have is 14.
How to calculate the value?From the information, the person has 56 pencils and 42 erasers and wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers.
It should be noted that this has to do with looking for the highest common factor.
The highest common factor for 56 and 42 is 14.
The students will have 14 pencils each.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
-2
Step-by-step explanation:
-2y^2=-2y^2
1. Bobbi is on a diet to lose weight. After losing 26 pounds, Bob weighs 231 pounds. What was Bobbi's weight
before his diet? Let x represent Bobbi's original weight.
Answers
Answer:
231+26=x
x=257 pounds
A(c-b)=d
Solve for c
Please and thank
Answers
[tex]a(c - b) = d \\ \frac{a(c - b}{a} = \frac{d}{a} \\ c - b = \frac{d}{a} \\ c = \frac{d}{a} + b \\ c = \frac{d}{a} + \frac{b}{1} \times \frac{a}{a} \\ c = \frac{d}{a} + \frac{ab}{a} \\ c = \frac{d + ab}{a} [/tex]
THIRD OPTION IS THE ANSWER.
HOPETHIS HELPS
if y=3x write 5y in terms of x
explanation?
Answers
The value of 5y in terms of x in the equation is 5y = 15x
How to solve equation?The equation is given as y = 3x
Therefore, we are ask to find 5y in terms of x.
This simply means we have to make 5y the subject of the formula in the equation.
In other words, we have to isolate 5y in terms of x in the equation.
Therefore,
y = 3x
multiply both sides by 5
5 × y = 3x × 5
5y = 15x
Therefore,
5y = 15x
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please help asap. due monday
Answers
if I am correct that is the solution.
Solve the answer
100*0.5=a
a*2=
Answers
Answer:
a = 50
50*2=100
Step-by-step explanation:
The length of Rectangle A is 5 inches more than its width. The perimeter of Rectangle B is 17. The difference between the perimeters of the rectangles is less than 9. What are the possible integer values for the width of Rectangle A? 1in. 2in. 3in. 4in.5in. 6in. 7in. 8in.
Answers
Answer:
Step-by-step explanation:
Let L and W be the length and width of a triangle.
Rectangle perimeter (Px) = 2L + 2W, where x is triangle a or b.
Rectangle A: La = 5Wa [The length of Rectangle A is 5 inches more than its width.]
Perimeter Rectangle A: Pa = 2La + 2Wa
Substitute L = 5Wa:
Pa = 2La + 2Wa
Pa = 5Wa + 2Wa
Pa = 7Wa
Perimeter Rectangle B: Pb = 17 [The perimeter of Rectangle B is 17]
Pb = 17
Difference between Pa and Pb: Is it < 9?
See the attached table. The perimeters of rectangle A are computed for each of the answer options that define the width. Length (rectangle A) is 5 inches more than the width. The perimeter is 2*Length + 2*Width, and shown as Pa.
The perimeter of rectangle b is 17, shown as Pb on the table. The last column of the table is the absolute value of the difference of Pa and Pb. If it is less than 9, the cell is green (it is a possible integer value for the width of rectangle A), Red mean it does not meet the "less than 9" requirement, One cell has the difference as 9. The problem states "less than 9," so it does not meet the requirement.
two packages of strawberries are sold for $10. how much could you buy with $25?
F.) 3
G.) 4
H.) 5
J.) 6
K.) 7
Answers
Answer:
G.) 4
Step-by-step explanation:
If you get two packs of strawberries for $10, with another $10 you could get another two packs. 2+2=4, and 10+10=20. So you could get 4 packs with with $20.
Answer the questions about the following function.
f(x) =
X+11
X-9
(a) Is the point (3,-9) on the graph of f?
Answers
Answer:
No
Step-by-step explanation:
I just graphed f(x)=x+11, f(x)=x-9, and (3,-9) in Desmos, and you can visibly see that it isn't.
80p as a fraction of £3
simplest form
Answers
Answer:
Step-by-step explanation:
4/15
Based on the concept of fraction, 80p is equivalent to 4p/15p as a fraction of £3.
What is a fraction?Fraction is a term that is used to describe the portion or part of the whole thing.
Generally, the term fraction represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator.
In this case, to find the fraction of 80p as a fraction of £3, we divide 80p by £3.
Since there are 100 pence in 1 pound the fraction can be expressed as 80p/£3.
To simplify the fraction divide both the numerator and the denominator by 10:
80p/£3 = 8p/30p
Simplifying further both the numerator and the denominator can be divided by 2:
8p/30p = 4p/15p
Therefore, in this case, it is concluded that 80p is equivalent to 4p/15p as a fraction of £3.
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What is rate of change for 3=2x-21
Answers
Answer:
Step-by-step explanation:
I believe I need 2 variables to properly work this out but x=12
3=2x-21
24=2x
12=x
Towns A and B are 240 km apart.
A bus takes 80 minutes longer than a car to travel between the two towns.
The car is travelling at 15 km/h faster than the bus which is travelling at × km/h.
(a) Find the time, in hours,
taken by the bus and the car to travel between the two towns in terms of x
(b) Form an equation in × and
show that it reduces to ×2 + 15x - 2700 = 0
(c) Solve the equation and find the speed of the bus and
the time taken by the car to travel between the two towns.
Answers
The time (in hours) taken by the bus and the car to travel between the two towns in terms of x is 5 hours 20 minutes and 4 hours respectively and the equation in x formed is [tex]x^2 + 15x -2700=0[/tex]
Given that:-
Distance between towns A and B = 240 km
A bus takes 80 minutes longer than a car to travel between the two towns.
The car is travelling at 15 km/h faster than the bus which is travelling at x km/h.
Let the speed of the bus be s km/hr and,
The time taken by the car to travel from A to B be t hours.
Hence,
(15+x)*t = (t + 80/60)*x
15t + xt = xt + 4x/3
15t = 4x/3
t = 4x/45 hours.
Hence,
(15 + x)*(4x/45) = 240
x(x + 15)/45 = 60
[tex](x^2 + 15x) = 60*45[/tex]
[tex](x^2 + 15x) = 2700\\x^2 + 15x -2700=0\\x^2-45x+60x-2700 = 0[/tex]
x(x-45) +60(x - 45) = 0
(x - 45)(x + 60) = 0
x = 45,-60
As the time cannot be negative,
x = 45 km/hr
t = (4*45)/45
t = 4 hours (time taken by car)
Time taken by bus = 4 hours + 80 minutes = 5 hours 20 minutes
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