On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit
what is a pentagon?A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.
vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).
Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]
Area = 1/2| 60 |
Area of pentagon = 30 sq unit
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Which exponential function has an initial value of 2?
Of(x) = 2(3)
Of(x) = 3(2)
X
-2
-1
TY
f(x)
18
f(x) =2(3ˣ) is an exponential function which has an initial value of 2.
What is an exponential function?Another word for "involving an exponent" in mathematics is exponential. For instance, an exponential rise in a number occurs when you raise it to the tenth power.
A mathematical function with the formula f(x) = aˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently seen. A variable is used as the exponent in exponential functions.
The exponential function that has an initial value of 2 is f(x) = 2ˣ.
f(x) = 2(3ˣ) can be written as f(x) = 2 × 3ˣ, so it starts at 2 × 3⁰ = 2 × 1 = 2.
f(x) = 3(2ˣ) can be written as f(x) = 3 × 2ˣ, so it starts at 3 × 2⁰ = 3 × 1 = 3
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Solve the system of linear equations by substitution. Check your solution.
3
1. y = -2x + 4 and -x +3y = -9
2. 3 over 4x -5y = 7 and x= -4y +12
3. 5x - y= 4 and 2x + 2y = 16
4. 2x + 3y = 0 and 8x +9y = 18
The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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Solving provided question, we can say that the given linear equation is y = -2x + 4 and -x -x +3(-2x + 4 ) + 9 = x = 7/3
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
the given linear equation is
y = -2x + 4 and -x +3y = -9
now,
-x +3(-2x + 4 ) + 9
-x - 6x - 12 +9 = 0
-7x = -3
x = 7/3
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What is tautology in math?
A statement which is known as tautology is a type of compound statement in whose result is always the truth value. We don't take in consideration the other individual values in consideration , the result in tautology is always true.
It is one of the most significant part in logical mathematics if we need to find the most accurate answers or findings among a given group of answers.
In mathematics, tautology is used so as to ensure that the results which is obtained are true and exact and not false . A tautology is a compound statement and it will always returns true value. The result in tautology is always true, regardless of what the constituent parts are.
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Water leaking onto a floor forms a circular pool. The circumference of the pool increases at a rate 24 cm/min. How fast is the area of the pool increasing when the radius is 5 cm
The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm
How quickly does the pool's area grow when the radius is 5 cm?Given:
radius of the pool increases at a rate of 24 cm/min
To Find:
How quickly does the pool's area grow when the radius is 5 cm?
Solution:
we are given with the circular pool
hence the area of the circular pool =
A = πr²-----------------------------(1)
The area of the pool os increasing at the rate of 24 cm/min, meaning that the area of the pool is changing with respect to time t
so differentiating eq (1) with respect to t , we have
dA/dt =π 2r dr/dt
we have to find dA/dt with dr/dt = 24 cm/min and r = 5cm
substituting the values
dA/dt = π 2(5)24
dA/dt = π 26*8
dA/dt = π 240
dA/dt =240π
dA/dt = 753.98
The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm
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What is the Contrapositive of P → Q?
"If p then q" is a conditional statement, and its contrapositive is If ~q then ~p.
Knowing about the inverse statement makes it simple to comprehend how to build a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite.
Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement. Adding "not" to both component statements and switching the order of the provided conditional statements will result in contrapositive assertions, in other words.
If a number n is even, then n2 is even, and vice versa, is the contrapositive statement to "If a number n is even, then n2 is even."
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Part of the population of 7,750 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 11 of them are infected. How many elk are likely to be infected?
Answer:
1,705 elk
Step-by-step explanation:
7,750 / 50 = 155 groups of elk
155 groups x 11 per group = 1,705 elk.
Select the correct answer. what is the height, x, of the equilateral triangle? an equilateral triangle with the angles labeled as 60 degrees and a side length of 8 inches, the height labeled as x
a. in.
b. in.
c. in.
d. in.
The height of the equilateral triangle when its side length is given as 8 inches is calculated to be 6.93 inches.
The equilateral triangle has all sides and angles equal. The angles are always equal to 60 degrees.
Given that,
Side length of the equilateral triangle = 8 inches
Angles = 60 degrees
Height = ?
Therefore, let us find the height of the triangle using the Pythagoras theorem,
c² = a² + b²
8² - 4² = b²
b² = 64 - 16
b² = 48
b = 6.93 inches
Thus, the height of the equilateral triangle is calculated to be 6.93 inches.
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solve by completing the square
-x^2=5x-14
Answer:
Roots: -7, 2
Step-by-step explanation:
-x² = 5x - 14
-x² -5x +14 = 0
x² + 5x - 14 = 0
(x + 7)(x -2) = 0
x = -7 or x = 2
How many solutions does this equation have?
9d − 8 = –8 + 9d
Answer:
Infinite many solutions
Step-by-step explanation:
9d − 8 = –8 + 9d
* add 8 to each side *
-8 + 8 cancels out
-8 + 8 cancels out
we're left with 9d = 9d
When the same number/variable is on each side of the equal sign there is an infinite amount of solutions
Need Help! How would I complete this table?
The number of feet is dependent on the number of yards. The table is completed as shown in the attachment.
Dependent variable.A variable whose value can be determined only if another variable's value is known is called a dependent variable. Thus the value of the variable depends on another variable.
In the given question, the number of feet can be known when that of yards is multiplied by a multiplicative factor. The value of the factor can be determined as;
multiplicative factor = 15/ 5
= 3
So that feet is related to that of yards by this expression;
feet = multiplicative factor * yards
Thus,
when yards is 2, then;
feet = 3 * 2
= 6
when feet = 12
12 = 3 * yards
yards = 12/ 3
= 4
Thus the complete table is herewith attached to this answer for more clarifications.
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It takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.What is the length (in meters) of the train
After solving, the length of the trains in meters is 60 meters.
In the given question, it takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.
We have to find the length (in meters) of the train.
Let the length of the train is x.
The length of the bridge is 100 meters.
As we know that the formula of the speed is the ratio of distance that he traveled in the certain duration of time.
So Speed = Distance/Time
So according to the question;
(x + 100)/40 = x/15
Now solving the expression using the cross multiplication
15x + 1500 = 40x
Subtract 15x on both side, we get
25x = 1500
Divide by 25 on both side, we get
x = 60 meters
Hence, the length of the trains in meters is 60 meters.
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Find the volume and round to the nearest hundredths place when necessary.
Answer:
The top looks like a trapezoid and so does the bottom so it's a prism.
lets find the area of the base!
15(base 1) + 7(base2) = 22
22 x 5(height) = 110
110 divided by 2( x 1/2) = 55
Now we multiply by the actual height of the TOTAL prism which is 11.
55 x 11 = 605 cubic feet, is your answer.
Formula for AREA of a trapezoid:
B1(base 1) + B2(base 2) x H(height) x 1/2 (basically just dividing by 2)
Two angles of a quadrilateral measure 210° and 20°. The other two angles are in a ratio of 6:7. What are the measures of those two angles?
Answer:The sum of first angle second angle =150
⇒ The ratio of third and fourth angle is 2:3
⇒ Let third angle fourth angle be 2x and 3x.
Step-by-step explanation:
150 +2x+3x=360
⇒ 5x=210
⇒ x=42
⇒ Now, 2x=2×42
=84
⇒ 3x=3×42
=126
⇒ The measure of two angles are 84
and 126
PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Sum of angles of quadrilateral = 360 degree
so 210+20+6x+7x = 360
230+13x= 360
13x= 360-230=130
x= 130/13=10
so third angle =6x= 6*10=60 degree
and 4th angle= 7x= 7*10=70 degree
what is the slope of the line
Find the measure of ∠c.
Answer:
79
Step-by-step explanation:
3x +16 + 5x - 4 = 180
8x +12 = 180
8x = 180 -12
8x = 168
x=21
3*21+16= 79
Describe people’s opinions using different verbs. Write at least 5 sentences.
PLEASE HELP I POSTED FOR THE 7TH TIME NO ANSWER WILL GIVE BRAINLIEST
Answer:
A mi encantar el arte.
A mis padres interesar el traje.
A ti importar las botas.
A Emelio encantar los deportos.
A Nosotros interesar viajar.
Find a value that
makes this inequality
true: 50 - 3x ≤ 20
50-3x<20
the answer is C. 11
сm
What is the area of
circle
with circumference of 10cm ? 3
It is 10
I REALLY HOPE THIS HELPS :D
Answer:
7.96 centimeters squared
Step-by-step explanation:
In the photo.
Last week, Alex took 90 selfies and Vic took 75 selfies. Today,
they each decided that some of these selfies were not very good
and deleted them. Alex deleted three times as many selfies
as Vic. Now, Alex has half as many selfies as Vic. How many
selfies did Alex delete?
Answer:
Alex deleted 37.5 selfies
Step-by-step explanation:
Let X be the number of selfies that Vic deleted.
Alex deleted 3X selfies.
After deleting selfies, Alex has 90-3X selfies left.
Vic has 75-X selfies left.
Since Alex has half as many selfies as Vic, we can set up the equation: 90-3X = (75-X)/2
Multiplying through the parentheses on the right side, we get: 90-3X = 75-X/2
Combining like terms, we get: 2X = 15
Dividing both sides by 2, we get: X = 7.5
Since X represents the number of selfies that Vic deleted, Vic deleted 7.5 selfies.
Since Alex deleted 3 times as many selfies as Vic, Alex deleted 37.5 = <<37.5=22.5>>22.5 selfies.
The number of selfies deleted by Alex is 51.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic. Now, Alex has half as many selfies as Vic.
Let Vic deleted x selfies and number of selfies deleted by Alex is 3x,
Therefore,
Since, Alex has half as many selfies as Vic, we can set up the equation: 90-3x = (75-x)/2
180 - 6x = 75 - x
5x = 105
x = 17
3x = 51
Hence, the number of selfies deleted by Alex is 51.
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Please Help !! (Geometry related question)
Answer:
i dont know the answer i just need points im sorry
Step-by-step explanation:
Cafe A offers 2 free bottled waters or juices for every 20 purchased. If you purchased 80 drinks at the café, how many free drinks would you get?
Answer:
8 free drinks
Step-by-step explanation:
80 ÷ 20 = 4
4 × 2 = 8
AYUDAAA ES PARA HOY.!!
HELP ME IS FOR TODAY.!!
¿Cual es el factor de escala para ir de la figura A a la figura B?
What is the scale factor to go from figure A to figure B?
!POR FAVOR AYUDENME.!
PLEASE HELP ME.!
Answer:
I think the answer is 3:1. found it by counting the no. of boxes
pls help I need help on this!!
Answer:
where are the angles or image
JUST SAY THE LETTER IM BEING TIMED HURRRYYYY. MARKING BRAINIEST
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Como sacar el área de un círculo sabiendo que el radio mide 5 cm y en el centro del circulo se encuentra un rombo?
Answer:
78.57cm²
Step-by-step explanation:
English
We need to find the area of the circle.
The area of the circle is given by pie r². We know the value of pie and r is given . Putting the values
Area= pie r².
Area= 22/7* 5² = 22/7*25= 78.57cm²
We are not bothered by the area of the rhombus or the rhombus because we need to find the area of the circle.
Area of the rhombus is given by the product of the length of diagonals divided by 2. So if the rhombus lies at the center the length of each of its diagonal will be 10 cm. Because the length from the center of the circle to any point on the circle is equal to its radius. And the diagonal is formed by 2 radii.
Area of rhombus= 10*10/2= 50 cm²
Area of the circle excluding the area of the rhombus= 78.57- 50 = 28.57 cm²
HELP ME PLEASE AND QUICK IT'S DUE 12:00PM
c) The height of each cylinder in a set of food-storage containers is 30 cm.
The radius of the largest container is 10 cm.
The volume of the smallest container is one-third the volume of the largest container.
The volume of the middle-sized container is two-thirds the volume of the largest
container. What is the volume of each container?
Answer:
The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3
The volume of the smallest cylinder is 3141.59cm^3
The volume of the medium cylinder is 6282.67 cm^3
Step-by-step explanation:
the equation for a cylinder's volume is pi(r)^2(height)
The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3 (remember the units!)
The volume of t he smallest cylinder is 1/3 the largest or: 9424.78/3 = 3141.59cm^3 (remember the units!)
The volume of the medium cylinder is 2/3 the largest or 9424.78(2/3) = 6282.67 cm^3
Jacob shares 4 sandwiches equally on 3 plates. How many sandwiches will be on each plate?
Answer:
1 1/3
Step-by-step explanation:
HELP DUE IN 15 MINS!
x =??
Answer:
Step-by-step explanation:
x = 1/2 ( arc(SF) + arc(RQ))
ARC SF = 50
Arc RQ (the large one ) = 200
Large Arc RQ = 200
Arc SF = 50
x = 1/2 (50 + 200)
x = 1/2 250
x = 125
If 2x = 20, then x is
a. 5. b. 10. c. 20.
Answer:
B. 10
Step-by-step explanation:
To find the answer we would plug each given number into x to see if it makes the equation true
A. 2(5) = 20
10 [tex]\neq[/tex] 20
B. 2(10) = 20
20 = 20
C. 2(20) = 20
40 [tex]\neq[/tex]20
As you can see, the only answer that makes the equation 2x=20 true, is answer B
Rodney models the factorization of a trinomial with algebra tiles as shown.
An algebra tile configuration. 4 tiles are in the Factor 1 spot: 1 is labeled + x, 3 are labeled +. 4 tiles are in the Factor 2 spot: 1 is labeled + x and 4 are labeled negative. 14 tiles are in the Product spot: 1 is labeled + x squared and below it is a tile labeled negative x. To the right of negative x in 3 columns and 4 rows are 12 tiles labeled negative.
Rodney forgot to place x-tiles in zero pairs in the model of the trinomial. How many zero pairs of x-tiles should he place in the model?
Answer:
c.3 got a 100
Step-by-step explanation:
C
Step-by-step explanation: