What is the area of parallelogram ABCD?
A. 12 units²
B. 30 units²
C. 24 units²
D. 55 units²
Answers
Answer:
C, 24 units^2
Step-by-step explanation:
The formula for area of a parallelogram is base times height.
The height of the parallelogram is 4 units
The base of the parallelogram is 6 units
4 times 6 is 24
Hope this helps:)
Answer:
C. 24 units²
Step-by-step explanation:
To calculate the area of a parallelogram we use the following formula:
A = B*h (B: base, h: height)
The base of the parallelogram is 6 units and the height is 4 units
4*6 = 24 units but, the area is presented in square units so the answer is 24 units²
Related Questions
Look at the rectangle and the square:
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 14 inches, and the width QR is labeled as 7 inches. The side LM of the square is labeled as 7 inches.
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answers
Answer:
Incorrect
Step-by-step explanation:
Formula:
the Diagonal of a square with side square of lengths a
is equal to a√2.
=============
Then
Diagonal of LMNO : 7√2
Then
OM = 7√2
…………………………………………
Using the Pythagorean theorem:
The diagonal of the rectangle PQRS is equal to :
√(14²+7²) = √245 = 7√5
Then
SQ = 7√5
………………
Conclusion:
7√5 ≠ 2×(7√2)
Therefore
Anna is not correct.
A balloon is falling. it falls 200 feet each minute. how far will it in 3 minutes?
Answers
Answer:
600ft
Step-by-step explanation:
The balloon falls 200 feet in one minute and we need the amount it fell in 3 minutes: 200feet*3minutes = 600 ft
Suppose the diameter is 35cm. what is its curumference?include the unit measure in your answer
Answers
The circumference of the circle of diameter 35cm is 109.9 cm.
Given the diameter of the circle is 35 cm.
We are required to find the circumference of the circle.
The circumference is the arc length of the circle, The perimeter is the curve length around any closed figure. It is equat to the length of the outer ring of a circle.
Formula of circumference=2πr where r is the radius of the circle.
Diameter=35 cm
Radius=35/2 cm (Radius is half of diameter)
Circumference=2π*35/2
=35π
Put the value of π =3.14 (it can be 22/7 as well.)
=35*3.14
=109.9 cm
Hence the circumference of the circle is 109.9 cm.
Learn more about circumference at https://brainly.com/question/20489969
#SPJ4
Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats . what is the probability that a kid who goes the doctor has a sore throat given that he has a fever? (when entering your answer remember that the probability is a number between 0 and 1)
Answers
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%. Computed using conditional probability.
The probability of any event A given that event B has already taken place is found using the formula P(A|B) = P(A ∩ B)/P(B). This is known as conditional probability, where P(A ∩ B) is the probability of events A and B, and P(B) is the probability of event B.
In the question, we are given that 70% of kids who visit a doctor have a fever and 21% of kids have a fever and sore throats.
We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever.
We suppose the event of going to the doctor while having a fever to be B, and going to a doctor while having a sore throat to be A.
We are given that 70% of kids who visit a doctor have a fever, that is, the probability of event B, P(B) = 70% = 0.7.
We are given that 21% of kids who visit a doctor have a fever and sore throats, that is, the probability of event A and event B, P(A ∩ B) = 21% = 0.21.
We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever, that is, we are asked to find the conditional probability of event A, when event B has already taken place, that is, P(A|B).
By formula, we know that:
P(A|B) = P(A ∩ B)/P(B) = 0.21/0.70 = 0.30.
Thus, the probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%.
Learn more about conditional probability at
https://brainly.com/question/10739997
#SPJ4
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Answers
F(x)= 2(x-2)^2 + 2 is the correct equation of F(x)
A quadratic function is a polynomial function of the second degree. The general form of a quadratic function is this: f (x) = ax^2 + bx + c, where a, b, and c are real numbers and a≠ 0.
Graphs of quadratic functions
The term "parabola" refers to the graph of a quadratic function. A parabola essentially resembles the letter "U," yet it can be inverted or exactly this shape depending on the situation. The leading coefficient determines whether the graph of a quadratic function opens up or down; if it is more than zero, the parabola opens up; if it is less than zero, the parabola opens down.
It is given that graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat.
We need to find the equation of F(x)
In the figure, parabola opens up, the leading coefficient is greater than zero ,So option (d) is correct
Hence the equation of F(x) is 2(x-2)^2 + 2
Learn more about parabola here:
https://brainly.com/question/4061870
#SPJ1
Travis jogged to his friend's house 10 miles away and then got a ride back home. It took him 2 hours longer to jog there than ride back. His jogging rate was 16 mph slower than the rate when he was riding. What was his jogging rate?
Answer asap please :)))
Answers
Using the relation between velocity, distance and time, it is found that his jogging rate was of 4.5 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, his velocity was of v, while the time was of t + 2, for a distance of 10 miles, hence:
[tex]v = \frac{10}{t + 2}[/tex]
Riding, his velocity was of 16, while the time was of t, also for a distance of 10 miles, hence:
[tex]v + 16 = \frac{10}{t}[/tex]
Then, considering the first equation and replacing in the second:
[tex]\frac{10}{t + 2} + 16 = \frac{10}{t}[/tex]
[tex]\frac{10}{t} - \frac{10}{t + 2} = 16[/tex]
[tex]\frac{10t + 20 - 10t}{t(t + 2)} = 16[/tex]
16t² + 32t - 20 = 0 -> t = 0.5.
Then his jogging rate in mph was:
[tex]v = \frac{10}{0.5 + 2} = 4.5[/tex]
More can be learned about the relation between velocity, distance and time at brainly.com/question/24316569
#SPJ1
PLS HELP ME PLEASE
To measure the distance across a lake, a surveyor has taken the measurements shown in the diagram below. Determine the distance across the lake.
Answers
Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.In this problem, the parameters are:
a = 800, b = 900, C = 70º.
Hence the distance across the lake is c, found as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
c² = 800² + 900² - 2(800)(900)cos(70º)
c² = 957491
[tex]c = \sqrt{957491}[/tex]
c = 978.5.
The distance across the lake is of 978.5 feet.
More can be learned about the law of cosines at https://brainly.com/question/2491835
#SPJ1
Which equation represents a population of 250 animals that decreases at an annual rate of 12% ?
Answers
Answer:
f(t)=250(1-0.12)^t
or
f(t)=250(0.88)^t
Step-by-step explanation:
Use the formula f(t)=P(1+b)^t
Plug in the information.
f(t)=250(1-0.12)^t
or
f(t)=250(0.88)^t
The only thing I did in the second equation is I subtract 0.12 from 1.
Hope this helps!
There are n cities in a OneWayCountry (country in which every road is a One-Way road). Every pair of cities is connected by exactly one direct one-way road. Show that there exists a city which can be reached from every other city either directly or via at most one other city.
Answers
The cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from [tex]C_{i}[/tex]-1 to [tex]c_{n}+1[/tex] and from [tex]c_{n}+1[/tex] to [tex]C_{i}[/tex]. Place [tex]c_{n}+1[/tex] between [tex]C_{i}[/tex]−1 and [tex]C_{i}[/tex] to get the desired path.
What is mathematical induction method?Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n. By generalizing this in form of a principle which we would use to prove any mathematical statement is 'Principle of Mathematical Induction'.
The question says that between any two cities X and Y, either there’s an
one-way road from X to Y or from Y to X, but not both. Then show that
there is a path from some city A which visits all the cities exactly once.
This problem is very similar to the Football league problem #7 in Homework 1. This problem can be modeled as a directed graph in which cities
are represented as vertices and there’s an edge from vertices X to Y if
there’s a road from cities X to Y. And then, our goal is to find a path
in this graph which visits every vertex in the graph.
The rest of the solution is very similar to the argument in Problem 7 of
homework 1. We use induction of number of cities, say n.
As a base case, if n = 2, there are only two cities X and Y and the path
is simply the edge between X and Y.
For induction hypothesis, assume that the statement is true for any set
of n cities. That is’ for any set of n cities, we can find a path which visits
all the cities exactly once.
Let’s prove the statement for n + 1 cities. Leave out n + 1 th city (say,
[tex]c_{n}+1[/tex]) and for the remaining n cities, by induction hypothesis, we can find a path which visits all these n cities exactly once. Let us label the cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from [tex]C_{i}[/tex]-1 to [tex]c_{n}+1[/tex] and from [tex]c_{n}+1[/tex] to [tex]C_{i}[/tex]. Place [tex]c_{n}+1[/tex] between [tex]C_{i}[/tex]−1 and [tex]C_{i}[/tex] to get the desired path.
To learn more about induction hypothesis from the given link :
https://brainly.com/question/24672369
#SPJ4
What are the solutions of the system of equations y = –(x + 2)2 + 1 and y = 2x + 5?
(–4, –3) and (–2, 1)
(–4, –3) and (2, 1)
(–4, 5) and (2, 1)
(–4, 5) and (–2, 1)
Answers
Answer:
(–4, 5) and (–2, 1)
Step-by-step explanation:
Answer: A: (-4,-3) (-2,1)
Step-by-step explanation:
I got this correct on the test. Using the substitution method give brainliest
n a chemical plant, 24 holding tanks are used for final product storage. Four tanks areselected at random and without replacement. Suppose that six of the tanks contain material inwhich the viscosity exceeds the customer requirements.(a) What is the probability that exactly one tank in the sample contains high-viscosity material
Answers
The probability that exactly one tank in the sample contains high-viscosity material is P(A) = 0,4607 or P(A) = 46,07 %
The probability of an event (A) is for definition:-The probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring. In the very simplest cases, the probability of a particular event A occurring from an experiment is obtained from the number of ways that A can occur divided by the total number of possible outcomes.P(A) = Number of favorable events/ Total number of events FE/TE
If A and B are complementary events ( the sum of them is equal to 1) then:
P(A) = 1 - P(B)
The total number of events is:
C ( 24,4) = 24! / 4! ( 24 - 4 )! ⇒ C ( 24,4) = 24! / 4! * 20!
C ( 24,4) = 24*23*22*21*20! / 4! * 20!
C ( 24,4) = 24*23*22*21/4*3*2C ( 24,4) = 24*23*22*21/4*3*2 ⇒ C ( 24,4) = 10626
TE = 10626
Splitting the group of tanks in two 6 with h-v and 24-6 (18) without h-v
we get that total number of favorable events is the product of:
FE = 6* C ( 18, 3) = 6 * 18! / 3!*15! = 18*17*16*15!/15!
FE = 4896
Then P(A) ( 1 tank in the sample contains h-v material is:
P(A) = 4896/10626
P(A) = 0,4607 or P(A) = 46,07 %
Learn more about probability
brainly.com/question/14210034
#SPJ4
Matthew is flying with his jet pack at 100m/min. A strong wind has blown him 10m east of his intended flight path in 2 minutes. By how many degrees is Matthew off his flight path? Include a diagram.
Answers
Mathew's speed of 100 m/min, and the distance of 10 m. east to which he is blown by the wind gives the angle in degrees Mathew is blown off his path as approximately 2.86°.
How can the angle of deflection be found from the given speeds?The given parameters are;
Speed at which Mathew is flying = 100 m/min
Distance and direction in which the strong wind blows him = 10 m. east
Time it takes the wind to deflect Mathew by 10 m. = 2 minutes
Therefore;
Speed and direction of the wind = 10/2 m/min east
Speed and direction of the wind = 5 m/min east
Mathew's flight path can be represented using a vector diagram (please see attached drawing)
Distance Mathew travels in 2 minutes = 100 m/min × 2 minutes = 200 m.
Tangent of the angle by which Mathew is off his flight path, A, can be found as follows;
tan(A) = 10/200 = 1/20
A = arctan(1/20) ≈ 2.86°Learn more about vectors here:
https://brainly.com/question/13432276
#SPJ1
Which expression is equivalent to startfraction 3 x superscript negative 6 baseline y superscript negative 3 baseline over 15 x squared y superscript 10 baseline endfraction? assume x not-equals 0, y not-equals 0.
Answers
The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline endFraction.
Given expression [tex](3x)^-6*y^-3/ 15x^2*y^10[/tex]
Lets simplify the equation:
[tex]= > (3x)^-6*y^-3/ 15x^2*y^10\\=1/5 x^-8*y^-13[/tex]
Expression:
An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
Hence the correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction.
Learn more about Expression on:
https://brainly.com/question/1280754
#SPJ4
Find the number of terms in this series: 3x + 5x + 7x + ... + 23x
Help asap please and thank you!
Answers
Homer mowed 5 lawns in his first month and increased the number he mows by two for each month following. Which of the following is the correct interpretation of the rate of change and the initial value?
Answers
The equation which represent the interpretation of the scenario is 5 + 2x
AlgebraNumber of lawns Homer mowed = 5Additional laws mowed each month = 2Number of months = xTotal laws mowed = Number of lawns Homer mowed + (Additional laws mowed each month × Number of months)
= 5 + (2 × x)
= 5 + 2x
Learn more about algebra:
https://brainly.com/question/4344214
#SPJ1
The rectangle pre-image has a length of 12 and width of 6. The rectangle image has a length of 6 and width of 3.
Find the scale factor of the dilation shown in the diagram.
1/2
1/3
2
3
Answers
Answer: 1/2
Step-by-step explanation:
Scale factor = (image)/(preimage) = 6/12 = 1/2
Figure ABCD is a rhombus. Rhombus A B C D is shown. Angle A is (5 x 25) degrees and angle D is (7 x minus 1) degrees. What is the value of x
Answers
Answer: 18
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so
[tex]5 \times 25=7x-1\\\\125=7x-1\\\\126=7x\\\\x=18[/tex]
Can someone do this please?
Answers
Answer:
<1 =73
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
72+ 35 + <1 = 180
Add like terms
107 + <1 = 180
Subtract 107 from each side
<1 = 180-107
<1 =73
On a sunny day, Andrew, who is 1.9 m tall, casts a shadow that is 3.5 m long. A nearby tree casts a shadow that is 28.0 m long. To the nearest tenth of a metre, how tall is the tree?
Answers
Answer:
15.2
Step-by-step explanation:
The explanation is in the photo.. but basically this question is about similar triangles and you need to find the scale factor to find the height.
Hope it helps
the height of the tree is approximately 15.2 meters.
To find the height of the tree, we can set up a proportion between Andrew's height and the height of the tree based on their respective shadow lengths.
Let's denote the height of the tree as "h" meters.
The proportion between the height and shadow lengths can be written as:
h / 28.0 = 1.9 / 3.5
Now, we can solve for "h":
h = (1.9 / 3.5) * 28.0
h ≈ 15.2 meters
To the nearest tenth of a meter, the height of the tree is approximately 15.2 meters.
Learn more about proportion here
https://brainly.com/question/28005428
#SPJ2
Your professor selects three students from your Stats class to form a study team. How many study teams are possible from a class of 30 students
Answers
Total number of teams are 10
Linear EquationAn equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is one that includes a variable, such as x.
As given in the problem,
total number of students in class=30
now professor want to create study teams .
one team consist of 3 members,
lets suppose professor will form n teams
So,
3×n=30
solve this equation to get value of n
n=30÷3
n=10 teams
hence total number of teams are 10 .
Learn more about linear equation here:
https://brainly.com/question/2263981
#SPJ4
Select the correct answer.
Consider these functions:
f(x) = 4x³ - 10
g(x) = 3x - 4/2
What is the value of g(f2))?
Answers
Answer:
3x - 4/2
Step-by-step explanation:
2 result(s) for "f(x) = 4x³ - 10 g(x)
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
Answers
The surface area of the composite figure shown in the figure attached is 233.6 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²
The surface area of the composite figure shown in the figure attached is 233.6 cm²
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Select the correct answer. What is the approximate solution to this equation? 4lnx - 8 = 12
A. x = 148.4
B. x = 10.5
C. x = 1.61
D. x = 59,874
Answers
Answer:
Step-by-step explanation:
hello :
4lnx - 8 = 12
4lnx - 8 +8= 12+8
4lnx =20
lnx =5
coclusion : x =e^5
A. x = 148.4
In a bag there are 3 red 4 white, and 5 blue marbles. once a marble is selected it is not required. find: p(white, red) find: p(blue, white, red.)
Answers
Answer:
Below in bold.
Step-by-step explanation:
Total number of marbles = 3+4+5 = 12
P(white, red) = 4/12 * 3/11
= 12/132
= 1/11,
P(blue, white, red) = 5/12 * 4/11* 3/10
= 60/1320
= 6/132
= 1/22.
Solve the congruence 3x=2(mod4)
Answers
Answer:
Step-by-step explanation:
jello :
3x=2(mod4)
multiply by ; 5
5×3x=5×2(mod4)
15x=10(mod4)
but : 15= -1 (mod4) and 10= 2 (mod4)
-x=2 (mod4)
now multiply by ; -1 you have : x= -2 (mod4)
-2=2(mod4)
conclusion : x=2 (mod4) means : x=4k+2 k in Z
Sumaya's smoothie store is planning to sell an extra-large size. the extra-large size will have three times the volume of the small size (the small size is (8,4) ). it will cost twice as much as the small size.
which coordinate pair represents the volume and cost of the extra-large size?
Answers
The coordinate pair that represents the volume and cost of the extra-large size is (24, 8).
A coordinate plane is a plane that can be used to represent the position of a point. The plane consists of x-axes and y-axes. The position of a point is referenced from the origin.
The small size of a pizza is represented by the coordinate pair (8, 4) ⇒ (volume, cost)
Since the volume of the extra-large size will have three times the volume of the small size, hence:
Volume of extra-large size = 8 * 3 = 24
The cost of an extra large is twice as much as the small size, hence:
Cost of extra large = 4 * 2 = 8
A coordinate plane is a graphing and outline machine for factors and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants inside the coordinate plane. The point at which these strains join is known as the starting place (0, zero).
Coordinates are written as (x, y) meaning the point on the x-axis is written first, followed by the point on the y-axis. a few children can be taught to keep in mind this with the phrase 'along the hall, up the stairs, that means that they must observe the x-axis first after which the y.
Learn more about coordinate plane here: https://brainly.com/question/13854649
#SPJ4
Find the perimeter of each of these rectangles
Answers
Answer:
a) 10√3 + 5√3 + 10√3 + 5√3 = 30√3 cm
b) (√10 + √2) + (√10 - √2) + (√10 + √2) + (√10 - √2)
= 4√10 cm
c) Simplifying √72: √36 x √2 = 6√2
Simplifying √18: √9 x √2 = 3√2
Finding the perimeter: 6√2 + 3√2 + 6√2 + 3√2 = 18√2 cm
Solve for X.
X = [?]
5x - 16 X + 10
Answers
[tex] \boxed{ \sf{ \color{purple}\huge Answer :}}[/tex]
[tex] \: \: [/tex]
[tex] \large \tt \purple↪ \: \: \: \: \: 5x - 16 = x + 10 [/tex]
[tex] \: \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \:5x - x = 10 + 16 [/tex]
[tex] \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \: 4x = 26[/tex]
[tex] \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \: x = \cancel\frac{26}{4} [/tex]
[tex] \: \: [/tex]
[tex] \underline{ \boxed{\large \tt \purple↪ \red{ \: \: \: \: x = \frac{13}{2} }}}{ \large✓}[/tex]
[tex] \: \: [/tex]
hope helps ~
Find the nth term of the sequence 4, 7, 10, 13, …
Answers
Answer:
3n+1
Step-by-step explanation:
Subtract one from all the values, you get multiples of 3 in the equation 3n=nth term
So when you add one back, your equation is 3n+1=nth term
what is the coefficient of (3y^2 + 9)5
Answers
The coefficient of (3y² + 9)5 is 15.
A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.
Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.
a₀ is the leading coefficient.
In the question, we are asked to identify the coefficient of (3y² + 9)5.
First, we expand the given expression:
(3y² + 9)5
= 15y² + 45.
Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.
Thus, the coefficient of (3y² + 9)5 is 15.
Learn more about the coefficients of a polynomial at
https://brainly.com/question/9071229
#SPJ1