Answer:
The answer is 6
Step-by-step explanation:
I just took the test and got a 100% on it
1. Analyze the following pattern: 1, 2, 5, 10, 17,
Answer:
n² - 2n + 2
Step-by-step explanation:
The difference in the pattern are odd numbers.
2 - 1 = 1
5 - 2 = 3
10 - 5 = 5
17 - 10 = 7
So there is a -2n in the nth term.
If we subtract 1 on each term.
0, 1, 4, 9, 16
We get whole squares.
So there is a n² in the nth term.
(1)² - 2(1)+ c = 1
1 - 2 + c = 1
-1 + c = 1
c = 2
The nth term is:
n²-2n+2
Hi someone please help me I'm not sure how to do thissss
If the longer base of triangle XYZ is three times the length of the shorter base, a, what is the length of the hypotenuse in terms of the shorter base?
Answer: (√10)*a
Step-by-step explanation:
In a triangle rectangle, we have 3 sides, in this case, the shorter base, a, the longer base, b and the hypotenuse h.
And the hypotenuse can be found with the Pythagorean's theorem.
a^2 + b^2 = h^2
now, we know that b = 3a, then we can replace it in the above equation:
a^2 + (3*a)^2 = h^2
a^2 + 9*a^2 = h^2
10*a^2 = h^2
now we can apply the square root to both sides and get:
√(10*a^2) = √h^2
(√10)*a = h
Then we have found the length of the hypotenuse in terms of the shorter side a.
Write the following using algebraic notation, using the letter x for any
unknown numbers
I think of a number, add one, then double the result.
Answer:
x+1=x *x
Step-by-step explanation:
Answer:
x+1= x*x
Step-by-step explanation:
hope this helps
A triangle has vertices at (4.-2), (2.2), and (4.6). What are the vertices of the image of the triangle after applying the
translation (x, y)=(x - 1, y + 2)?
Answer:
see explanation
Step-by-step explanation:
The translation rule (x, y ) → (x - 1, y + 2 )
Means subtract 1 from the original x- coordinate and add 2 to the original y- coordinate, thus
(4, - 2 ) → (4 - 1, - 2 + 2 ) → (3, 0 )
(2, 2 ) → (2 - 1, 2 + 2 ) → (1, 4 )
(4, 6 ) → (4 - 1, 6 + 2 ) → (3, 8 )
Haroldo, Xerxes, Regina, Shaindel, Murray, Norah, and Georgia are invited to a dinner party. They arrive in a random order and all arrive at different times. What is the probability that Xeres arrives first AND Regina arrives last?
Answer:
1/7
Step-by-step explanation:
There are seven people in all on person will arrive at a different time than others. Every single one of them arrives at different times so it's 1/7
The sum of the interior angles of a polygon is 9x². If x is 3 greater than the number of side of the polygon, how many sides does the polygon have?
Answer:
17
Step-by-step explanation:
This is a very neat problem -- for teachers.
Let the number of sides = y
The sum of the interior angles is 180*(y - 2)
We are told that this sum equals 9x^2
So far the equation is
(y - 2)*180 = 9x^2 Divide both sides by 9
(y - 2)*20 = x^2 Remove the brackets on the left.
20*y - 40 = x^2
We need another fact. We get that from the statement that x is three greater than the number of sides (y). Therefore y = x - 3
20*(x - 3) - 40 = x^2
20x - 60 - 40 = x^2 Combine like terms on the left
20x - 100 = x^2 Bring the left side to the right side.
0 = x^2 - 20x + 100 You have a quadratic.
a = 1
b = - 20
c = 100
When you solve the quadratic equation, you get
x = 20
Therefore the number of sides is 17.
Mathematical Statement Justification
4(x + 5) = 2x + 2 Given
4x + 20 = 2x + 2
2x + 20 = 2
2x = -18
x = -9
Fill in the missing justifications in the correct order.
Answer:
Look at the explanation
Step-by-step explanation:
after the second line (4x-2x) +20= 2
--------------
after the 3rd line
2x=2-20=-18
-------------------
after 4th line x=-18/2
-----------------------------------------------------------------------------
At the end
4(-9+5)=2(-9)+2
-36+20=-18+2
-16=-16 so it is right
the diagram shows a right-angled triangle. what is the value of h? give your answer correct to 1 decimal place.
Step-by-step explanation:
Hello there!!
You can find it through simple way of ratio of sin or also by using cosine rule.
Lets do it simply as i can see your just 1st pic not second one so, i will answer you according to it.
so, here in question a Right angled triangle is given, with one angle 31° and one side 15 cm.
let's take sin angle as sin 31°.
so, p=h
h=15
We dont need base (b) here.
As we know that, thesin in ratio angle is
sin thita = p/h
or, sin 31°=h/15
or, 0.515038×15=h (using calculator sin 31°=0.515038.)
Therefore, the answer is 7.722557cm or 8cm.(as 7>5 and rounding off it we get 8).
Hope it helps...
The value of h in the right angled triangle is 7.7 cm.
What is trigonometric ratio?Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
In the diagrams, using trigonometric ratio:
a) sin(31) = h/15
h = 7.7 cm
b) cos(24) = h/13
h = 11.9 cm
c) sin(37) = h/15
h = 9 cm
d) cos(47) = h/12
h =8.2 cm
e) sin(48) = h/18
h = 13.4 cm
The value of h in the right angled triangle is 7.7 cm.
Find out more on trigonometric ratio at: https://brainly.com/question/24349828
I NEED HELP PLEASE, THANKS! :)
Answer: [tex]\bold{b)\quad \dfrac{2\pi}{3},\dfrac{4\pi}{3},0}[/tex]
Step-by-step explanation:
Note the following identities: tan² x = sec²x - 1
[tex]\sec x=\dfrac{1}{\cos}[/tex]
tan² x + sec x = 1
(sec² x -1) + sec x = 1
sec² x + sec x - 2 = 0
(sec x + 2)(sec x - 1) = 0
sec x + 2 = 0 sec x - 1 = 0
sec x = -2 sec x = 1
[tex]\dfrac{1}{\cos x}=-2\qquad \dfrac{1}{\cos x}=1\\\\\cos x=-\dfrac{1}{2}\qquad \cos x=1\\\\x=\dfrac{2\pi}{3}, \dfrac{4\pi}{3}\qquad x=0[/tex]
Answer:
Option B
Step-by-step explanation:
We have tan^2( x ) + sec( x ) = 1.
First subtract 1 from either side, applying the identity tan^2( x ) = - 1 + sec^2( x ) = - 2 + sec( x ) + sec^2( x ) = 0
One key method that you should use to solve like problems, is to substitute a rather large value with a variable, such as say a. Let sec( x ) = a,
- 2 + a + a^2 = 0,
By the zero product property, a = 1, a = - 2. Substitute this value of a back into sec( x ) -
sec( x ) = 1, sec( x ) = - 2
From this we can create inequality( s ) as follows -
sec( x ) = 1, 0 ≤ x ≤ 2π, x = 0 and x = 2π
sec( x ) = - 2, 0 ≤ x ≤ 2π, x = 2π / 3 and x = 4π / 3
As you can see, x is the following solutions -
0, 2π, 2π / 3, 4π / 3
Eliminate 2π, and it should be that your solution is option B
Which of the following is the solution to the following system of inequalities? Let the green region represent the answer region.
Answer:
Option (A)
Step-by-step explanation:
There are two inequalities drawn on a graph.
x + 2y ≤ 4 ------(1)
3x - y ≤ 2 -------(2)
Here solution set of the inequality (1) will be represented by the shaded area below the solid line (in blue) represented by "x + 2y = 4".
(Line x + 2y = 4 will have the slope slanting down and y-intercept as 2)
Second inequality will represent the shaded area on the left of the solid red line represented by "3x - y ≤ 2".
(Line 3x - y = 2 will have the slope upwards and y-intercept as -2)
Solution area of these inequalities will be the common area shaded in green.
Graph given in Option (A) will be the answer.
Construct the described data set. The entries in the data set cannot all be the same. The median and the mode are the same. What is the definition of median? A. The value that lies in the middle of the data when the data set is ordered. B. The sum of the data entries divided by the number of entries. C. The data entry that occurs with the greatest frequency. D. The data entry that is far removed from the other entries in the data set.
Answer:
Option A
Step-by-step explanation:
The median is the value that lies in the middle of the data when the data set is ordered.
It is also the value that separates the higher half of the dataset from the lower half of the dataset.
Answer:
B
Step-by-step explanation:
Find the volume of the prism
Answer:
152.4
Step-by-step explanation:
All circles are similar figures. A Single transformation is applied to the circle with center M to create another circle with center N. Which statement about the transformation is true?
Answer:
A dilation was applied because the diameter of the circle decreased.
Step-by-step explanation:
Dilation is a process of either increasing or decreasing the size of a given figure without changing its shape. The resizing process make use of a scale factor to produce a dilated image of the given figure.
In the given question, it can be observed that the circle with center M has a diameter of 6 units, while that with center N has a diameter of 3 units. Thus circle M has been dilated with a scale factor of [tex]\frac{1}{2}[/tex] to produce circle N.
Therefore, a dilation was applied because the diameter of the circle decreased.
Answer:
I believe it is A
Classify the triangle shown below. Check all that apply.
53
5
3
90°
37
4
O A. Equilateral
B. Isosceles
O C. Right
O D. Obtuse
E. Acute
O F. Scalene
Answer:
C. and F.
Step-by-step explanation:
A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures. Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent. Right angle are 90 degrees
Answer:
C and F
Step-by-step explanation:
This triangle is not an equilateral triangle because their lengths are not equivalent to each other. It is not an isosceles triangle because no two lengths are equivalent to each other. It is a right triangle because it has one right angle(A 90 degrees angle.) It is not an obtuse triangle because there isn't an angle that is obtuse(More than 90 degrees but less than 180 degrees angle.) It isn't an acute triangle either because not all three angles are acute(Less than90 degrees angle.) Lastly, it is also a scalene triangle because none of the triangle lengths are equivalent to each other.
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 30 mm and standard deviation 7.8 mm [suggested in the article "Reliability Evaluation of Corroding Pipelines Considering Multiple Failure Modes and Time-Dependent Internal Pressure" (J. of Infrastructure Systems, 2011: 216–224)].
What values separate the largest 80% from the smallest 20% of the defect length distribution.
Answer:
[tex]z=-0.842<\frac{a-30}{7.8}[/tex]
And if we solve for a we got
[tex]a=30 -0.842*7.8=23.432[/tex]
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.
Step-by-step explanation:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(30,7.8)[/tex]
Where [tex]\mu=30[/tex] and [tex]\sigma=7.8[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.80[/tex] (a)
[tex]P(X<a)=0.20[/tex] (b)
As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.20[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.20[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=-0.842<\frac{a-30}{7.8}[/tex]
And if we solve for a we got
[tex]a=30 -0.842*7.8=23.432[/tex]
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.
Last year Mr. John Q. Public received an inheritance. He paid $20\%$ in federal taxes on the inheritance, and paid $10\%$ of what he had left in state taxes. He paid a total of $\$10{,}500$ for both taxes. How many dollars was the inheritance?
Answer:
37,500
Step-by-step explanation:
0.2x+0.1(x−0.2x)=105000.2x+0.1(x−0.2x)=10500
0.3x−150x=105000.3x−150x=10500
15x−x50=1050015x−x50=10500
x=10500∗5014=1500∗25=37500
please please help meee
Answer:
z = 110°
Step-by-step explanation:
Since the figures are similar then corresponding angles are congruent, thus
∠ H = ∠ D = 110°, that is
z = 110°
I need help with this question
Answer:
y = -3x + 8
Step-by-step explanation:
You have to find the slope first using the formula [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Insert any two points in the equation (1,5) and (2,2) and you get -3.
Then, you do any x value times the slope (1*-3 = -3) and add so that it equals the corresponding y value (8).
This makes it y = -3x + 8.
Which of the following is a parent function?
Answer:
B
Step-by-step explanation:
A parent function is the simplest function that still satisfies the definition of a certain type of function. One of those functions is exponential, which is b.
Option (B) will be the correct option.
Definition of a parent function:A parent function is simplest function which represents the entire family of that kind of functions.
We will check each option given for the definition of a parent function.
Option (A)
[tex]f(x)=-2^{x+1}[/tex]
Parent function will be,
[tex]f(x)=2^x[/tex]
Option (B),
[tex]f(x)=4^x[/tex]
It's a simplest form of an exponential function.
Therefore, it's a parent function.
Option (C),
[tex]f(x)=e^{3x}-2[/tex]
Parent function → [tex]f(x)=e^{3x}[/tex]
Option (D),
[tex]f(x)=4x^2[/tex]
Parent function → [tex]f(x)=x^2[/tex]
Learn more about the parent function and the transformation here,
https://brainly.com/question/11474649?referrer=searchResults
please help me in this because i am not able to understand this answer from any side
Answer:
7, 5929, 77
Step-by-step explanation:
The prime factorization of 847 is 7 · 11², therefore, to make it a perfect square you need to multiply it by 7 to make 5929 which has a square root of 7 · 11 = 77.
Keisha had $405 in her bank account. Over the summer, she made 4 withdrawals of $45 each a) What is the balance in Keisha's account? * b) Write an integer expression to represent this problem. Solve the problem. *
Answer:
see below
Step-by-step explanation:
The amount she withdrew is 45*4 =180
405 - 4*45=
405 -180 =225
There is 225 in the account
Answer: a) $225
Step-by-step explanation:
405 - 45 (4) = x
405 - 180 = x
225 = x
A bag of sweets contains only two different flavours - strawberry and orange The probability that a sweet is strawberry flavour is 0.8 What is the probability that a sweet is orange flavour?
Answer:
out of 1 would be 0.2
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hello
The answer is 0.2
1 - 0.8 = 0.2
A pattern is made from four congruent squares. The sides of the squares are parallel to the axes. Point A has coordinates (3,2) Point b has the coordinates (27,30) Point C is marked on the diagram. Work out the coordinates of C
Answer:
(13, 16)
Step-by-step explanation:
Point A has coordinates (3,2) Point b has the coordinates (27,30)
Therefore the width of the diagram = 27 - 3 = 24 units and the height of the diagram = 30 - 2 = 28 unit
The length of the square = 28 unit / 4 square = 7 unit
Also, half of the height of the diagram = 28/2 = 14 unit
Therefore the x coordinate is given by:
27 - (2 × 7) = 27 - 14 = 13 or 27 - 14 (=13) or 3 + 7 + (24 - 3 × 7) = 13
Also, the y coordinate is given by:
30 - (2 × 7) = 30 - 14 = 16 or 30 - 14 (=16) or (30 + 2)÷2 = 16
Therefore the coordinate for point C is given by (13, 16)
Help i cant get this wrong
Answer:
D
Step-by-step explanation:
I'm not the greatest in this subject, but I think that it's D/If the roof leaks, then the ceiling gets damaged because it clearly says that in the statement. It could be all of them, though, but this is my answer. Hope it helps!
Answer:
D. If it rains, then the ceiling gets damaged.
Explanation:
So, if it rains, then the roof leaks, and if the roof leaks, then the ceiling gets damaged, is the exactly the structure of the syllogism law that permits to conclude if it rains, then the ceiling gets damaged.
Hellen has 10 sweets,shelly has 30 sweets.Faith has 4 fewer sweets than the average number of sweets that hellen,shelly and faith have.How many sweets do they have altogether
Answer:
The sum of all the sweets is 54 sweets
Step-by-step explanation:
Here, we want to calculate the number of sweets the three have altogether.
Let the number of sweet Faith has be x
Mathematically;
Faith has 4 sweets fewer than the average number of sweets
The average is the sum of all the sweets divided by 3
The average will be (10 + 30 + x)/3
Thus;
(10 + 30 + x)/3 - 4 = x
(40 + x)/3 = x + 4
40 + x = 3(x + 4)
40 + x = 3x + 12
40-12 = 3x -x
28 = 2x
x = 28/2
x = 14 sweets
So the sum of all the sweets would be 10 + 30 + 14 = 54 sweets
A winter recreational rental company is fencing in a new storage area. They have two options. They can set it up at the back corner of the property and fence it in on four sides. Or, they can attach it to the back of their building and fence it in on three sides. The rental company has decided that the storage area needs to be 100 m2 if it is in the back corner or 98 m2 if it is attached to the back of the building. Determine the optimal design for each situation
Answer:
The optimal side length for a storage area at the back corner of the property fenced on four sides and having an area of 100 m² is 10 meters
The optimal side length for a storage area attached to the back of their building fenced on three sides and having an area of 98 m² is 7·√2 m
Step-by-step explanation:
The optimal design to conserve building material will be to build the storage area to have equal sides which gives square shaped storage area
For a storage area at the back corner of the property fenced on four sides and having an area of 100 m², we have;
Storage area size = 100 m²
The number of sides = 4
The dimension of each side = Equal sides, s₁
Therefore we have;
s₁ × s₁ = 100
s₁² = 100
s₁ = √100 = 10 m
The side length = 10 m
For a storage area attached to the back of their building fenced on three sides and having an area of 98 m², we have;
Storage area size = 98 m²
The number of sides = 4
The dimension of each side = Equal sides, s₂
Therefore we have;
s₂ × s₂ = 98
s₂² = 98
s₂ = √98= 7·√2 m
The side length = 7·√2 m
The perimeter of a square is 80 minus 64 y units. Which expression can be used to show the side length of one side of the square? 16 (5 minus 4 y): Each side measures 5 minus 4 y units. 16 y (5 minus 4): Each side measures 5 minus 4 units. 4 (20 minus 16 y): Each side measures 20 minus 16 y units. 4 y (20 minus 16): Each side measures 20 minus 16 units.
Answer: 4 (20 minus 16 y): Each side measures 20 minus 16 y units.
Step-by-step explanation:
Hi, to answer this question we have to know the formula of the perimeter of a square:
Perimeter = side length x 4
Since:
p = 80-64y = s x 4
Solving for s (side length)
80-64y /4 = s
s = 20- 16 y
So, the correct option is:
4 (20 minus 16 y): Each side measures 20 minus 16 y units.
Feel free to ask for more if needed or if you did not understand something.
Answer:
i believe its C
Step-by-step explanation:
Which equation could be used to find the length of the hypotenuse?
А
С
5 cm
С
B
8 cm
Answer:
The first option (5^2 + 8^2 = c^2).
Step-by-step explanation:
According to the Pythagorean Theorem, a^2 + b^2 = c^2.
If a is 5 cm, and b is 8 cm, you would have the following equation...
5^2 + 8^2 = c^2.
That matches with the first option.
Hope this helps!
Two similar triangles are shown below:
a
6
8
2
3
b
4
Which two sets of angles are corresponding angles?
O
O
O
O
Answer:
<a and <d; <b and <c.
Step-by-step explanation:
When two triangles are said to be similar, the ratio of the corresponding sides of both triangles is always the same, also, their corresponding angles are congruent. That is, they are equal.
The 2 set of angles that are corresponding angles of the two similar triangles given in the question above are:
<a and <d; <b and <c.
Both set of angles are congruent to each other. In other words, they are equal.
Speedy texting 3a: Lydia wants to text at least 8 characters per second, like James, then the equation would be 10r+4=8 could be used to model this situation. Solve this equation for R. 3b: Explain what the variable r represents in the equation given in question 3a.
Answer:
Speedy Texting
3a. In the equation, 10r + 4 = 8
r = 0.4 or 40%
3b. The variable r represents an independent variable in the equation. An independent variable is a variable that is not dependent on another variable, instead other variables depend on it. Whatever its value is changes the value of other variables in the equation.
Step-by-step explanation:
a) Solving the equation:
10r + 4 = 8
10r = 8 - 4
10r = 4
r = 4/10 = 0.4 or 40%