Answer:
28 + 12xStep-by-step explanation:
Given,
Sides of a square is = 7 + 3x
Therefore,
Perimeter of a square = 4 × side
= 4 × (7 + 3x )
= 28 + 12x (Ans)
A universal set U consists of elements. If sets A, B, and C are proper subsets of U and n(U), n(A B)n(A C)n(B C), n(A B C), and n(A B C), determine each of the following.
a. n(AUB)
b. n(A'UC)
c. n(AnB)'
Answer:
[tex]n(A\ u\ B) = 10[/tex]
[tex]n(A'\ u\ C) = 10[/tex]
[tex]n(A\ n\ B)' = 6[/tex]
Step-by-step explanation:
Given
[tex]n(U) = 12[/tex]
[tex]n(A\ n\ B) =n(A\ n\ C) = n(B\ n\ C) =6[/tex]
[tex]n(A\ n\ B\ n\ C)=4[/tex]
[tex]n(A\ u\ B\ u\ C)=10[/tex]
Required
Solve a, b and c
There are several ways to solve this; the best is by using Venn diagram (see attachment for diagram)
Solving (a):
[tex]n(A\ u\ B)[/tex]
This is calculated as:
[tex]n(A\ u\ B) = n(A) + n(B) - n(A\ n\ B)[/tex]
From the attachment
[tex]n(A) = 0+2+4+2 = 8[/tex]
[tex]n(B) = 0+2+4+2 = 8[/tex]
[tex]n(A\ n\ B) = 4 +2 = 6[/tex]
So:
[tex]n(A\ u\ B) = 8 + 8 - 6[/tex]
[tex]n(A\ u\ B) = 10[/tex]
Solving (b):
[tex]n(A'\ u\ C)[/tex]
This is calculated as:
[tex]n(A'\ u\ C) = n(A') + n(C) -n(A'\ n\ C)[/tex]
From the attachment
[tex]n(A) = n(U) - n(A) = 12 - 8 = 4[/tex]
[tex]n(C) = 0+2+4+2 = 8[/tex]
[tex]n(A'\ n\ C) = 2[/tex]
So:
[tex]n(A'\ u\ C) = 4 + 8 - 2[/tex]
[tex]n(A'\ u\ C) = 10[/tex]
Solving (c):
[tex]n(A\ n\ B)'[/tex]
This is calculated as:
[tex]n(A\ n\ B)' = n(U) - n(A\ n\ B)[/tex]
[tex]n(A\ n\ B)' = 12- 6[/tex]
[tex]n(A\ n\ B)' = 6[/tex]
Using the quadratic formula to solve x2 = 5 – X, what are the values of x? -1 + 21 2 -12/19/ 2 5+21 2 1+ 191 2
Answer:
[tex] {x}^{2} = 5 - x \\ { \tt{ {x}^{2} + x - 5 = 0 }} \\ \\ { \bf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }} \\ \\ { \tt{x = \frac{ - 1± \sqrt{21} }{2} }} \\[/tex]
The parent function f(x)=x^3 is transformed to g(x)=(x-1)^3+4. Which graph represents function g?
Find the equation of a line containing the points (5,1) and (5,−4).
Answer:
The equation is x = 5
Answer:
x = 5
Step-by-step explanation:
In ΔFGH, the measure of ∠H=90°, FH = 8, OF = 17, and HG = 15. What ratio represents the sine of ∠G?
Answer:
[tex]\sin(G) = \frac{8}{17}[/tex]
Step-by-step explanation:
Given
[tex]\angle H = 90^o[/tex]
[tex]FH = 8[/tex]
[tex]GF = 17[/tex]
[tex]HG = 15[/tex]
See attachment for illustration
Required
The ratio of [tex]\sin(G)[/tex]
[tex]\sin(G)[/tex] is calculated as:
[tex]\sin(G) = \frac{Opposite}{Hypotenuse}[/tex]
From the attachment, we have:
[tex]\sin(G) = \frac{FH}{GF}[/tex]
This gives:
[tex]\sin(G) = \frac{8}{17}[/tex]
PLS HELP!! I NEED TO FIND THE SURFACE AREA OF THIS CYLINDER!!!!!
Answer:
923.63
Step-by-step explanation:
the formula for the surface area of a cylinder is 2πrh + 2πr^2 ( i just looked it up lol)
Minimum value is
41
42
46
48
54
56
57
Answer:
41
Step-by-step explanation:
The minimum value of the data set is located at the end of the whisker on the left side of the box plot.
The minimum value is 41
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Answer:
~~~~~~~~~~~~~~~~~~~~~~~~~.~~~~~~~~~~~~~~~~~~~~~~~~~
Step-by-step explanation:
The formula for perimeter of a rectangular field is P = 2L + 2W.
Find the length of the field if the perimeter is 24m and the width is 5m.
Answer:
The length is 7 meters
Step-by-step explanation:
Formula: P = 2L + 2W
Plug in 24 for the perimeter and 5 for the width
New equation: 24 = 2L + 2(5)
Simplify: 24 = 2L + 10
Subtract 10 from both sides: 24 - 10 = 2L + 10 - 10
Simplify: 14 = 2L
Divide both sides by 2: L = 7
Answer: L = 7
There are 36 male and 24 female students in a cultural competition
a ) Write the percentage of students in the competition
b ) Write the percentage of female students in the competition
Answer:
a. 24/60 = 40%
b. 24/60 = 40%
Explanation:
it seems both the questiona have the same answer. how many students in the competition is what you are looking for, the total of people in the competition is 60(36+24). there are 24 students, so you divide 24 by 60 and you will get 40% for both questions.
Choose the definition for the function. please help me
9514 1404 393
Answer:
A
Step-by-step explanation:
It is usually sufficient to look at one section of the graph to answer a question like this. Often the best choice is the section that has a solid dot at the end of the curve. Here, that is the right section.
The left end of the right section is at x=-2, so that part of the function is defined for x ≥ -2. The line to the right has a positive slope, so the coefficient of x will be positive.
Only one answer choice has a positive x-coefficient for x ≥ -2.
[tex]\textbf{A. }\begin{cases}-x-2&\text{if }x<-2\\x+4&\text{if }x\ge-2\end{cases}[/tex]
Answer:
Step-by-step explanation:
This graph is made up of two different, separate line segments. In other words, it comes in two pieces which can be described as a pair of linear functions.
We call this a "piecewise linear" function. Choice A is the best one.
find the y-intercept for the parabola
defined by this same equation:
y = 2x2 – 8x + 5
Answer:
y=5
y int
x=0
y=2(0)^2-8(0)+5
y=5
note everything multiplied by 0 is 0
3. Find the sector area of the circle. Use 3.14 for the value of Round your answer to the nearest tenth.
11 ft
150°
Answer:
a = 158.3 units²
Step-by-step explanation:
a = (∅/360) * πr²
using 11 ft as the radius
a = (150/360) * 3.14 * 11²
a = 158.3 units²
Select the correct answer.
The volume of one of the Great Lakes is 3.5 × 103 cubic kilometers. If there are 6.3 × 107 fish in the lake, what is the average number of fish per cubic kilometer?
A.
2.205 × 1011
B.
1.8 × 104
C.
1.8 × 1010
D.
2.205 × 104
Which graph shows the solution set of the inequality 2.9(x+8) <26.1?
O
+++
-10
-5
0
5
10
-10
-5
0
5
10
O
-10
-5
0
5
5
10
-10
-5
5
5
10
9514 1404 393
Answer:
D
Step-by-step explanation:
The inequality symbol is < (not ≤), which means the end point of the graph will be an open circle.
After dividing by the coefficient of x, you have an inequality of the form ...
x +( ) < ( )
which means the solution will be left of the (open circle) end point of the graph. Only one graph has that form.
__
If you actually work through the numbers, you get ...
x +8 < 9 . . . . . . divide both sides by 2.9
x < 1 . . . . . . . . . subtract 8 from both sides
Ms.Smith notices that a roulette wheel lands on red 4 times in a row. Should she suspect that the wheel is rigged?
No, 50 by 50 chance.
Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 30 centimeters to 60 centimeters?
Answer:
The work done is 202.50Nm
Step-by-step explanation:
Given
[tex]F =450N[/tex]
[tex]x_1 = 30cm[/tex]
[tex]x_2 = 60cm[/tex]
Required
The work done
First, we calculate the spring constant (k)
[tex]F = kx_1[/tex]
[tex]450N = k *30cm[/tex]
[tex]k = \frac{450N}{30cm}[/tex]
[tex]k =15N/cm[/tex]
So:
[tex]F = kx_1[/tex]
[tex]F(x) = 15x[/tex]
The work done using Hooke's law is:
[tex]W =\int\limits^a_b {F(x)} \, dx[/tex]
This gives:
[tex]W =\int\limits^{60}_{30} {15x} \, dx[/tex]
Rewrite as:
[tex]W =15\int\limits^{60}_{30} {x} \, dx[/tex]
Integrate
[tex]W =15 \frac{x^2}{2}|\limits^{60}_{30}[/tex]
This gives:
[tex]W =15 *\frac{60^2 - 30^2}{2}[/tex]
[tex]W =15 *\frac{2700}{2}[/tex]
[tex]W =15 *1350[/tex]
[tex]W =20250N-cm[/tex]
Convert to Nm
[tex]W =\frac{20250Nm}{100}[/tex]
[tex]W =202.50Nm[/tex]
Which linear function represents the line given by the point-slope equation y - 8 = % (x - 4)?
?? Pls help :0
Answer:
option 2
Step-by-step explanation:
[tex]y - 8 = \frac{1}{2} (x - 4)\\\\y = \frac{1}{2}x - 2 + 8\\\\y = \frac{1}{2}x + 6\\\[/tex]
Kenny recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-x-4 = 0 and calculate its properties
hope this helps!
Need help with this problem (listing BRAINLIST and giving points) =)
I hope this is help full to you
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
(-3, 1)
(0,0)
Answer:
y=-3x
Step-by-step explanation:
The y intercept is zero because it goes through (0,0)
The slope is -3 because the line goes through -3 at 1, so it goes down 3 on the y axis for every 1 right on the x axis.
my question is in the document
What is the slope of the line below? Pls help asap
Answer:
D. -2/7
Step-by-step explanation:
Mr. Osborne needs two students to help him with a demonstration. He decides to draw two names out of a bag to make things fair. There are 9 girls and 12 boys in his class. What is the probability that he draws the names of two boys?
Determine the value of x
Answer:
the answer will be Root 2
Step-by-step explanation:
x^2 = 1^2 + 1^2
We take the unmentioned side as 1 because it is an isosceles triangle and thus 2 of the sides will have the same measure
x^2 = 1 + 1
x^2 = 2
taking square root on both the sides
x = root of 2
The value of x is [tex]\sqrt 2[/tex] by using the concept of isosceles right-angled triangle and applying the Pythagoras theorem.
Given that in a right-angled triangle, base is equal to1 and hypotenuse is equal to x.
To find the value of x by using the concept of isosceles right-angled triangle and applying the Pythagoras theorem, follow steps:
Step 1: Given right-angled triangle whose two angles are of equal measures that is equal to [tex]45^{\circ}[/tex]. That implies the triangle is an isosceles triangle.
That implies, perpendicular = base = 1 .
Step 2: Applying the concept of Pythagoras theorem:
Pythagoras theorem states that (perpendicular[tex]{)}^2[/tex] +(base[tex]{)}^2[/tex] = (hypotenuse[tex]{)}^2[/tex]
Plugging the given and data from step 1 gives:
[tex](1)^{2}+1^2=x^{2}[/tex]
On substituting the square of 1 equal to 1 (gives):
[tex]x^{2} = 1+1[/tex]
On adding gives:
[tex]x^{2} =2[/tex]
Taking square root gives:
[tex]x=\sqrt{2}[/tex]
Therefore, the value of x is [tex]\sqrt 2[/tex] by using the concept of isosceles right-angled triangle and applying the Pythagoras theorem.
Learn more about Pythagoras theorem here:
https://brainly.com/question/17179659
#SPJ6
Find the indicated Arc length in bold . Use 3.14 for pi!
find the regression equation of the following ages of husband and wives at marriage
husband 23,27 ,28,28,29, 30,31,33,35,36
wife 18,20,22,27,21,29,27,29,28,29
Answer:
Ŷ = -1.7391+0.8913X
Step-by-step explanation:
Given the data :
husband 23,27 ,28,28,29, 30,31,33,35,36
wife 18,20,22,27,21,29,27,29,28,29
Taking :
Husband as (X)
Wife as (Y)
We could use technology to fit the data and obtain a regression model.
Using technology ; the regression equation obtained is:
Y = -1.7391+0.8913X
Where
Y = wife
X = husband
Slope = 0.8913
Intercept = - 1.7391
Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses. After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks She writes the equation of the function like this E(x)=7x-25where the number of doors she knocks on during the week and is her earnings for the week in dollars.Which of the following are reasonable interpretations of the -intercept of Jessica's function?Check all that apply.
A. She can earn $7 per week even if she does not knock on any doors.
B. If she does not knock on any doors during the week, she will lose 25$.
C. She will lose 7$ per week if she does not knock on any doors
D. Her expenses are 25$
Answer:
D. Her expenses are $25
Step-by-step explanation:
option D.
B might sound plausible mathematically, but in reality no expenses arise by doing nothing at all
Fill in the missing number to make these fractions equivalent 15/25 = ?/5
Answer:
3
Step-by-step explanation:
25 divided by 5 is 5
therefor 15 divided by 5 is 3
15/25 = 3/5
Answer:
3
Step-by-step explanation:
[tex]\frac{15}{25} =\frac{?\\}{5}[/tex] 25 divided by ? = 5? The number 5 so divide 15 as well
15 ÷ 5 = 3
[tex]\frac{15}{25} =\frac{3}{5}[/tex]
Hence, 3 is the answer
Please mark me as brainliest if you can or give me a thanks
HELP PLEASE HELP HELP
Answer:
here
Step-by-step explanation:
C and D is the answer
Evaluate the expression(ab) for a = 10 and b= 4
Answer:
40
Step-by-step explanation:
A x B = 10 x 4 = 40
Answer:
ab=40
Step-by-step explanation:
pleaee mark as brain list