Answer:
The sum is 6
Step-by-step explanation:
Given
[tex]Vertices: (0,1), (3,4), (4,3), (3,0)[/tex]
[tex]Perimeter: a\sqrt{2} + b\sqrt{10}[/tex]
Required
[tex]a + b[/tex]
The first step is to name each points, as follows
[tex]A: (0,1)\\B: (3,4)\\C: (4,3)\\D: (3,0)[/tex]
Next is to calculate the distance between each consecutive point
We'll calculate the distance AB, BC, CD and DA
Distance between points is calculated as thus;
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Calculating distance AB
[tex]A: (0,1)\\B: (3,4)[/tex]
Here,
[tex]x_1 = 0; x_2 = 3[/tex]
[tex]y_1 = 1; y_2 = 4[/tex]
[tex]AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}[/tex]
[tex]AB = \sqrt{(- 3)^2 + (-3)^2}[/tex]
[tex]AB = \sqrt{9+9}[/tex]
[tex]AB = \sqrt{18}[/tex]
Expand 18 as 9 * 2
[tex]AB = \sqrt{9 * 2}[/tex]
Split surds
[tex]AB = \sqrt{9} * \sqrt{2}[/tex]
Take square root of 9
[tex]AB = 3 * \sqrt{2}[/tex]
[tex]AB = 3 \sqrt{2}[/tex]
Calculating distance BC
[tex]B: (3,4)\\C: (4,3)[/tex]
Here,
[tex]x_1 = 3; x_2 = 4[/tex]
[tex]y_1 = 4; y_2 = 3[/tex]
[tex]BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}[/tex]
[tex]BC = \sqrt{(-1)^2 + (1)^2}[/tex]
[tex]BC = \sqrt{1 + 1}[/tex]
[tex]BC = \sqrt{2}[/tex]
Calculating distance CD
[tex]C: (4,3)\\D: (3,0)[/tex]
Here,
[tex]x_1 = 4; x_2 = 3[/tex]
[tex]y_1 = 3; y_2 = 0[/tex]
[tex]CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}[/tex]
[tex]CD = \sqrt{(1)^2 + (3 )^2}[/tex]
[tex]CD = \sqrt{1 + 9}[/tex]
[tex]CD = \sqrt{10}[/tex]
Calculating distance CD
[tex]D: (3,0)\\A: (0,1)[/tex]
Here,
[tex]x_1 = 3; x_2 = 0[/tex]
[tex]y_1 = 0; y_2 = 1[/tex]
[tex]DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}[/tex]
[tex]DA = \sqrt{(3)^2 + (- 1)^2}[/tex]
[tex]DA = \sqrt{9 + 1}[/tex]
[tex]DA = \sqrt{10}[/tex]
At this point, the perimeter can then be calculated
[tex]Perimeter = AB + BC + CD + DA[/tex]
[tex]Perimeter = 3 \sqrt{2} + \sqrt{2}\ + \sqrt{10} + \sqrt{10}[/tex]
[tex]Perimeter = 4 \sqrt{2} + 2\sqrt{10}[/tex]
From the given parameters;
[tex]Perimeter: a\sqrt{2} + b\sqrt{10}[/tex]
This implies that;
[tex]a\sqrt{2} + b\sqrt{10} = 4 \sqrt{2} + 2\sqrt{10}[/tex]
By comparison;
a = 4 and b = 2
Hence;
[tex]a + b = 4 + 2[/tex]
[tex]a +b = 6[/tex]
Calculate the mean of this data set: 12, 35, 44, 74, 23, 49, 45, 18, 90, 56, 84,
38, 7. What is the sample proportion of numbers that are within +10 of
the mean? (Round off the mean to the nearest integer for your calculations.)
Answer: 0.38
Step-by-step explanation:
The mean is the sum of all the observations divided by the number of observations. It is 44.2 (rounded off to 44) Next is fraction observations that lie between 34-35 (just answered this and it is correct)
Determine the measure of ∠A. ANSWWER: 1) 192° 2) 88° 3) 84° 4) 168°
Answer:
3) 84°
Step-by-step explanation:
The angle formed by a chord and a tangent measures half of the intercepted arc.
m<A = (1/2)m(arc) = (1/2) * (168 deg) = 84 deg
Answer:
84 degrees
Step-by-step explanation:
Tim explained a function in words and Paul wrote an equation. Tim: The amount of money in a savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it. Paul: y−1,400=56(x+26)
Whose function has the smaller y-intercept?
A. Tim’s with a y-intercept of $2,700
B. Paul’s with a y-intercept of $2,856
C. Paul’s with a y-intercept of $2,800
D. Tim’s with a y-intercept of $2,780
Answer:
D. Tim’s with a y-intercept of $2,780
Step-by-step explanation:
The function with the smaller y-intercept is Tim’s with a y-intercept of $2,780
The equation of Paul's savings is given as:
y-1400=56(x+26)
Set x to 0, to calculate the y-intercept
y-1400=56(0+26)
Evaluate the sum
y-1400=56(26)
Evaluate the product
y-1400=1456
Add 1400 to both sides
y = 2856
For Tim, we have the following equation
y = 225x + c
Where c represents the y-intercept
After eight months, the bank account has $4,580
So, we have:
4580 = 225*8 + c
Evaluate the product
4580 = 1800 + c
Subtract 1800 from both sides
c = 2780
2780 is less than 2856
Hence, the function with the smaller y-intercept is Tim’s with a y-intercept of $2,780
Read more about y-intercepts at:
https://brainly.com/question/1884491
Help please, Topic: Arrangments
Answer: B: 120
Step-by-step explanation:
You multiply these choices together to get your result: 5 x 4 x 3 x 2 (x 1) = 120.
Since there are 5 choices to choose from.
For f(x) = 2x +1 and g(x) = x^2-7, find (f/g) (x)
Answer:
(2x + 1)/(x^2 - 7), x ≠ ±√7
Step-by-step explanation:
I'm not sure if this is what your looking for.
20 poinst plzzzzzz help me
Answer:
Step-by-step explanation:
Jason saw a shoes tat cost 41 dollars, he already ave 19 dollars in his saving account, his neighbor asked him to walk the dog for 4 dollars an hour, how many hours Jason need to walk the dog so e will be able to buy the shoes?
4x+19≥41
second one: A sign on abridge says that max. weight is 41 ton, a truck weighs 19 ton without any loads, the driver needs to pass by the bridge loading 3 boxes, how much the boxes should weigh so he will be able to pass the bridge.
3x+19≤ 41
third riddle: A cellphone company charges 19 dollars , and charge 0.05 cents for every text message. what limit of text message jason needs to keep his bill under 41 dollars.
19+0.05≤41
pls help i give brainliest
Answer: B no
Step-by-step explanation:
Plot in the x and y coordinates into the equation to solve it.
The x coordinate is 4 and the y coordinate is 1
-4(4) +3(1)= 2
-16 + 3 = 2
-13 ≠2
-13 does not equal 2 so (4,1) is not a solution.
Answer: NO
Step-by-step explanation:
[tex]Substitute \\\\-4(4)+3(1)=2\\\\Multiply\\\\-16+3=2\\\\Combine \\like \\terms\\-13=2[/tex]
-13 does NOT equal 2, so it is not a solution
Hope it helps <3
Please Help Soon! A 4-foot by 8-foot rectangular piece of plywood will be cut into 4 congruent rectangles with no wood left over and no wood lost due to the cuts. What is the positive difference, in feet, between the greatest possible perimeter of a single piece and the least possible perimeter of a single piece?
Answer: 6 feet
Step-by-step explanation:
Given that a 4-foot by 8-foot rectangular piece of plywood will be cut into 4 congruent rectangles with no wood left over and no wood lost due to the cuts
Let assume that the 4 rectangles will be of the same area since they are congruent.
The area of the big rectangle will be
Area = 4 × 8 = 32
Divide 32 by 4
32/4 = 8
Suggest the two possible numbers in which their product will be equal to 8
4 and 2 or 8 and 1
If 4 and 2
The perimeter = 2L + 2B
Substitute the 4 and 2 into the formula
Perimeter = 2(4) + 2(2)
Perimeter = 8 + 4
Perimeter = 12
If 8 and 1
Perimeter = 2(8) + 2(1)
Perimeter = 16 + 2 = 18
The positive difference, in feet, between the greatest possible perimeter of a single piece and the least possible perimeter of a single piece will be:
18 - 12 = 6 feet
For which value of b can the expression x^2+bx+18 be factored?
Answer:
b=9
Step-by-step explanation:
You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost? Include a let statement in your answer.
Answer:
5$??.
Step-by-step explanation:
If a magazine was 5$, 25-5= 20. So then, 20÷4= 5. There fore an eraser costs 5$.
Answer:
5 dollars
Step-by-step explanation:
Let x be the price of each eraser
We bought a magazine and 4 erasers with 25 dollars
so : 5+4x = 25⇒ 4x= 20⇒x= 20/4⇒ x=5
The eraser costs 5 dollars
Which inequality is shown in this graph?
Answer:
B.
Step-by-step explanation:
y- int. = - 2
Slope is negative because the line is going down. So, it is B. or C.
The shaded area is under the line, so it is ≤. The answer is B.
Find the slope of the line on the graph.
Answer:
m = -3/4
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Simply plug in 2 coordinates into the formula:
(0, 1) y-int
(4, -2) random
m = (-2 - 1)/(4 - 0)
m = -3/4
work out the length of AB. give your answer to 3 significant figures.
Answer:
Distance formula = √(x₂ - x₁)² + (y₂ - y₁)²
(x₁, y₁) = (1, 7) and (x₂, y₂) = (10, 3)
AB = √(10 - 1)² + (7 - 3)²
= √9² + 4²
= √81 + 16
= √97
= 9.85
Find the area of ΔDEF to the nearest tenth. ANSWERS: A) 127.8 square units B) 46.5 square units C) 63.9 square units D) 23.3 square units
Answer:
C) 63.9 square units
Step-by-step explanation:
From the above diagram, we can see that the triangle has 2 sides and and angle
The formula for the area of a triangle that has 2 sides and an angle = 1/2absinθ
θ = 70°
a = DE = 8 units
b = EF = 17 units
Area of ΔDEF = 1/2 × 8 × 17 × sin 70°
Area of ΔDEF = 63.9 square units.
Answer:
63.9 square units
Step-by-step explanation:I took the test
In how many different ways can 5 people be seated at a round table?
Answer:
120
Step-by-step explanation:
there is a simple way to solve these
the equation is
1 x 2 x 3 x 4 x 5
up to whatever number of objects
Answer:
There are 120 ways that 5 people can b seated if they are at a round table.
Step-by-step explanation:
What you do to find this out in a simple way is to multiply.
1 x 2 x 3 x 4 x 5 = 120
Write a direct variation equation that relates x-miles and y- kilometers.
Answer:
Step-by-step explanation:
is this the whole question or is there answers i will edit this once i know
I NEED HELP CAN SOMEONE PLEASE ANSWER THIS ASAP PLEASE!!!
Answer:
y = 5x - 3
Step-by-step explanation:
ok so perpendicular just means the opposite reciprocal of the slope of the normal equation. It just means that they form a 90 degree angel when they intersect.
Answer all please number 2
Answer:
(a) 26.43%
(b) 189 seconds
Step-by-step explanation:
(a) Data
mean: 3 minutes and 48 seconds = 3*60 + 48 = 228 s standard deviation, sd: 19 svalue of interest, x: 4 minutes = 4*60 = 240 sZ-score is calculated as follows:
z = (x - mean)/sd
z = (240 - 228)/19
z = 0.63
We want to find the next probability P(Z>0.63), which is equivalent to 1 - P(Z≤0.63)
From table, 1 - P(Z≤0.63) = 1 - 0.7357 = 0.2643 or 0.2643*100 = 26.43%
(b) We want to find z1 at which P(Z≤z1) = 0.2. From the second table, z1 is between -2.05 and -2.06.
z = (x - mean)/sd
-2.055 = (x - 228)/19
(-2.055)*19 + 228 = x
x = 189 s
(b) In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two exam scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third exam that will give an A? What about a B? [8 marks]
(c) Factorize completely [2 marks]
(d) (i) The cost of six hens and one duck at the university poultry farm is GH₵40. While four hens and three ducks cost GH₵36. What is the cost of each type of bird? [13 marks]
(ii) A circular coffee table has a diameter of 5 m. What will it cost to have the top refinished if the company charges GH₵3 per square metre for the refinishing? [take ] [7 marks]
Answer:
Step-by-step explanation:
ii) circumference of the circular coffee table= πd= 3.14× 5=15.7m
Therefore the cost of the refinishing a circular coffee table = 15.7 × GH¢3=GH¢47.10
In the diagram of circle A, what is m?
Answer:
upload ur diagram so we can solve it for u
Which statement is true about the given function?
fx) > 0 over the interval (-0,3).
f(x) > 0 over the interval (-:-).
f(x) <0 over the interval (-0,3).
f(x) <0 over the interval (- : -).
Answer:
Option C.
Step-by-step explanation:
If the graph of a function f(x) lies above the x-axis, then f(x) > 0.
If the graph of a function f(x) lies below the x-axis, then f(x) < 0.
From the given graph it is clear that the graph of f(x) intersect the x-axis at x=3.
Before x=3 the graph lies below the x-axis. So,
[tex]f(x) < 0[/tex] over the interval [tex](-\infty,3)[/tex].
After x=3 the graph lies above the x-axis. So,
[tex]f(x) > 0[/tex] over the interval [tex](3,\infty)[/tex].
Therefore, the correct option is C.
Which of the following is equivalent to: -5 - 4?*
Answer:
-9
Step-by-step explanation:
-5 - 4 = -5 + (4)
You are adding two negative numbers, so add the absolute values of the numbers, and the sign of the answer is negative.
-5 - 4 = -(|-5| + |4|) = -(5 + 4) = -9
Find the equation of the line: With an x intercept of 4 and a y intercept of 1. PLEASE HELP I ONLY HAVE 15 MINUTES LEFT
Answer:
y = -1/4x + 1
Step-by-step explanation:
that is (0,1) and (4,0)
gradient
can be -1/4
c can be y = mx + c
we'll take anyone of the equation
1 = 0 + c
c = 1
Hi can someone plz help me with this question
Answer: n/4-1
Step-by-step explanation:
n/4 means how much each friend would have eaten if the pizza was equally divided and - 1 references to the one slice less he ate.
If there are 7 frankfurters to the pound, how
many pounds of frankfurters are needed for a
picnic to supply 19 pupils with 2 frankfurters
each?
Answer:
6lbs
Step-by-step explanation:
Total # of Frankfurters needed.
[tex]19*2=38[/tex]
Divide the total needed by the amount in a lb, to find out how many lbs we need.
[tex]\frac{38}{7}=5.4[/tex]
Therefore, we need 6 full lbs in order to create at least 38 Frankfurters.
If we only have 5lbs, we can only create 35 Frankfurters.
5.4 pounds of frankfurters are needed for a picnic.
there are 7 frankfurters to the pound
let x pounds of frankfurters needed for a picnic. to supply 19 pupils with 2 frankfurters each.
What is the Ratio?The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
since there are 19 pupil and each of has 2 frankfurters.
total frankfurters = 19 x 2
= 38
required pound,
x =38/7
x = 5.4
Thus, 5.4 pounds of frankfurters are needed for a picnic to supply 19 pupils with 2 frankfurters each.
Learn more about Ratio here:
brainly.com/question/13419413
#SPJ2
which side of the quadrilateral abcd
has a length equal to 10?
Answer:
AD
Step-by-step explanation:
You must measure the difference between A and D. To get to this answer you should try all available combinations.
If it takes 13 cup of flour to make 14 of a cake, how many cups of flour are needed to make a whole cake? i need help plz
Answer:
1-1/3 if its 14
1/52 if its 1/4
Step-by-step explanation:
what is the volume of a right triangle with the dimesions 24 20 12
Answer:
Assuming you mean area the answer is 120
Step-by-step explanation:
a right triangle has too shorter sides who are perpendicular and one longer side that you can't use. the longer side is 24 since 24>20>12
so 24 is the hypontenuse (longer side)
the two perpendicular sides are 20 and 12
the area for a triangle is b*h*1/2
the base (20) times the height (12) is 240. 240 times 1/2 is 120.
PLSSS HELP!!! I really need help with this i have tried everything! Please provide instructions so I could learn how to do it! You are interested in finding a 98% confidence interval for the average number of days of class that college students miss each year. The data below show the number of missed days for 11 randomly selected college students. Round answers to 3 decimal places where possible. 9, 1, 2, 2, 9, 10, 1, 3, 7, 4, 2 a. To compute the confidence interval use a ? distribution. b. With 98% confidence the population mean number of days of class that college students miss is between ? and ? days. c. If many groups of 11 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About ? percent of these confidence intervals will contain the true population mean number of missed class days and about ? percent will not contain the true population mean number of missed class days.
Step-by-step explanation:
a. When the sample size is below 30 or the population standard deviation is not known, use a t distribution rather than a normal distribution.
b. The confidence interval is:
CI = x ± CV × SE
where x is the sample mean,
CV is the critical value (in this case, t).
and SE is the standard error (the sample standard deviation).
For the data given, the mean is x = 4.545, and the standard deviation is SE = 3.503.
There are 11−1 = 10 degrees of freedom, and the confidence level is 98%. For a t-table, the critical value is CV = 2.764.
So the confidence interval is:
CI = 4.545 ± 2.764 × 3.503
CI = (-5.1, 14.2)
c. The confidence level is 98%, so 98% of these confidence intervals will contain the true population mean, and 2% will not.
What is the value of q?
Answer:
14
Step-by-step explanation: