Answer:
Our two numbers are:
[tex]2+4\sqrt{2} \text{ and } 4\sqrt{2}-2[/tex]
Or, approximately 7.66 and 3.66.
Step-by-step explanation:
Let the two numbers be a and b.
One positive real number is four less than another. So, we can write that:
[tex]b=a-4[/tex]
The sum of the squares of the two numbers is 72. Therefore:
[tex]a^2+b^2=72[/tex]
Substitute:
[tex]a^2+(a-4)^2=72[/tex]
Solve for a. Expand:
[tex]a^2+(a^2-8a+16)=72[/tex]
Simplify:
[tex]2a^2-8a+16=72[/tex]
Divide both sides by two:
[tex]a^2-4a+8=36[/tex]
Subtract 36 from both sides:
[tex]a^2-4a-28=0[/tex]
The equation isn't factorable. So, we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = -4, and c = -28. Substitute:
[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}[/tex]
So, our two solutions are:
[tex]\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66[/tex]
Since the two numbers are positive, we can ignore the second solution.
So, our first number is:
[tex]a=2+4\sqrt{2}[/tex]
And since the second number is four less, our second number is:
[tex]b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66[/tex]
Answer:
[tex]2+4\sqrt{2}\text{ and }4\sqrt{2}-2[/tex]
Step-by-step explanation:
Let the large number be [tex]x[/tex]. We can represent the smaller number with [tex]x-4[/tex]. Since their squares add up to 72, we have the following equation:
[tex]x^2+(x-4)^2=72[/tex]
Expand [tex](x-4)^2[/tex] using the property [tex](a-b)^2=a^2-2ab+b^2[/tex]:
[tex]x^2+x^2-2(4)(x)+16=72[/tex]
Combine like terms:
[tex]2x^2-8x+16=72[/tex]
Subtract 72 from both sides:
[tex]2x^2-8x-56=0[/tex]
Use the quadratic formula to find solutions for [tex]x[/tex]:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] for [tex]ax^2+bx+c[/tex]
In [tex]2x^2-8x-56[/tex], assign:
[tex]a\implies 2[/tex] [tex]b \implies -8[/tex] [tex]c\implies -56[/tex]Solving, we get:
[tex]x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}[/tex]
Since the question stipulates that [tex]x[/tex] is positive, we have [tex]x=\boxed{2+4\sqrt{2}}[/tex]. Therefore, the two numbers are [tex]2+4\sqrt{2}[/tex] and [tex]4\sqrt{2}-2[/tex].
Verify:
[tex](2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark[/tex]
Question 2 - Cost of a Paver
The pavers cost $8 per square metre ($8/m?). There are 4 pavers in a
square metre.
Calculate how much one paver costs. Show your working
2$ each
Answer:
8$ divided by 4.which is equal to 2
Help asappppp hbshhshshhshshsshshshs
9 on the top as well so 9 x 2 18 3x2 6 3
Here is some information about a holiday.
7 night holiday
$340 per person
8% discount if you book before 31 March
On 15 February, Naseem books this holiday for 2 people.
Calculate the total cost of his holiday.
Answer:
$625.6
Step-by-step explanation:
Information about a holiday:
7 night holiday
$340 per person
8% discount if you book before 31 March
Number of people Naseem booked the holiday for = 2
Date of booking of the holiday = 15 February
Total cost of the holiday per person = cost per person - discount before March 31
= $340 - 8% of $340
= 340 - 8/100 * 340
= 340 - 0.08 * 340
= 340 - 27.2
= $312.8
Total cost of the holiday for 2 persons = 2 × Total cost of the holiday per person
= 2 * $312.8
= $625.6
Which number is a rational number?
Answer:
C
Step-by-step explanation:
17.156 is the irrational number as it is terminating(means it ends)
Rest all are irrational
C) –7c^5 + 13c^5 + c^5=
Answer:
please mark as brilliant thanks for the above
Name the marked angle in 2 different ways.
Answer:
<NKM is the first.the second is <MKN
Answer:
< NKM and <MKN
Step-by-step explanation:
What is the total number of digits required in numbering the pages of a book, which has 1, 150 pages?
Answer:
3,493 digits
Step-by-step explanation:
Total pages of the book = 1,150
Page 1 - 9 = 9 digits
Page 10 - 99
= 2 * 90 pages
= 180 digits
Page 100 - 999
= 3 × 900 pages
= 2,700 digits
Page 1000 - 1,150
= 4 × 151 pages
= 604 digits
Total digits required in numbering 1,150 pages = 9 + 180 + 2,700 + 604
= 3,493 digits
Total digits required in numbering 1,150 pages = 3,493 digits
Ryan draws a trend line through the following data
points. Did he draw the line correctly?
Answer: C, You can tell the trend line is incorrect since all of the points are below it. A trend line should be in-between all of the points to give the best estimate.
Step-by-step explanation:
Name the marked angle in 2 different ways.
1) Angle UWV
2) Angle VWU
When the park opened for the day, four people were in attendance. Every hour, the number of people tripled from the previous hour's attendance.
Part A: Determine the common ratio between the attendance each hour.
Part B: Write an equation that can be used to determine the attendance for the nth hour the park is open.
Part C: How many people were at the park during the second, fifth, and eighth hours the park was open? Show all work.
sin(A+B-C) find the equation
Answer:
[SInA][CosB][CosC] + [CosA][SinB][CosC] - [CosA][CosB][SinC] - [SinA][SinB][SinC]
Step-by-step explanation:
Given:
Sin (A + B - C)
Find;
Expansion of given expression
Computation:
Sin (A + B - C)
Sin [(A + B) - C]
Sin(A + B)CosC - Cos(A + B)SinC
[SInACosB + CosASinB]CosC - [CosACosB - SinASinB]SinC
SInACosBCosC + CosASinBCosC - CosACosBSinC - SinASinBSinC
[SInA][CosB][CosC] + [CosA][SinB][CosC] - [CosA][CosB][SinC] - [SinA][SinB][SinC]
A newsletter publisher believes that 30% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.02 level of significance, the testing firm fails to reject the null hypothesis. What is the conclusion regarding the publisher's claim
Answer:
The evidence is not sufficient at the 0.02 level of significance to reject the claim that the percentage is 30%.
Step-by-step explanation:
Let's first state the null and alternative hypotheses for this research;
H0: p = 0.30
Ha: p ≠ 0.30
Now, since the bull hypothesis is the claim and he fails to reject the null hypothesis from the research, we will conclude that;
The evidence is not sufficient at the 0.02 level of significance to reject the claim that the percentage is 30%.
Find the median of the data.
The number of girls per classroom.
11, 3, 1, 12, 5, 3, 2
Median: [?] girls
oto
Answer:
3
Step-by-step explanation:
To find the median, first we have to put the data in ascending order:
1, 2, 3, 3, 5, 11, 12
The median is the middle number. In this case, that is 3.
The median of the data "The number of girls per classroom" which has values as 11, 3, 1, 12, 5, 3, 2 is 3.
To find the median of the given data, we first need to arrange the numbers in ascending order:
1, 2, 3, 3, 5, 11, 12
The median is the middle value when the data is arranged in ascending order. In this case, since the total number of data points is odd (7 data points), there is one middle value. The median is the fourth value in the ordered list, which is 3.
The median is a measure of central tendency that represents the middle value in a dataset. It is often used to describe the typical or central value of a set of data and is particularly useful when dealing with skewed distributions or outliers.
In this case, the median of 3 tells us that, when sorted in ascending order, the middle value of the number of girls per classroom is 3, which gives us an indication of the central tendency of the data.
To learn more about median click on,
https://brainly.com/question/27353809
#SPJ2
find the equation to the line below *pls help asap* brainliest too the first answer and 30 points
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
If you just plug in the answers, so lets take (1,6) and plug it into y = 6x
You could just solve it so it'd be like
6 = 6(1) and
12 = 6(2)
Pick the geometric term that matches the real-world object. rectangular prism sphere cylinder triangular prism cube
Answer:
Assuming this is the book one the answer is rectangular prism.
Find the measure of angle 1
I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Answer:
∠ 1 = 128°
Step-by-step explanation:
∠6 = 7x + 3 [ vertically opposite angles ]
∠6 = 4x + 24 [ corresponding angles ]
7x + 3 = 4x + 24
7x - 4x = 24 - 3
3x = 21
x = 7
∠1 + ( 4x + 24 )= 180° [ straight line angles ]
∠1 + 4 ( 7 ) + 24 = 180° [ Substituting x = 7 ]
∠ 1 + 28 + 24 = 180°
∠ 1 = 180 - 24 - 28
∠ 1 = 128°
x^(2)-2x+7 I need to find Find the vertex and the axis of symmetry.
Answer:
Vertex: (1, 6)
Axis of symmetry: x = 1
Step-by-step explanation:
a tablet is on sale for 30% off. the regular price is $185. how much money will you save?
Answer:
185×30÷100=55.5
HERES YOUR answer
Please help meeee
Similar Figures Activity - Dilations Not at the Origin
Step-by-step explanation:
∆ABC =>by reflection over x-axis and then dilation with scale factor 2, the point of center (5, -1) ==> ∆ XYZ
What transformation has taken place on the coordinate grid pleaseee help my final! I'll give rate and heart etc
Answer:
Translation across the coordinate plane
Step-by-step explanation:
Here, we want to get the kind of transformation that has occurred to the shape
from the given coordinate diagram, we can see that A shifted from (2,3) to (-3,6)
B shifted from (2,-2) to (-3,1)
and C shifted from (-1,-4) to (-6,-1)
If we look at these, we can observe that there is a change in the x-axis coordinate in each by (-1-(-6) or 2-(-3) = 5 units
and there is a change in the y-axis value by (3-6) = -3 units
so the transformation here can be represented generally as;
(x -5, y+ 3)
With this, we can see that what we have represented is simply a translation across the coordinate plane
Subtract (7x-3) from (5-3x)
what is the solution to the equation below?
please help!!
Answer:
Have you tried photo math.? It can help you find the answer
Step-by-step explanation:
here is the answer bae. Feel free to ask for more
a)gc
b)a..f
c)bc
d)ed
which one please help
Answer:
b
Step-by-step explanation:
Answer:
b......................
Step-by-step explanation:
.
Quadrilateral qrst is a square what is pst
if QRST is indeed a quadrilateral, then, Check the picture below.
please help!! I'm really confused
Answer:
(0,-4)
Point B is on (0,-4)
Hope this helped :)
which of the following numbers must be added to complete the square in the equation below x^2+16x=5
Answer:
8
Step-by-step explanation:
I was stumped on this question too so I figured I might as well learn how to do it. All you have to do is divide the middle number (16x) by 2. Pretty easy! Hope this helps anyone who needs it!
Find f(-3) PLEASE HELP
Answer:
2
Step-by-step explanation:
When the point on the x-axis is on -3, the point on the y-axis is 2. Therefore, f(-3) is equal to 2.
If this helps please mark as brainliest
Need help seriously
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Vowels: A, E, I, O, U
There are only 2 vowels out of 8 on the spinner, which means that 6 out of 8 aren't vowels.
[tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
Hope this is helpful
Explain how to convert measurements in the metric system
Answer:
You can use similar processes when converting from smaller to larger units. When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide.
Example look at the pic please 7,225 cm = ___ m
Meters are larger than centimeters, so you expect your answer to be less than 7,225.
Using the factor label method, write 7,225 cm as a fraction and use unit fractions to convert it to m.
Cancel similar units, multiply, and simplify.
7,225 centimeters = meters
Answer:
Sample Response: If you move from smaller to larger units, divide by a power of 10 or move the decimal to the left. If you move from larger to smaller units, multiply by a power of 10 or move the decimal to the right.
(a+b)^2*(a-b)
please answer me fast
Answer:
a^3b + 2a^2b^2 + ab^3
Step-by-step explanation:
(a+b)^2
= a^2 + 2ab + b^2
ab(a^2 + 2ab + b^2)
= a^3b + 2a^2b^2 + ab^3
