Answer:
[tex]52.8cm^{2}[/tex]
Step-by-step explanation:
Perimeter = 26.4 cm
Apothem = 4.0 cm
The area of an regular octagon can be defined as the [tex]\frac{perimeter*apothem}{2}[/tex]
when we plug in our values we get the equation [tex]\frac{26.4cm*4.0cm}{2}=52.8cm^{2}[/tex]
The sum of two positive integers is 31. If the sum of the squares of these numbers is 625,find the smaller of the numbers.
Step-by-step explanation:
It is given that, the sum of two positive integers is 31 and the sum of the squares of these numbers is 625 and we are to find the smaller of the numbers.
So, let the two positive integers be x and y.
Therefore,
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x + y = 31 \: \: ........ \: (i) }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + y {}^{2} = 625 \: ...... \: (ii)}}} \\ \\[/tex]
Now, From the first equation we have,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x + y = 31 }}} \\ \\ [/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad y = 31 - x \: ...... \: (iii)}}} \\ \\ [/tex]
Now, substituting the value of y in equation (ii) we get :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x {}^{2} + (31 - x) {}^{2} = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + (31 {}^{2} - 2.x.31 + x{}^{2} ) = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + (961 - 62x + x{}^{2} ) = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + 961 - 62x + x{}^{2} - 625 = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2 x {}^{2} + 336 - 62x = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2 x {}^{2} - 62x + 336 = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2( x {}^{2} - 31 + 168) = 0}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad \frac{2}{2} ( x {}^{2} - 31 + 168) = \frac{0}{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} - 31 + 168 = 0}}} \\ \\[/tex]
Now using the quadratic formula :
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}} \\ \\[/tex]
Where,
a = 1b = -31c = 168[tex] \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ - (- 31) \pm \sqrt{ {31}^{2} - 4(1)(168)} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm \sqrt{ 961 -672} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm \sqrt{ 289} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm 17 }{2(1)} }}} \\ \\[/tex]
Now, we have two equations,
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 + 17 }{2} \: ... .....\: (iv)}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 - 17 }{2} ... .....\: (v)}}} \\ \\[/tex]
So, Equation (iv) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 + 17 }{2} }}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 48 }{2} }}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x = 24 }}} \\ \\ [/tex]
Now, Equation (v) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 - 17 }{2}}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 14 }{2}}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \: 7}}}\\ \\ [/tex]
So, the value of x is 7 or 24Now, we are to find the value of y.
Substituting the value of x (24) in equation (iii) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad y = 31 - x \:}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad y = 31 - 24 \:}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad y = 7 \:}}} \\ \\ [/tex]
Again, Substituting the value of x (7) in equation (iii) :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad y = 31 - x \:}}} \\ \\ [/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad y = 31 - 7 \:}}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad y = 24 \:}}} \\ \\ [/tex]
Therefore,
The value of y is also 7 or 24.[tex] \\ [/tex]
So, The smaller of the numbers is 7 .
The sum of two positive integers is 31. If the sum of the squares of these numbers is 625, find the smaller of the numbers.
Given : -Sum of two positive numbers = 31Sum of squares of these numbers = 625To Find : - We have to find the smaller of the numbers .Concept : -This question belongs to quadratic equations so we have to find the answer by making equation and solving it .
To Assume : -Let the first no. be x Let the second no. be ySo let's get started with Solution :According to question , sum of two positive integers is 31 . So ,
x + y = 31 --------- ( Equation 1 )According to question , sum of square
of these numbers is 625 . So ,
x² + y² = 625 --------- ( Equation 2 )From equation 1 ( x + y = 31 ) , Value
of x :
x = 31 - yNow , putting value of x in eq. 2 :
x² + ( 31 - x )² = 625 x² + ( 31 )² - ( 2 × 31 × x ) + x² = 6252x² + 961 - 62x = 6252x² - 62x = 625 - 9612x² - 62x = -3362x² - 62x + 336 = 0 2(x² - 31x + 168 ) = 0x² - 31x + 168 = 0Solving it by using middle term
splitting :
x² -24x -7x + 168 = 0x ( x - 24 ) -7 ( x - 24 ) = 0( x - 7 ) ( x - 24 )So ,First number ,
x - 7 = 0x = 7 { Smaller Number }Second Number ,
x - 24 = 0x = 24Verification :According to question ,
Sum of numbers is equal to 31 :
x + y = 317 + 24 = 31L.H.S = R.H.SSum of squares of these numbers is equal to 625 :
x² + y² = 6257² + 24² = 62549 + 576 = 625625 = 625L.H.S = R.H.STherefore , our value for x and y are true. Thus our answer is valid.#[tex] \rm{Keep \: Learning}[/tex]please help me I need help please
Answer:
p = 4
Step-by-step explanation:
Given equation:
[tex]x^2+(p-3)y^2-4x+6y-16=0[/tex]
Standard equation of a circle:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
(where [tex](a,b)[/tex] is the centre of the circle, and [tex]r[/tex] is the radius)
If you expand this equation, you will see that the coefficient of [tex]y^2[/tex] is always one.
Therefore, [tex]p-3=1[/tex]
[tex]\implies p=1+3=4[/tex]
Additional information
To rewrite the given equation in the standard form:
[tex]\implies x^2+y^2-4x+6y-16=0[/tex]
[tex]\implies x^2-4x+y^2+6y=16[/tex]
[tex]\implies (x-2)^2-4+(y+3)^2-9=16[/tex]
[tex]\implies (x-2)^2+(y+3)^2=16+4+9[/tex]
[tex]\implies (x-2)^2+(y+3)^2=29[/tex]
So this is a circle with centre (2, -3) and radius √29
Please help me out! I would also love an explanation on how to find the ratio and the answer
Answer:
A
Step-by-step explanation:
This will have slope in it, so bear with me.
We will use the equation [tex]\frac{y(2) - y(1)}{x(2) - x(1)}[/tex] (keep in mind (2) means second and (1) means first)
Lets fill it out.
[tex]\frac{-4-(-1)}{-4-3}[/tex]
It should be [tex]\frac{-3}{-7} or \frac{3}{7}[/tex]
So it is A
How long does it take for a $5000 investment to turn into a $7000 investment if it is compounded
semi-annually at 5.2%
Answer:
well over 3 years and almost over 4 months
Xavier and Carlos have a bet to see who can get more “friends” on a social media side after 1 month. Carlos has 10 more friends than Xavier when they start the competition. After much work, Carlos doubles his amount of friends and Xavier triples his. In the end they have a total of 160 friends.
a. Write a system of equation that matches the verbal description given below if
c = number of Carlos’ friends and x = number of Xavier’s friends.
The system of equations that describes the situation is given by these two following equations:
c = 10 + x.2c + 3x = 160.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are c and x.
Carlos has 10 more friends than Xavier when they start the competition, hence:
c = 10 + x.
Carlos doubles his amount of friends and Xavier triples his. In the end they have a total of 160 friends, hence:
2c + 3x = 160.
More can be learned about a system of equations at https://brainly.com/question/24342899
Find the value of x.
х
30°
24
Answer:
Step-by-step explanation:
x is the opposite side of angle 30°
34 is the adjacent side of 30°
So, find the value of x, we have use tan
[tex]\bf \boxed{ tan \ \theta = \dfrac{opposite \ side}{adjacent \ side}}}[/tex]
[tex]tan \ 30^\circ = \dfrac{x}{24} \\\\\\0.58 = \dfrac{x}{24}\\\\\\0.58*24=x[/tex]
x = 13.92
You roll a number cube ten times and it lands on a 5 two times. What is the theoretical probability that it lands on a 5 on your next roll?
Answer:
2/10 = 1/5
Step-by-step explanation:
It landed five 2 times and you rolled it 10 times
Which fractions are equivalent to 1 2 ? Select all that apply. A. 2 4 B. 3 6 C. 3 4 D. 4 8
Answer:
A , B And D
2/4 divide both numbers by to and you get 1/2
3/6 divide both numbers by 3 and you get 1/2
4/8 divide both numbers by 4 and you get 1/2
Use the number line below to determine which of the following answer choices has statements that are all true.
Answer:
1st option, and 4th option
Step-by-step explanation:
Is it select one, or select all that are correct?
Is anyone good at math and can help me solve my math problems
Answer:
Hi! I'm not too bad at math so I hope I can help you. Except, I can't seem to find your question so please comment your question(s) to me so that I can help you. Have a great day:)
Han and Priya want to know the mean height of the 30 students in their dance class. • The mean height for Han’s sample is 59 inches. • The mean height for Priya’s sample is 61 inches.
Answer:
60 inches
Step-by-step explanation:
Add 59+61 =120 which you divide by 2 for the mean of 60.
A stainless steel patio heater is a square pyramid. The length of one side of the base is 19.8 in. The slant height of the pyramid is 93.8 in. What is the height of the pyramid?
What scale factor was used to dilate STUV to S’T’U’V?
A. 0.20
B. 0.50
C. 0.25
D. 0.75
Answer: C. 0.25
Step-by-step explanation:
Large Shape: S (-4, 12) T (2, -4) U (6, -8) V (-12, -8)
Small Shape: S (-1, 3) T (0.5, -1) U (1.5, -2) V (-3, -2)
For the smaller shape the distance between V and U is 4.5
For the larger shape the distance between V and U is 18
So when you divide [tex]\frac{4.5}{18}[/tex] you should get 0.25
S: [tex]\frac{-4}{-1}=4[/tex] [tex]-4 *0.25=-1[/tex]
T: [tex]\frac{2}{0.5}=4[/tex] [tex]2*0.25=0.5[/tex]
U: [tex]\frac{6}{1.5}=4[/tex] [tex]6*0.25=1.5[/tex]
V: [tex]\frac{-12}{-3} =4[/tex] [tex]-12*0.25=-3[/tex]
I hope this helps
PLSSS HELP ME
(5x5)/[10x22]-4\52
Answer: 21/572
[tex]\frac{5.5}{10 . 22} - \frac{4}{52}[/tex]
The dots stand for multiplication
Choose the angle which is vertical to angle BFC in the following figure.
answer A angle CFD
answer B angle DFE
answer C angle AFC
answer D angle EFA
Use the equation A = bh to calculate the height of a parallelogram with an area of 36 square inches and a base of 9 inches
Answer:
4 inches
Step-by-step explanation:
A = b x h
A = 36
b = 9
36 = 9 x h
4 = h
height = 4 inches
what is an equation of the line that passes through the points (6,3) and (-6,1)
Answer: y = [tex]\frac{1}{6}[/tex]x + 2
Step-by-step explanation:
[1] First, we will graph the points given. See the attachment with [1] in the corner.
[2] Next, we will find the slope.
(2a) Using rise over run. See the attachment with [2] in the corner.
(2b) Use the slope equation:
[tex]\displaystyle \frac{1-3}{-6-6}= \frac{-2}{-12} =\frac{1}{6}[/tex]
[3] Find the y-intercept. Look to the graph. See the attachment with [3] in the corner.
This gives us a final answer of y = [tex]\frac{1}{6}[/tex]x + 2
Jacob had x apple pies. For each lemon pie sold, 10 more than twice the number of apple pies are sold. If jacob has sold 80 lemon pies, how many apple pies were sold.
A) 70
B) 25
C) 35
D) Not Here
Answer:
C) 35
Step-by-step explanation:
The answer is C because he sold 80 lemon pies and as the question states ten more than twice the number of apple pies were sold .
Subtract 80 by 10 and divide it by 2
80-10=70÷2 = 35
pls answer i give u anything
Answer:
the first one is 0.5 inches 1.27 centimeters
the second is 0.25 inches or 0.635 centimeters
Step-by-step explanation:
i don’t understand this question
Step-by-step explanation:
to figure this out you would have to take all the numbers and do the rise over run technique
evaluate: 3 /7 + ( −11 /4 ) + 16 /5 − ( −18 /7 )
Answer:
This is hard
Step-by-step explanation:
I'm so sorry I can't do it
Answer:
[tex]\frac{69}{20}[/tex]
Step-by-step explanation:
[tex]\frac{3}{7} -\frac{11}{4} +\frac{16}{5} +\frac{18}{7}[/tex]
= [tex]\frac{3}{7} +\frac{18}{7}-\frac{11}{4} +\frac{16}{5}[/tex]
= [tex]\frac{21}{7} -\frac{11}{4} +\frac{16}{5}[/tex] As both denominators have 7 you can add their numerators
=[tex]\frac{21}{7} -(-\frac{9}{20})[/tex] L.C.M
=[tex]\frac{21}{7} +\frac{9}{20}[/tex] L.C.M
=[tex]\frac{69}{20}[/tex]
Question 7 options:
5/7
7/5
2
9/7
Answer:
5/7.
Step-by-step explanation:
The rise = 5 and the corresponding run si 7.
Answer:
5/7
Step-by-step explanation:
so we start at the point (0,0). the slope is essentially
Rise/Run
so in this graph we see a point of (7,5)
the rise was 5 along the y axis and the run was 7 along the x axis.
so 5/7 is correct
3.
Laura multiplied 27,890 by a fraction with a numerator of 12. The product
was less than 27,890. Which of the following statements is true about the
denominator of Laura's fraction?
Answer:
I don't see any optional answers, but the denominator must be greater than 12.
Step-by-step explanation:
27,890*(12/X) < 27,890
Therefore (12/X) < 1
and X > 12
BRAINLIEST TO WHOEVER GETS IT RIGHT
Which of the following accurately shows the first step when solving the following system of equations by substitution?
f(x) = -4x^2 + 3x + 1
g(x) = -6x +5
a -4x^2+ 3x + 1 = -6x +5
b 4x^2 + 3x +1 - 6x + 5 = 0
c g(x)= -6(-4x^2 + 3x + 1) + 5
df() = -4(-6x + 5)^2 +3(-6x + 5) +1
Answer:
c and d
Step-by-step explanation:
because
- In f(x),evey time you find X you write(-6x+5) instead
4x²-----------4(-6x+5)²
3x+1------------3(-6x+5) +1
-In g(x),evey time you find X you write(-4x² +3x+1) instead
600 people visited the mall today and 8% of these people made a purchase. How many people made a purchase?
Answer:
48 made a purchase
Step-by-step explanation:
8% of 600
= [tex]\frac{8}{100}[/tex] × 600 ( cancel 100 and 600 by 100 )
= 8 × 6
= 48
The results of a standardized test are normally distributed. The mean test score is 312. Of the scores, 16% are under 307. What is the standard deviation?
A: 10
B:5
Answer:
the answer is B five
Step-by-step explanation:
three hundred and seven minus three hundred and twelve
Sarah bought 1250 grams of sugar. how many kilograms of sugar did she buy? A. 1.250 B. 12.50 C. 125.0 D 12500
Answer:
1.25 kg
Explanation:
1 kilograms is equal to 1000 grams============
1 g = (1/1000) kg======
So, 1250 gram = (1250/1000) kg
1250 gram = 1.25 kgWe know
1kg=1000gNow
Mass in kg:-
1250/10001.250kgOption A
Work out
21
% of
£
944.13
Give your answer rounded to 2 DP. I need right awnsers you can use calculators
Answer: £198.27
Step-by-step explanation:
944.13x0.21=198.2673Rounded to 2 decimal places that is 198.27What is the domain of the function graphed below?
Answer:
The second option
Step-by-step explanation:
Hello!
The domain of a graph is the interval in which the graph is on the x values.
This graph has all the x values that are greater than or equal to -3, as the graph is to the right of it.
The answer would be the second option: [tex]D : x/x \geq -3[/tex]
The range is the y-values of the graph. The y value of this graph is above 0, so it would be y ≥ 0
Does anybody know this? I really need help.
Answer:
22 is th area
Step-by-step explanation:
