Answers
Answer:
320/420 = 4/3
Step-by-step explanation:
4/7= x /560
Cross multiply
7x = 2240
Divide by 7:
x=320
The school has 320 boys and 240 girls
I hope this helps u:)
Answer:
Problem(1): [tex]21[/tex]
Problem(2): Side length = [tex]\frac{1}{4}[/tex] Area = [tex]\frac{1}{16}[/tex]
Problem(3): Boys = [tex]320[/tex] Girls = [tex]240[/tex]
Step-by-step explanation:
(Notes steps are cut from this answer so that it isn't too long)
1. Problem (1)
One is given the following information:
[tex]x+\frac{1}{x}=5[/tex][tex](x-\frac{1}{x})^2[/tex]The most logical first step is to solve for the value of (x). One can solve for the numerical value of (x) with the first equation.
[tex]x+\frac{1}{x}=5[/tex]
Multiply the entire equation by (x),
[tex]x^2+1=5x[/tex]
Inverse operations put the equation in the general format of a quadratic equation. The general format of a quadratic equation is as follows,
[tex]ax^2+bx+c=0[/tex]
Put the given equation in this format,
[tex]x^2-5x+1=0[/tex]
Now use the quadratic formula to solve for the value of (x). The quadratic formula uses the coefficients of the terms in a quadratic equation to find the roots of the equation. The quadratic formula is as follows,
[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]
Use the coefficients of the terms in the given quadratic equation in the formal, then simplify to solve for solutions of the given equation,
[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]
Simplify,
[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]
[tex]\frac{5(+-)\sqrt{21}}{2}[/tex]
Now substitute these values into the equation and simplify, even though there are two values of (x), there will only be one solution,
[tex]((\frac{5+\sqrt{21}}{2}-\frac{1}{\frac{5+\sqrt{21}}{2}})^2[/tex] [tex]((\frac{5-\sqrt{21}}{2}-\frac{1}{\frac{5-\sqrt{21}}{2}})^2[/tex]
[tex](\frac{5+\sqrt{21}}{2}-\frac{2}{5+\sqrt{21}})^2[/tex] [tex](\frac{5-\sqrt{21}}{2}-\frac{2}{5-\sqrt{21}})^2[/tex]
Convert to a common denominator,
[tex](\frac{5+\sqrt{21}}{2}*\frac{5+\sqrt{21}}{5+\sqrt{21}}-\frac{2}{5+\sqrt{21}}*\frac{2}{2})^2[/tex] [tex](\frac{5-\sqrt{21}}{2}*\frac{5-\sqrt{21}}{5-\sqrt{21}}-\frac{2}{5-\sqrt{21}}*\frac{2}{2})^2[/tex]
[tex](\frac{(5+\sqrt{21})^2-4}{2(5+\sqrt{21})})^2[/tex] [tex](\frac{(5-\sqrt{21})^2-4}{2(5-\sqrt{21})})^2[/tex]
Simplify,
[tex](\frac{25+10\sqrt{21}+21-4}{10+2\sqrt{21}})^2[/tex] [tex](\frac{25-10\sqrt{21}+21-4}{10-2\sqrt{21}})^2[/tex]
[tex](\frac{42+10\sqrt{21}}{10+2\sqrt{21}})^2[/tex] [tex](\frac{42-10\sqrt{21}}{10-2\sqrt{21}})^2[/tex]
[tex]\frac{1764+840\sqrt{21}+2100}{100+40\sqrt{21}+84}[/tex] [tex]\frac{1764-840\sqrt{21}+2100}{100-40\sqrt{21}+84}[/tex]
[tex]\frac{3864+840\sqrt{21}}{184+40\sqrt{21}}[/tex] [tex]\frac{3864-840\sqrt{21}}{184-40\sqrt{21}}[/tex]
[tex]21[/tex]
2. Problem (2)
All four sides of a square are congruent (have the same measure), thus dividing the perimeter of a square by (4) will yield the side length of the square,
[tex]Perimeter\ of\ the\ square: 4\\Side\ length: \frac{1}{4}[/tex]
The area is the two-dimensional space that a figure takes up, in the case of a square, the area is the side length times itself:
[tex]A=(\frac{1}{4})^2=\frac{1}{16}[/tex]
3. Problem (3)
Let (x) represent the amount by which the ratio of boys to girls was scaled down. Assuming that these are the only two genders in the school, one can state that the sum ratio coefficients times the scaling value for both boys and girls, will equal the total number of people in the school. Thus, one can form the following equation and solve it with inverse operations and simplification,
[tex]boys + girl = total\ students\\4x + 3x = 560\\7x = 560\\x = 80[/tex]
Now substitute this into the expression for the two genders in this scenario, respectively, to solve for the actual number of students of that gender,
Boys, Girls,
[tex]4(x)[/tex] [tex]3(x)[/tex]
[tex]4(80)[/tex] [tex]3(80)[/tex]
[tex]320[/tex] [tex]240[/tex]
Related Questions
Find the equation of the line perpendicular to the 13x-3y=9 and passing through (-5,0)
Answers
9514 1404 393
Answer:
x +4y = -5
Step-by-step explanation:
The equation of the perpendicular line can be found by swapping the x- and y-coefficients and negating one of them. The new constant can be found by substituting the point values into the equation.
3x +12y = 3(-5) +12(0)
3x +12y = -15
We notice that all of the values include a factor of 3. We can divide that out to put the equation in standard form:
x + 4y = -5
How to solve this
6x times 1/6
Answers
mr. Johnson the owner of the candy store keeps 37 jars behind the candy counter each jar contains 286 pieces of candy how many pieces of candy are behind the counter all together
Answers
Answer:
10,582 pieces of candy.
Step-by-step explanation:
1 jar contains 286 pieces
Therefore, 37 jars contain:
37 × 286
= 10,582 pieces of candy.
Answer:
10,582 pieces of candy behind the counter
Step-by-step explanation:
multiply 37 by 286 and you get 10,582
if 3/4 part of the distance between two places is 45 km find the distance between the places.
Answers
Let distances be x
ATQ
[tex]\\ \rm\hookrightarrow \dfrac{3}{4}x=45[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{3x}{4}=45[/tex]
[tex]\\ \rm\hookrightarrow 3x=45(4)[/tex]
[tex]\\ \rm\hookrightarrow 3x=180[/tex]
[tex]\\ \rm\hookrightarrow x=\dfrac{180}{3}[/tex]
[tex]\\ \rm\hookrightarrow x=60[/tex]
A number of tourist were interviewed on their
choice of
means
of travell Two-thirds said
they had travel by road, 13 by air. 4
the by
both
air and road. If
20 tourist had not travel
road
Represent the information on
on a Vena
diagram:
by either
air
or road. Represent the information on a venn diagram
Answers
Answer:
A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, 1330 by air and 415 by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?
The price of a printer is $349.00, plus 6% sales tax. What is the sales tax on this printer in dollars and cents?
Answers
The sales tax on this printer is $20.94
What is sales tax?A sales tax is a consumption tax imposed by the government on the sale of goods and services.
Given that, the price of a printer is $349.00 having a 6% sales tax.
Sales tax = 6% of $349.00
$349.00 x 0.06 = $20.94
Hence, the sales tax on this printer is $20.94
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calculate the amount of ₹30000 at the end of 2 years 4 months , compounded annually at 10% per annum
Answers
Fv = 30,000*(1+10%/12)^28
Fv= 37,847.46
find the decimal equivalent of the fraction 1/6
Answers
Answer:
0.16666666666
Step-by-step explanation:
I don't understand what the question is asking.
Answers
Answer:
You are supposed to find how much 2 packages of chicken costs when each package is 12.36, 1/2 lb of broccoli when one pound costs 1.98, and 1 gallon of milk with 3.49 per gallon. After that, you need to find how much Susan paid with when she recieved 80 cents in change.
(2*12.36)+(1.98*0.5)+3.49+0.80=x
find out what x is to get the answer.
What number is 1/10 of 8,000,000
Answers
Answer:
8,00,000
Step-by-step explanation:
I think this is
The product of the numbers 1/10 and 8,000,000 will be 800,000.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The numbers are given below.
1/10 and 8,000,000
The product of the numbers 1/10 and 8,000,000 will be
⇒ (1/10) x 8,000,000
⇒ 800,000
The product of the numbers 1/10 and 8,000,000 will be 800,000.
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WOULD A KIND S0UL PLEASE HELP ME OUT???!!!!!!!!!!!!
triangle RST is reflected across the line y = x to form triangle R’S’T’. Find the coordinates of the points R’, S’ and T’.
please show your work so I can see if your answer makes sense!!!!
Answers
Answer:
(-2,1) (-8,2) (-4,7)
Step-by-step explanation:
just look at the points r's't
Which of the following describes the correct process for solving the equation 2x − 6 = 22 and arrives at the correct solution?
Answers
Answer:
Subtract 6 from both sides and then divide by 2. The solution is x = 8.
Thank You
Answer:
x=8
Step-by-step explanation:
Estimating Irrational Numbers
Answers
2 is between 1 and 4.
sqrt(1) = 1 and sqrt(4) = 2.
Since 2 is between 1 and 4, sqrt(2) is between sqrt(1) and sqrt(4).
This means sqrt(2) is between 1 and 2.
4 |m - n|
-if m = -7 and n= 2
Answers
Answer:
9
Step-by-step explanation:
I m - n I = I -7 - 2 I
{ Both are negative integers. So, add and result will have the negative sign}
= I -9 I
= 9
Answer:
-36
Step-by-step explanation:
We have the equation 4 lm - nl , along with the values, m is equal to -7 and n is equal to 2.
To solve, we need to only substitute the values of each variable into the original equation :
4 |-7 - 2|
First solve the equation within the absolute value, any value that comes out of those brackets become positive :
|-7 - 2|
|-9|
4|-9|
4(-9)
Now multiply to get our answer:
4(-9)
-36
Find the degree of the monomial 3x4y3
Answers
The degree of the monomial 3x4y3 is 7
plz help me find the slope
Answers
Answer:
4/5
Step-by-step explanation:
Find 2 defined points like (-2,0)(3,4) in other to reach the point (3,4) from (-2,0) it moves 5 times front and 4 times up
Up is Y value
Front is X value
To solve it is adding the value that you get from moving it in this case
5 front X equals to 5
4 up Y equals to 4
Then is 4/5
because the formula is Y/X
a) 7 + (15 – 6) simplify
Answers
Answer:
7+9
16
Step-by-step explanation:
first apply bodmas rule
Answer:
16
Step-by-step explanation:
Using BODMAS
Firstly we will simplify the brackets one
So (15 - 6)=9
Now 7+9=16
You have 2 five-dollar bills, 4 one-dollar bills, 2 quarters, I nickel, and 2 pennies. a. What is the value of the bills? b. What is the value of the coins? c. How much money do you have?
Answers
Answer:
a: [tex]\$ 14[/tex] or [tex]14[/tex] dollars
b: [tex]\$0.57[/tex] or [tex]57[/tex] cents
c: [tex]\$14.57[/tex] or [tex]14[/tex] dollars and [tex]57[/tex] cents
Step-by-step explanation:
a: We have [tex]2[/tex] [tex]\$5[/tex] bills, which have a total value of [tex]2*5= \$10[/tex]. We also have [tex]4[/tex] [tex]\$1[/tex] bills, which have a total value of [tex]4*1= \$4[/tex]. Adding these up gives us [tex]10+4= \bf \$14[/tex] or [tex]\bf 14[/tex] dollars for the total value of the bills.
b: Remember that a quarter is worth [tex]\$0.25[/tex], a nickel is worth [tex]\$0.05[/tex], and a penny is worth [tex]\$0.01[/tex]. Therefore, [tex]2[/tex] quarters are worth [tex]2*0.25=\$0.50[/tex], [tex]1[/tex] nickel is worth [tex]1*0.05=\$0.05[/tex], and [tex]2[/tex] pennies are worth [tex]2*0.01=\$0.02[/tex]. Adding these up gives us [tex]0.50+0.05+0.02=\bf \$0.57[/tex] or [tex]\bf 57[/tex] cents for the total value of the coins.
c: We know that the total value of the bills is [tex]\$ 14[/tex] (or [tex]14[/tex] dollars) from Part A and the total value of the coins is [tex]\$0.57[/tex] (or [tex]57[/tex] cents) from Part B. Therefore, we have [tex]14+0.57=\bf \$ 14.57[/tex] in total or [tex]\bf 14[/tex] dollars and [tex]\bf 57[/tex] cents.
Hope this helps!
a) A shopkeeper sold a mobile set for Rs 9,600 and made a loss of 5%. For what price should he sell it to gain 10%?
Answers
Step-by-step explanation:
Click this photo.Hope it is helpful...I didn’t know how to put the question so the image below is the question
Answers
Answer:
b) (I think)
Step-by-step explanation:
What exactly is the question?
Hope this helps!
Have a nice day! :-)
3(4+2)/9=
help me please
Answers
Answer:
2
Step-by-step explanation:
3(4+2)/9= 3(6)/9=18/9 = 2
Answer:
2
Step-by-step explanation:
3(4+2)/9=(12+6)/9
=18/9
=2
How many solutions exist for -2|3x − 1| = 0?
A. 0
B. 1
C. 2
D. 3
Answers
Answer:
B. 1
Step-by-step explanation:
-2|3x − 1| = 0
Divide by -2
|3x − 1| = 0
There is only one solution since 3x-1 must equal 0
3x = 1
x = 1/3
Answer:
The correct choice is option B. 1
See attached image for my step-by-step explanation, the final answer is in red.
What is the answer ?
Answers
Answer:
27
Step-by-step explanation:
36 divided by 4 equals 9 which is what the sea turtle can swim in 1 second. Multiply 9 by 3 and you'll get 27.
Answer:
Step-by-step explanation:
classify the following numbers as rational or irrational root 27
Answers
Answer:
Irrational
Step-by-step explanation:
[tex]\sqrt{27}=\sqrt{3*3*3} =3\sqrt{3}\\\\\sqrt{3} \ is \ a \ irrational \ number. \ So, \ 3\sqrt{3} \ is \ a \ irrational \ number.[/tex]
Answer:
Root 27 is Irrational.
As it doesnt comes in fraction or decimal.
It is non terminating non repitiong.
Its value will be 3.134635366363535
Um- Please help me, Thanks in advance
Answers
(1) Combining fractions is just a matter of writing each individual fraction in terms of a common denominator. The least common multiple of 6, 4, and 8 is
LCM(6, 4, 8) = 24
since 6×4 = 4×6 = 8×3 = 24. So
2/6 = (2×4)/(6×4) = 8/24
1 1/4 = 4/4 + 1/4 = 5/4 = (5×6)/(4×6) = 30/24
13 4/8 = 104/8 + 4/8 = 108/8 = (108×3)/(8×3) = 324/24
Then
2/6 + 1 1/4 + 13 4/8 = 8/24 + 30/24 + 324/24 = 362/24 = 181/12
(2) We have
LCM(12, 9) = 36
since 12×3 = 9×4 = 36. Then
121 2/12 = 1452/12 + 2/12 = 1454/12 = (1454×3)/(12×3) = 4362/36
781 6/9 = 7029/9 + 6/9 = 7035/9 = 2345/3
what is the domain of the function y=6x+2
a. all real numbers greater than or equal to zero
b.all whole numbers
c.all real numbers
d.all integers
please help i will give brainly
Answers
Answer:
c
Step-by-step explanation:
y = 6x + 2 is a straight line, that is a linear function
It is valid for all real numbers , then
domain is all real numbers
The domain of the function y=6x+2 is all real numbers.
What is a function?A relation is a function if it has only One y-value for each x-value.
The domain of a function is the set of all possible input values (also known as the independent variable).
In the function y = 6x + 2, x can be any real number.
There are no restrictions or conditions on the values that x can take.
The domain of this function is all real numbers.
Hence, the domain of the function y=6x+2 is all real numbers.
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You are looking at your power bill for the month, you pay 12 cents per kilowatt-hour. Your power bill came out to $74.80 how many KWH of energy were used in your house this month?
Answers
Answer:
623.33 KWH
Divide 74.80 by .12
list of all numbers less than 30 are divisible by 8?
Answers
16
24
Hope this helps
Answer:
Step-by-step explanation:
The numbers less than 30 that are diviisible by 8 are,
24, 16, 8
i think this is all because these are the only numbers 8 can divide into to get a whole number.
Which is further away from zero on the number line -8 or 8
Answers
Answer:
Both are equally distant from 0 on a number line.
Step-by-step explanation:
Both are equally distant from 0 on a number line, they are just in opposite directions.
Answer:
Both are same distance
Step-by-step explanation:
-8 is in the opposite direction of the positive 8
Can someone please help me I don’t know how to do this (Due today)
Answers
Answer:
The answers are in the photo taken
Step-by-step explanation:
Pls mark as brainlest