Step-by-step explanation:
A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.
help whhhahahahaha Helpppppppp
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]
How to do this? Please help
Step-by-step explanation:
This equations are quadratic equations, which is on standard form,
[tex] {ax}^{2} + bx + c[/tex]
where a is the leading coefficient, b is the second coefficient, and c is the constant.
Both a and b are in quadratic equation so we need to find the constant separately.
Both sides are equal to zero so we can just subtract the terms not containing a or b in them to the opposite side.
[tex] {x}^{2} - 4 x + a = 0[/tex]
[tex] {x}^{2} + a = 4x[/tex]
[tex]a = - {x}^{2} + 4x[/tex]
For b,
[tex]2 {x}^{2} - 6x + b + 7 = 0[/tex]
[tex] - 6x + b + 7 = - 2 {x}^{2} [/tex]
[tex]b + 7 = - 2 {x}^{2} + 6x[/tex]
[tex]b = - 2 {x}^{2} + 6x - 7[/tex]
A line is parallel to the x-axis and passes through the point (-5,4)
What is the equation of that line, the slope of that line, and what would be the slope of a line perpendicular to that given line?
9514 1404 393
Answer:
y = 4slope: 0slope of perpendicular: undefinedStep-by-step explanation:
The x-axis is a horizontal line. As such, it has a slope of zero. The equation of a horizontal line is ...
y = constant
__
For the line through (-5, 4), the constant must match the y-coordinate: 4. The equation is ...
y = 4
As we said above, the slope of that horizontal line is zero.
The perpendicular line will be a vertical line of the form x=constant. The slope of a vertical line is undefined.
Imran can row at 3 m/s against the current and at 6 m/s with the current. Find the speed of the current.
komhnyrtgfdedavfbfsfb
Does #6 look right? Im struggling on this
Answer and Step-by-step explanation:
-2 is the correct answer.
But, you should set up your number line like this:
-6 4
<-|-----------|----------|->
-2
4 - 6 = -2
#teamtrees #PAW (Plant And Water)
I hope this helps!
What are the coordinates of A' after a 180 degree rotation about (-5, 3)?
Answer: (5,3)
Step-by-step explanation:
A 180 degree rotation will take you to sector b which is (+,+), so I knew it was going to be positive.
measure at least pairs of corresponding angles in XJYN and ZSCH using a protractor. Record your measurements to the nearest 5. what do you notice?
Answer:
any file to have a reference?
can you figure out what 2x° equals and (90-x)°
I HOPE IT WILL HELP YOU.
Have a great day ahead.
The function f(x)=x^2+2 is not one to one. Determine a restricted domain that makes it one to one and find the inverse function
Answer:
Hope it helped
Step-by-step explanation:
The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
What is inverse of a function?An inverse function or an anti function is defined as a function, which can reverse into another function.
Now the given quadtratic function is,
f(x) = x² + 2
Now vertex of the given quadratic function is (0,2)
Thus the range of the function is [2,∞)
If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.
Now the inverse function is given as,
y = x² + 2
Upon interchanging x and y, we get:
x = y² + 2
⇒ y² = x - 2
or, y = ±[tex]\sqrt{x-2}[/tex]
Hence, the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
To learn more about function :
https://brainly.com/question/17210215
#SPJ2
8. 7.6 + (-7.1) = what does it equal plz help
Answer:
vsddddddddddddddddddddddddddddddddddddddddddddddddddddddbgtresxvzjdhdf;lsjb
Step-by-step explanation:
any advice on geometry
Answer:
Just study and pay attention in class and take good notes. I would say that you should pay more attention when they teach you the trigonometry unit.
Solve the fraction problems and reduce the answer to its lowest form:-
1)7/10×2/21
2)9/16×10/21
3)11/12×26/55
4)2/6×18/12×2/3
5)5/6×9/10
Answer:
1/1515/5613/301/33/4Step-by-step explanation:
1) 7/10 × 2/21
1/15
2) 9/16 × 10/21
90/336
15/56
3) 11/12 × 26/55
13/30
4) 2/6 × 18/12 × 2/3
72/216
1/3
5) ⅚ × 9/10
45/60
3/4
Is the image an example of a ray?
B
A
O Yes; AB has an endpoint and continues in one direction forever.
O Yes; AB is one-dimensional.
O No; AB continues forever in both directions.
O No; AB has two endpoints.
Answer:
O No; AB has two endpoints.Step-by-step explanation:
Ray - a continuous line therefore, do not have two endpoints.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
AB is not a ray. It has two endpoints.
What is ray?"It is a part of a line that has a fixed starting point but no end point."
For given example,
We have been given a part of a line AB.
The starting point is A and the end point is B.
We know, one of the end of the ray is denoted by arrow.
Since both the ends of given figure are fixed, it is not ray.
AB is called as line segment.
Therefore, AB is not a ray. It has two endpoints.
Learn more about ray here:
https://brainly.com/question/17491571
#SPJ2
Seven less than four times a number is nine. FIND the number
Answer:
4
Step-by-step explanation:
4 times 4 is 16. 7 less than 16 is 9.
Answer:
4
Step-by-step explanation:
You can use a simple formula for finding the answer to problems like these. You read it out and put your information in order and use a variable (such as x) in place of the number.
4 * x - 7 = 9
Then solve by getting your variable alone on one side.
Add 7 to both sides: 4 * x = 16
Divide both sides by 4: x = 4
What is -(11+2b) in simplified form?
Answer and Step-by-step explanation:
To simplify, distribute the negative number.
-(11 + 2b)
-11 - 2b is the answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
Answer:
-11 -2b
Step-by-step explanation:
-(11+2b)
Distribute the minus sign
-11 -2b
(7-4) + 17 / -14 + 2 x 5
Answer:
165/14
Step-by-step explanation:
(7-4) + 17 / -14 + 2 x 5
3 + 17/-14 + 2 x 5
3 - 17/14 + 2 x 5
3 - 17/14 + 10
165/14
Domain and range from graph
What is the domain of g?
Answer: A
Step-by-step explanation:
Answer:
-6 < x < 6
Step-by-step explanation:
Domain refers to the list of all x-values included in the function. In this instance, the list of x-values in this function is between -6 and 6.
Evaluate (2-5i)(p+q) when p=2 and q=5i
Answer:
(2-5i)(p+q)
p=2
q=5i
(2-5i)(2+5i)
a²-b²=(a+b)(a-b)
2²-(5i)²
4-(5i)²
i²=-1
4+25=29
answer 29
Find the slope and y intercept
(Please show work)
Answer:
slope = - 6, y- intercept = 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
0 = 2x - [tex]\frac{5}{3}[/tex] + [tex]\frac{1}{3}[/tex] y ( multiply through by 3 to clear the fractions )
0 = 6x - 5 + y ( subtract 6x - 5 from both sides )
- 6x + 5 = y , that is
y = - 6x + 5 ← in slope- intercept form
with slope m = - 6 and y- intercept c = 5
Someone help me with this please
MACARONI AND AN POT THATS AN WAAAAAPP
(50 POINTS!!!!!) I NEED THE CORRECT ANSWER... FAST!
Answer:
don't know sorry forgive me
Solve for x: -2 - 4 > 8
(9th grade Algebra 1)
Answer:
A
Step-by-step explanation:
-2x-4>8
-2x>12
-x>6
x<-6
Answer:
[tex]x < - 6[/tex] (first option)
Step-by-step explanation:
[tex] - 2x - 4 > 8[/tex]
[tex] - 2x > 8 + 4[/tex]
[tex] - 2x > 12[/tex]
[tex] = x < - 6[/tex]
Rational number between 3.623623 and 0.484848
Answer:
1
Step-by-step explanation:
A rational number between 3.623623 and 0.484848 is 1.
Answer:
Remember: rational numbers are numbers that can be written as fractions and decimals that either terminate or repeat. Here are some rational numbers:
0.5, 3/4, 1, 1.5...3, 3.5
Step-by-step explanation:
BRAINLIEST, PLEASE!
600 miles/day into miles per hour
Cho 2 tập hợp A = {1;3;5;8}, B = {3;5;7;9}. Tìm A∩B và A∪B.
Answer:
gien
Step-by-step explanation:
solve using substitution
y = 3x - 4
3x + y = -4
y= 3x –4
3x + y = –4
3x + (3x –4) = –4
3x+3x – 4 = – 4
6x = – 4 +4
6x=0 —> x= 0/6 —> x=0
x = 0y = 3x – 4 —> y = 3(0) – 4 = – 4
y = – 4So; (x , y) —> (0 , – 4 )I hope I helped you^_^
Answer:
(0,-4)
Step-by-step explanation:
3x + y = -4
3x + (3x - 4) = -4
3x + 3x - 4 = -4
6x = 0
x = 0
y = 3(0) - 4
y = -4
I’ve been stuck on this for days I just need a simple answer
Answer:
408
Step-by-step explanation:
Surface area formula is A=2(wl+hl+hw)
Substituting these values into the formula you would get
2·(3·8+4·8+4·3)=136
136 accounts for one rectangular prism.
Since you have 3 multiply 136 by 3 which would leave you with 408
Answer:
280 in²
Step-by-step explanation:
The opposite faces are congruent , then surface area (SA ) is
SA = top/ base + front/ back + 2 sides
note for the front/ back and 2 sides we have 3 + 3 + 3 = 9 in
SA = 2(8 × 4) + 2(8 × 9) + 2(4 × 9)
= 2 × 32 + 2 × 72 + 2 × 36
= 64 + 144 + 72
= 280 in²
Hayden had 2 1/2 gallons of water in his watering can. The seed packet said to use 1/4 of a gallon for peppers and 5/8 of a gallon for tomatoes. Hayden then used some of the water for lettuce. If Hayden had 3/4 gallons of water left over, about how much water did he use for lettuce?
Answer:
7/8
Step-by-step explanation:
1/4 + 5/8 = 2/8 + 5/8 = 7/8
= amount used for pepper and tomatoes
2 1/2 - 3/4 = 5/2-3/4 = 10/4 -3/4 = 7/4
= total amount used
so
7/4 - 7/8 = 14/8 - 7/8 = 7/8 for lettuce
PL help meeeeeee!!! Im stuck
ALGEBRA II! i need help with #2 with the same steps i took on #1
