Answer:
[tex] \frac{1}{3} (2x - y) = z \\ \frac{2}{3} x - \frac{y}{3} = z \\ \frac{2}{3} x = z + \frac{y}{3} \\ \frac{2}{3} x = \frac{3z + y}{3} \\ x = \frac{3z + y}{3} \div \frac{2}{3} \\ x = \frac{3z + y}{3} \times \frac{3}{2} = \frac{3(3z + y)}{6} \\ \\ x = \frac{3z + y}{2} \\ \\ x = \frac{3z}{2} + \frac{y}{2} [/tex]
I hope I helped you^_^
A sum of Rs 105 is divided into two parts.if two times the greater part is 15 less than three times the smaller part, find the parts of the sum.
Answer:
Step-by-step explanation:
Let the greater part = x
Smaller part = 105 - x
2*(greater part) = (3*smaller part) - 15
2*x = 3*(105 -x) - 15
Use distributive property
2x = 3*105 - 3*x - 15
2x = 315 - 3x - 15
2x = 300 - 3x
Add 3x to both sides
2x +3x = 300
5x = 300
Divide both sides by 5
x = 300/5
x =60
Smaller part = 105 - 60 = 45
Greater part = Rs. 60
Smaller part = Rs. 45
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:
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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
can you figure out what 2x° equals and (90-x)°
I HOPE IT WILL HELP YOU.
Have a great day ahead.
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.
PL help meeeeeee!!! Im stuck
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
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.
4 1/6 = 3 1/3c
WAHT?!? HOW IN THE WORLD DO YOU EVEN DO THIS?!?
Answer:
1 1/4 =c
Step-by-step explanation:
4 1/6 = 3 1/3c
Change the mixed numbers to improper numbers
4 1/6 = ( 6*4+1)/6 =25/6
3 1/3 = ( 3*3+1)/3 = 10/3
25/6 = 10/3c
Multiply each side by 3/10
25/6 * 3/10 = 10/3c * 3/10
3/6 * 25/10 = c
1/2 * 5/2 =c
5/4 =c
Change back to a mixed number
1 1/4 =c
What is the transformation shown in the graph?
6
c
A
360° rotation
180° rotation
90° rotation
reflection
Answer:
Reflection is shown in the graph.
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] .
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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
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]
what is the value of x when the distance between the points (-2,-3) (-3,x) is equal to 5
Answer:
(-3,-4)
Step-by-step explanation:
Half the difference of a number n and 20 is 30. What is the number?
Answer:
80Step-by-step explanation:
Half the difference of a number n and 20 ⇒ (n - 20)/2... is 30 ⇒ = 30Solve the equation for n:
(n - 20)/2 = 30n - 20 = 30*2n - 20 = 60n = 60 + 20n = 80The number is 80
Answer:
Number is 40
Step-by-step explanation:
Let the number be n
(n - 20)/2 = 30
(n - 20) = 2 × 30
n = (2 × 30) + 20
n = 60 + 20
n = 80
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
How much money does an employee working
for a salary of $52,000 per year get paid
monthly?
A. $52,000 per month
B. $1,000 per month
C. $2,000 per month
D. $4,333 per month
Answer:
433
Step-by-step explanation:
433. . . . . . . ............,.. srry it made me write this much to answer
Answer:
The correct answer would be D!Step-by-step explanation:
Employee's salary: $52,000
Months in a year: 12
52000 / 12 = 4,333.333(r)
Closest answer: D
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?
Denver is 5,280 ft above sea level. Stone Mountain is 1,686 ft above sea level. How much higher is
Denver than Stone Mountain? Explain how you got your answer.
Answer:
3,594
Step-by-step explanation:
It is asking *than* which means subtraction. so simply subtract and you get the answer
not hard!
8. 7.6 + (-7.1) = what does it equal plz help
Answer:
vsddddddddddddddddddddddddddddddddddddddddddddddddddddddbgtresxvzjdhdf;lsjb
Step-by-step explanation:
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
find the value p with working
Answer:
64/672/882(986)*866772
(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
Need help on this hm THE MIDDLE ONE
Answer:
{0, 1, -1}
Step-by-step explanation:
2x - 6 = 3x + 1 - x - 7
2x - 6 = 2x - 6
0 gives you -6 = -6
1 gives you -4 = -4
-1 gives you -8 = -8
Point Q is the image of Q (0,6) under the translation (x,y) (x+7,y-5)
What are the coordinates of Q?
Answer
7, 1
Step-by-step explanation:
do math
b) Convert 101, into denary number
If 101 is given in base b, then in base 10 you have
[tex]101_b = 1\times b^2 + 0\times b^1 + 1\times b^0 = b^2 + 1[/tex]
For instance, if b = 2, then
101₂ = 2² + 1 = 5₁₀
If b = 3, then
101₃ = 3² + 1 = 9₁₀
If b = 4, then
101₄ = 4² + 1 = 17₁₀
The answer depends entirely on the base of the given number.
I need help solving this systems of equations problemn
Answer:
thequantity in column b is greater
Step-by-step explanation:
7a+b=33......(1)
3a-b=7.........(2)
(1)+(2)
7a+b+3a-b=33+7
10a+b-b=40
10a=40
a=4
in equation (1)
7*4+b=33
28+b=33
b=33-28
b=5
b>a
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]
600 miles/day into miles per hour
Write an algebraic expression for each verbal expression. 1. the sum of k and 8
2. 17 less than a number x times 9
6. four times the difference of a cubed and 8
PLZ HELP ASAP
Answer:
k + 8 = y
9x - 17
4(x²-8)
