This is tricky because it has a lot of variables, but we just have to treat this problem normally.
[tex]yp+yn=x[/tex]
separate y from p + n (feel free to check that you can do this by multiplying y out again and seeing that we have the same thing as before)
[tex]y(p+n)=x[/tex]
divide p + n on both sides
[tex]y = \frac{x}{p+n}[/tex]
Answer:
[tex]y = \frac{x}{p+n}[/tex]
To solve the equation yp + yn = x for y, factor out y to get y(p + n) = x, then divide both sides by (p + n) to isolate y, resulting in y = x / (p + n).
To solve the equation yp + yn = x for y, you need to factor y out of the left side of the equation.
This gives you y(p + n) = x.
To isolate y, you then divide both sides of the equation by (p + n), assuming p + n
eq 0, to get y = x / (p + n).
evaluate the problem below -4 1/6 + 5 2/3
Answer:
3/2 (or 1 1/2)
Step-by-step explanation:
-4 1/6 + 5 2/3 (express as improper fractions)
= -25/6 + 17/3 (convert fractions common denominator i.e 6)
= -25/6 + (17/3)(2/2)
= -25/6 + (17 x 2)/6
= -25/6 + 34/6
= 9/6
= 3/2
=1 1/2
5(b+6)=18
solve this, please...!
Answer:
b = - [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Given
5(b + 6) = 18 ← distribute left side
5b + 30 = 18 ( subtract 30 from both sides )
5b = - 12 ( divide both sides by 5 )
b = - [tex]\frac{12}{5}[/tex] = - 2.4
Good evening
_______
Answer:
b= -12/5
_______________
Step-by-step explanation:
5(b+6)=18
5b+30=18
5b=18-30
5b=-12
b= -12/5.
:)
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
<-1, -1>, square root of two
<1, 1>, square root of two
<1, 1>, 2
<-1, -1>, 2
Answer:
<1 ,1>..., square root of two
Step-by-step explanation:
Component of vector PQ...,
; Q - P...where you subtract the x coordinate of Q by the x coordinate of P and the same for the y coordinate
; <(6-5),(9-8)>
; < 1,1 >
And the magnitude of PQ...,
;square root of( 1^2 + 1^2 )
;square root of 2
Final answer:
The component form of vector PQ is <1, 1>, and the magnitude is the square root of 2, thus the correct answer is <1, 1>, square root of 2.
Explanation:
To find the component form and magnitude of vector PQ, we calculate the difference in the x-coordinates and the y-coordinates of points P and Q. The component form of a vector is obtained by subtracting the coordinates of the initial point from the coordinates of the terminal point. In this case, the initial point is P(5, 8) and the terminal point is Q(6, 9).
The component form of vector PQ is therefore:
Vector PQ = (Qx - Px, Qy - Py)
Vector PQ = (6 - 5, 9 - 8)
Vector PQ = <1, 1>
Next, to find the magnitude of vector PQ, we use the Pythagorean theorem, which is the square root of the sum of the squares of the components:
Magnitude of PQ = √(1^2 + 1^2)
Magnitude of PQ = √(2)
Magnitude of PQ = √2
Therefore, the correct answer is <1, 1>, √2.
Which graph of ordered pairs shows a proportional relationship?
Answer:
c
Step-by-step explanation:
Graph C of ordered pairs shows a proportional relationship.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other.
What is a proportional relationship on a graph?A proportional relationship is one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y=3x is proportional), but usually, a linear equation has a proportional component plus some constant number (for example y=3x +4).
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Which equation is equivalent to Vx+11 = 15?
x + 11 = 225
x + 121 = 225
x = 15+11
x = 15-11
The equation which is equivalent to √x + 11 = 15 is: C. √x = 15 - 11.
Given the following equation:
√x + 11 = 15.To evaluate the given mathematical equation:
How to evaluate an equation.In this exercise, you're required to evaluate the given mathematical equation. Thus, we would make x the subject of formula in the equation and then simplify as follows:
√x = 15 - 11 (equivalent)
√x = 4
Taking the square of both sides, we have:
x = 4²
x = 16.
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If h(x) = 6 - X, what is the value of (10)
Answer:
-4 = h(x)
Step-by-step explanation:
[tex]6 - 10 = -4[/tex]
I am joyous to assist you anytime.
S = 2lw + 2wh + 2lh; solve for l
Answer:
l = (S - 2wh)/(2w + 2h)
Step-by-step explanation:
S = 2lw + 2wh + 2hl
S - 2wh = 2lw + 2hl
S - 2wh = l (2w + 2h)
(S - 2wh)/(2w + 2h) = l
The equation S = 2lw + 2wh + 2lh the value of l is given by l = S / (2w + 2h + 2wh)
To solve for l in the equation S = 2lw + 2wh + 2lh, we'll isolate l on one side of the equation. Here are the steps to do that:
Step 1: Start with the given equation:
S = 2lw + 2wh + 2lh
Step 2: Factor out l from the terms that contain it:
S = l( 2w + 2h + 2wh )
Step 3: Divide both sides of the equation by (2w + 2h + 2wh) to solve for l:
S / ( 2w + 2h + 2wh ) = l
So, the value of l is given by:
l = S / ( 2w + 2h + 2wh )
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If n represents a number then write an expression for a number that’s twice than n
Final answer:
An expression for a number that's twice another number represented by n is written as 2n.
Explanation:
If n represents a number, then the expression for a number that's twice n can be written as 2n. This stems from the definition that multiplying a number by 2 effectively doubles it. To better understand this concept, consider the next statement, N=N*2, which tells us that the new value of N is twice the original value. So, if we substitute N with n, we can express a number that's twice n as 2n.
HELP! PLEASE SHOW WORK.
Answer:
2⅖
Step-by-step explanation:
Set this up as a proportion:
⅘ ? [parts of the necklace]
__ = __
⅓ 1 [hours]
Divide four-fifths by one-third to get 2⅖.
I am joyous to assist you anytime.
** ⅓ hour = 20 minutes
what is equivalent to the square root of -98
Answer:
7√2 i
Step-by-step explanation:
√(-98)
=√{(-1) .98}
=√(-1 . 2 . 7²)
=√-1 .√2 . √7²
= i . √2 . 7 [∵√-1 = i ]
=7√2 i
Answer:
[tex]\large\boxed{\sqrt{-98}=7\sqrt2\ i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-98}=\sqrt{(-1)(49)(2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{-1}\cdot\sqrt{49}\cdot\sqrt2\qquad\text{use}\ \sqrt{-1}=i\ -\text{an imaginary unit}\\\\=i\cdot7\cdot\sqrt2\qquad\sqrt{49}=7\ \text{because}\ 7^2=49\\\\=7\sqrt2\ i[/tex]
The height of a cone is twice the radius of its base. What expression represents the volume of the cone, in cubic units?
A)2/3πx^3
B) 4/3πx^2
C) 2πx^3
D) 4πx^3
Answer:
A
Step-by-step explanation:
The general formula for the volume of a right cone is as follows (also see attached):
V = (1/3) π r² h; where r = radius of base and h = height
In this case, it is given that r = x
also given :
height = 2 (base radius)
or
h = 2x.
Hence the formula becomes:
V = (1/3) π r² h
V = (1/3) π x² (2x)
V = (2/3) π x³ (answer A)
Lainey bought a set of 20 markers for $6
Final answer:
To find the unit price of markers in a set, divide the total cost by the number of markers to find that each marker costs $0.30 when 20 are purchased for $6.
Explanation:
Lainey's purchase of a set of 20 markers for $6 can be used to illustrate a simple mathematical concept known as unit price, which is the cost per individual item when items are sold in a set or batch. To calculate the unit price, you divide the total cost by the number of items in the set. Here's how you can do this calculation:
Determine the total cost of the set of markers, which is $6.
Count the number of markers in the set, which is 20.
Divide the total cost by the number of markers to find the unit price: $6 ÷ 20 = $0.30 per marker.
Therefore, the cost of each individual marker from the set is $0.30. Starting small, such as with markers, pencils, sharpeners, and erasers, and gradually adding other items like construction paper or magnets, are good practices in both purchasing supplies and understanding incremental costs in financial literacy.
-2 (5) + 4 help plzzz
Answer:
-6
Step-by-step explanation:
-2 * 5 = -10
-10 + 4 = -6
Answer is -6
-2(5)+4
You multiply '-2' to '(5)' which equals to '-10' then you add '4' and the correct answer is '-14'
Hope this helped, my dude
Suppose karl uses 5 cups of tomatoes how many salqds can he make? Write a division equation and multiplication equation
Assuming one salad requires 1 cup of tomatoes, Karl can make 5 salads as shown by the division equation 5 cups / 1 salad = 5 salads. The multiplication equation 5 salads x 1 cup = 5 cups demonstrates the amount of tomatoes needed for 5 salads.
Explanation:To properly answer this question, we first need to know the number of cups of tomatoes required to make one salad. However, if we suppose that one salad requires 1 cup of tomatoes, then the division equation is 5 cups / 1 salad = 5 salads. This equation illustrates that Karl can make 5 salads with the amount of tomatoes he has.
On the other hand, the multiplication equation would be 5 salads x 1 cup = 5 cups. This equation pertains to how many cups of tomatoes are needed to make 5 salads. Please note that these equations assume that 1 cup of tomatoes is needed for a single salad, but the proportions may vary depending on the actual recipe.
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Karl can make 5 salads using 5 cups of tomatoes.
Assuming Karl makes salads that require 1 cup of tomatoes each, we can determine the number of salads he can make using division:
Number of salads = Total tomatoes (cups) / Tomatoes per salad (cups)
Number of salads = 5 cups / 1 cup/salad
Therefore, Karl can make 5 salads using 5 cups of tomatoes.
A multiplication equation can be used to express the relationship between the number of salads, the number of tomatoes per salad, and the total number of tomatoes:
Total tomatoes (cups) = Number of salads × Tomatoes per salad (cups)
5 cups = 5 salads × 1 cup/salad
Both equations demonstrate the same relationship between the number of salads, the number of tomatoes per salad, and the total number of tomatoes.
Write an equation of the line that passes through (−3,7) and is perpendicular to the line y=−2x−5.
Answer:
Step-by-step explanation:
an equation is : Use the point-slope formula.
y - y_1 = m(x - x_1) ; m : the slope when : x_1 = -3 and y_1 = 7
- 2 ×m = - 1 because this line is perpendicular to the line y= -2x-5 when the slope is -2
so : m= 1/2
an equation is : y - 7 =(1/2)(x+3)
Answer:
The desired equation is
y = (1/2)x + 17/2
Step-by-step explanation:
The slope of the perpendicular line is the negative reciprocal of -2: m = 1/2.
Start with y = mx + b.
Substituting 7 for y, 1/2 for m and -3 for x, we get:
7 = (1/2)(-3) + b. Then 7 = -3/2 + b, so that b = 17/2.
The desired equation is
y = (1/2)x + 17/2
The subject of the formula below is y.
y = x + a-b
Rearrange the formula to make x the subject.
Pls help
Answer:
x = y + b - a
Step-by-step explanation:
Given
y = x + a - b ( add b to both sides )
y + b = x + a ( isolate x by subtracting a from both sides )
y + b - a = x
Patty needs a total of $80 to buy a bicycle. She has already saved $35. If she saves $10 a week from her earnings, what is the least number of weeks she must work to have enough money to buy the bicycle?
F.3
G.4
H.5
J.8
Answer:
h
Step-by-step explanation:
80-35=45
4days x10=40
leaving 5 dollars left so u need another week to save 5 dollars more
in total of 5 weeks
The answer is She has to work at least for 4.5 to be able to buy the bicycle i.e x≥4.5
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: price of the bicycle is $80 and she has $35 in hand
If she earns $10 in a week then let x weeks be the minimum number of weeks she has to work then we have
x= 45/10
=4.5 weeks
Hence, She has to work at least for 4.5 to be able to buy the bicycle
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ANSWER PLS ITS URGENT NEED DONE IN ONE MIN BUS IS COMING!!!! pls dont let me fail!!!!! (will mark as brainliest)
(answer the circled ones) its quadratic equation factoring
Answer:
8.) x = 5, x=-12
9.)x = 5, x = -8
10.)x = -1/5, x = -2
Hope I helped :)
Answer:
10. -2, -⅕ = x
9. -8, 5 = x
8. -12, 5 = x
7. -5, 6 = x
Step-by-step explanation:
10. [tex]5{x}^{2} + 11x + 2 = 0 \\ \\ (5{x}^{2} + x) + (10x + 2) = 0 \\ x(5x + 1) + 2(5x + 1) \\ \\ (x + 2)(5x + 1) = 0 \\ \\ -2, \: - \frac{1}{5} = x[/tex]
9.
[tex]2{x}^{2} + 6x - 80 = 0 \\ \\ (2{x}^{2} + 16x) - (10x - 80) = 0 \\ 2x(x + 8) -10(x + 8) = 0 \\ \\ (x + 8)(2x - 10) = 0 \\ \\ -8, \: 5 = x[/tex]
8.
[tex] {x}^{2} + 8x - 65 = x - 5 \:→ {x}^{2} + 7x - 60 \\ \\ ({x}^{2} - 5x) + (12x - 60) \\ x(x - 5) + 12(x - 5) \\ \\ (x + 12)(x - 5) = 0 \\ \\ 5, \: -12 = x[/tex]
7.
[tex] {x}^{2} = x + 30 → - {x}^{2} + x + 30 \\ \\ (-{x}^{2} - 5x) + (6x + 30) \\ -x(x + 5) + 6(x + 5) \\ \\ -(x - 6)(x + 5) = 0 \\ \\ -5, \: 6 = x[/tex]
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When measuring the length a and the width b of a rectangle, it was found that 5.4< a< 5.5 and 3.6< b< 3.7 (in centimeters). Find the possible values of: the perimeter of the rectangle
Answer:
The possible values of the perimeter of the rectangle is between 18 and
18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm
Step-by-step explanation:
* Lets explain how to solve the problem
- The perimeter of any quadrilateral is the sum of the length of its
four sides
- The rectangle is a quadrilateral with each two opposite sides are
equal in lengths, then its perimeter = 2l + 2w, where l, w are its
length and width
∵ The the length of the rectangle is a
∵ 5.4 < a < 5.5 cm
∵ The perimeter of the rectangle = 2a + 2b
- Lets multiply the inequality by 2
∴ 5.4 × 2 < a × 2 < 5.5 × 2
∴ 10.8 < 2a < 11 ⇒ (1)
∵ The width of the rectangle is b
∵ 3.6 < b < 3.7 cm
- Lets multiply the inequality by 2
∴ 3.6 × 2 < b × 2 < 3.7 × 2
∴ 7.2 < 2b < 7.4 ⇒ (2)
- Add inequalities (1) and (2)
∵ 10.8 < 2a < 11
+ 7.2 < 2b < 7.4
∴ 18 < 2a + 2b < 18.4
∵ 2a + 2b represents the perimeter of the rectangle
∴ The possible values of the perimeter of the rectangle is between
18 and 18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm
A crayon company makes 87,491 blue crayons, 36,262 red crayons, and 25,063 gray crayons. how many more blue crayons are made than red and gray crayons combined?
Answer:
26 166
Step-by-step explanation:
Blue = 87 491
Red = 36 262
Green = 25 063
-(Red + green) = - 61 325
Blue - (red + green) = 26 166
The company makes 26 166 more blue crayons than red and green combines.
points -3,2 rotated 90 clockwise
its a maze i need help o thank u
Answer:
(2,3)
Step-by-step explanation:
Rotation through 90 clockwise gives the expression
( x , y )___ ( y ,- x )
so when you put the points -3 ,2 in the relation , it becomes
( -3 , 2 ) ___ ( 2, - -3 )
= ( x, y ) __ ( 2, 3 ). meaning when you rotate -3,2 through 90 clockwise you will get the image ( 2 ,3 )
Chandresh has several fishing rods that she would like to pack in boxes. One box is shown below.
Which fishing rod will fit in the box shown?
A. 17-inch fishing rod
B. 24-inch fishing rod
C. 27-inch fishing rod
D. 32-inch fishing rod
Answer: A, 17 inch
The box is 21 inches long, anything longer and it won't fit. 17 inch is the only thing shorter than 21.
Answer:
the green means its right at the top
Step-by-step explanation:
What is n? -4n - 5 = -3n + 4
Move n terms on one side and other terms on the other side. Note that by moving we are essentially subtracting and adding to both sides so the prefix of a term changes from - to + or from + to -.
[tex]
-4n-5=-3n+4 \\
-4n+3n=4+5 \\
-n=9 \\
n=-9
[/tex]
Hope this helps.
[tex] \sqrt[3]{216} [/tex]
reduce the index of the radical and exponent with 3, rhen you get your answer, 6
The local football team won the championship several years ago, and since then, ticket
prices have been increasing $4 per year. The year they won the championship, tickets were
$20. Write an explicit formula for a sequence that will model ticket prices. What will the ticket
price be 10 years after that championship year?
Answer:
60$
Step-by-step explanation:
if 4$ is per year 20 ÷4 is 5, 5 years have passed and if 10 uears after the champion ship it will be 60 because 4 × 10 is 40 plus the 5 years since it was 20 therefore 20+40 =60
The explicit formula for the ticket price after n years is T(n) = 20 + 4n. Plugging in 10 for n, we find that the price 10 years after the championship will be $60.
Explanation:The question asks us to create an explicit formula to model the increasing price of football tickets after the local team won a championship. If tickets were originally $20 and the price increases by $4 each year, we can use the formula T(n) = 20 + 4n to represent the price of football tickets after n years.
For 10 years after the championship year, we plug 10 into our equation for n: T(10) = 20 + (4 \times 10) = 20 + 40 = $60. Thus, the ticket price will be $60, 10 years after the championship year.
Marco has a piece of wood that measures 9 x 1/10 + 6 x 1/100 + 4 x 1/1000 how can this measurement be written as a decimal? you miss ONE DAY OF SCHOOL
Answer:
The decimal number is 0.964
Step-by-step explanation:
we have
[tex]9(\frac{1}{10})+ 6(\frac{1}{100})+4(\frac{1}{1,000})[/tex]
step 1
Multiply each fraction by the whole number
[tex](\frac{9}{10})+ (\frac{6}{100})+(\frac{4}{1,000})[/tex]
step 2
Convert each fraction in a decimal number
Remember
Move the decimal point to the left as many places as there are zeros in the factor.
Move the decimal point one step to the left (10 has one zero).
Move the decimal point two steps to the left (100 has two zeros)
Move the decimal point three steps to the left (1000 has three zeros)
[tex]0.9+0.06+0.004[/tex]
step 3
Adds the number
[tex]0.964[/tex]
Which lines are parallel? Check all that apply.
89.5°
91.51
88.5°
89.5°
90.5°
The lines that are parallel to each other are as follows;
b║fc║eHow to know lines that are parallel from the angles?When parallel lines are cut by a transversal, angles relationship are formed.
This angle relationship includes corresponding angles, alternate angles, vertical angles and many more.
Therefore, the lines that are parallel are as follows;
b║f : If you use alternate angle theorem you will notices line b and f are parallelc║e: using alternate and corresponding angle theorem you will notice both line c and e are parallel.learn more on parallel lines here: https://brainly.com/question/10652739
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I also need some help on this part of the geometry homework.please help me if you can.
Answer:
They are mirrored
Step-by-step explanation:
When you cut it in half horizontally you can see both sides are mirrored so the lines have the same length
Find the distance between P(2, 8) and Q(5, 3).
Answer:
The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((X2-X1)2+(Y2-Y1)2)
d = √ (5-2)2+(3-8)2
d = √ ((3)2+(-5)2)
d = √ (9+25)
d = √ 34
The distance between the points is 5.8309518948453
The midpoint of two points is given by the formula
Midpoint= ((X1+X2)/2,(Y1+Y2)/2)
Find the x value of the midpoint
Xm=(X1+X2)/2
Xm=(2+5)/2=3.5
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(8+3)/2=5.5
The midpoint is: (3.5,5.5)
Graphing the two points, midpoint and distance
P1 (2,8)
P2 (5,3)
Midpoint (3.5,5.5)
The length of the black line is the distance between the points (5.8309518948453)
Find the slope of the line connecting the two points
Slope = (Y2-Y1) = (3-8) = (-5) = -1.66666666666667
(X2-X1) (5-2) (3)
Find the equation of the line passing through the two points
The general equation for a straight line is
y = mx + b
Where m represents the slope of the line which we found in the previous step to be -1.66666666666667
y = -1.67x + b
We substitute x and y for the values from one of our points (2,8)
8 = -1.67×2 + b
8 = -3.33 + b
8--3.33 = b
11.33 = b
Knowing both b and m, we can contruct the equation of the line
y= -1.67x+ 11.33
X and Y intercepts
The x-intercept is a point on the graph where y is zero
Using the equation we found in the previous step and substituting zero for y
y= -1.67x+ 11.33
0= -1.67x+ 11.33
1.67x= 11.33
x= 11.33/1.67 = 6.80
The x intercept for this straight line is 6.80
The y-intercept is a point on the graph where x is zero
Using the equation we found in the previous step and substituting zero for x
y= -1.67×0+ 11.33
y= 11.33
The y intercept for this straight line is 6.80
References
refernce image showing the distance between two points on the xy plane
Step-by-step explanation:
The distance between the two points will be √34. The correct option is c
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
The distance (d) between two points (x₁,y₁) and (x₂,y₂) is given by the formula:-
d = √ ((X₂-X₁)²+(Y₂-Y₁)²)
d = √ (5-2)²+(3-8)²
d = √ ((3)²+(-5)²)
d = √ (9+25)
d = √ 34
Therefore, the distance between the two points will be √34. The correct option is c
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What is the multiplication inverse of 1/4 A. 1.8
B. 1/2
C. 4
D 8/1
The inverse of 1/4 is 4.
Choice C