guys this Question is about system of equation word problem
please assist me !
Answers
.. f - s = 200 . . . . . . . . the first is 200 lb heavier than the second
.. s = (1/3)f . . . . . . . . . . the second was 1/3 the weight of the first
In augmented matrix form, the equations can be written
.. f - s = 200
.. f - 3s = 0
The solution is
.. f = 300
.. s = 100
Their total weight is 400 lb, not enough to kill Mr. Boddy. The physics-loving professor is apparently innocent.
Related Questions
Use the quadratic formula to determine the exact solutions to the equation. 6x2+4x−3=0
Answers
The correct answer is [tex]x = \frac{-4 + 2\sqrt{22}}{12}$ and $x = \frac{-4 - 2\sqrt{22}}{12}[/tex]
To find the exact solutions to the equation [tex]6x^2 + 4x - 3 = 0[/tex]using the quadratic formula, we can follow these steps:
Given quadratic equation: [tex]6x^2 + 4x - 3 = 0[/tex]
[tex]a = 6, b = 4, c = -3[/tex]
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]x = \frac{-4 \pm \sqrt{4^2 - 4(6)(-3)}}{2(6)}[/tex]
[tex]x = \frac{-4 \pm \sqrt{16 + 72}}{12}[/tex]
[tex]x = \frac{-4 \pm \sqrt{88}}{12}[/tex]
[tex]x = \frac{-4 \pm \sqrt{4 \cdot 22}}{12}[/tex]
[tex]x = \frac{-4 \pm 2\sqrt{22}}{12}[/tex]
Solution 1: [tex]x = \frac{-4 + 2\sqrt{22}}{12}[/tex]
Solution 2: [tex]x = \frac{-4 - 2\sqrt{22}}{12}[/tex]
Therefore, the two exact solutions to the equation [tex]6x^2 + 4x - 3 = 0[/tex] are:
[tex]x = \frac{-4 + 2\sqrt{22}}{12}$ and $x = \frac{-4 - 2\sqrt{22}}{12}[/tex]
what is the area of a regular pentagon with an apothem of 25.1 and a perimeter of 182mm
Answers
perimeter = 182
one side = 182/5 = 36.4
area = (5 * 36.4 * 25.1) / 2
area = 2,284.1
Place the indicated product in the proper location on the grid.
(5c +2/3 )(5c -2/3 )
Answers
25c^2-4/9
Explanation
In this question you are expected to expand (5c+2/3)(5c-2/3)
(5c+2/3)(5c-2/3)=(5c×5c)-(5c×2/3)+(5c×2/3)-(2/3×2/3)
=25c^2-10c/3+10c/3-4/9
25c^2-4/9
The expanded form of (5c+2/3)(5c-2/3) is 25c^2-4/9 and this is what the question requires of you to do.
Answer:
The product of the polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)=25c^2-\frac{4}{9}[/tex]
Step-by-step explanation:
given : The polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)[/tex]
We have to place the indicated product in the proper location o the grid.
Consider the given polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)[/tex]
Apply identity of difference of square
[tex]\left(a+b\right)\left(a-b\right)=a^2-b^2[/tex]
We have,
[tex]=\left(5c\right)^2-\left(\frac{2}{3}\right)^2[/tex]
Simplify, we have,
[tex]=25c^2-\frac{4}{9}[/tex]
Thus, The product of the polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)=25c^2-\frac{4}{9}[/tex]
Location on gris shown below.
A yoga membership costs $16 and an additional $7 per class. Write a linear equation modeling the cost of a yoga membership.
y = 16x + 7
y = 7x + 16
y = 23x + 7
y = 23x + 16,
Answers
find the positive value of x in the geometric sequence 7x-2,4x+4,3x
Answers
Let's assume k the ratio.
[tex] \left \{ {{3x=k*(4x+4)} \atop {4x+4=k*(7x-2)}} \right. \\\\ \left \{ {{3x-4kx=4k} \atop {4x-7kx=-2k-4}} \right. \\\\ \left \{ {{x(3-4k)=4k} \atop {x(4-7k)=-2k-4}} \right. \\\\ \left \{ {{x=\dfrac{4k}{3-4k} \atop {x=\dfrac{-2k-4}{4-7k} \right. \\\\ \dfrac{4k}{3-4k}=\dfrac{-2k-4}{4-7k}\\\\ 36k^2-6k-12=0\\ 6k^2-k-2=0\\ \boxed{k= \dfrac{2}{3} \ or\ k= -\dfrac{1}{2}}\\\\ x=\dfrac{4*\dfrac{2}{3} }{3-4*\dfrac{2}{3} }=8\\ x=\dfrac{4*\dfrac{-1}{2} }{3-4*\dfrac{-1}{2} }=-\dfrac{2}{5}\\ [/tex]
[tex] \boxed{x= 8 \ or\ x= -\dfrac{2}{5}}\\\\ [/tex]
The value of x = 8.
We have a geometric sequence.
We have to determine the positive value of x.
Define Geometric Sequence.A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio.
According to the question -
The Geometric sequence is -
7x - 2, 4x + 4, 3x
According to the concept of Geometric sequence -
[tex]$\frac{a(2)}{a(1)} =\frac{a(3)}{a(2)}[/tex]
[tex]$\frac{4x+4}{7x-2} =\frac{3x}{4x +4}[/tex]
(4x + 4)(4x + 4) = 3x(7x - 2)
16[tex]x^{2}[/tex] + 16x + 16x + 16 = 21[tex]x^{2}[/tex] - 6x
16[tex]x^{2}[/tex] + 32x + 16 = 21[tex]x^{2}[/tex] - 6x
38x + 16 = 5[tex]x^{2}[/tex]
5[tex]x^{2}[/tex] - 38x - 16 = 0
Solve the above quadratic equation, you will get two roots -
x = 8 and x = 0.4
Since, we need positive value, therefore -
x = 8.
Hence, the value of x = 8.
To solve more questions on Geometric sequence, visit the link below -
https://brainly.com/question/19201330
#SPJ2
Help see the picture
Answers
697 rounds to 700
89 rounds to 90
90 x 700 = 63000
hope i could help
A globe in a brass stand has a diameter of 40 in . what is the volume of the globe to the nearest cubic inch?
Answers
2* 3.14* 20 = 125.6in cubed
Don't forget to put 2 above inches for volume.
--------------------------------------------------------------------
Formula: Volume of a sphere
--------------------------------------------------------------------
[tex]Volume \ of \ a \ sphere = \frac{4}{3} \pi r^3[/tex]
--------------------------------------------------------------------
Given Diameter, Find Radius
--------------------------------------------------------------------
Diameter = 40 in
Radius = 40 ÷ 2 = 20 in
--------------------------------------------------------------------
Apply Formula
--------------------------------------------------------------------
[tex]Volume \ of \ the \ sphere = \frac{4}{3} \pi (20)^3[/tex]
[tex]Volume \ of \ the \ sphere = 33510 in^3[/tex]
--------------------------------------------------------------------
Ans: Volume of the Globe is 33510 in³
--------------------------------------------------------------------
Determine 10th term : 5,-25,125
Answers
Keep doing this until you reach the tenth term.
You will get -9,765,625.
Hope this helps!
point j has coordinate (-2,8) and point r has coordinates (-7,-3. find the coordinate of point A that partition line segment JR in the ratio of 5:2
Answers
[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ j(-2,8)\qquad r(-7,-3)\qquad \qquad \stackrel{\textit{ratio from \underline{j} to \underline{r}}}{5:2} \\\\\\ \cfrac{j\underline{A}}{\underline{A} r} = \cfrac{5}{2}\implies \cfrac{j}{r} = \cfrac{5}{2}\implies 2j=5r\implies 2(-2,8)=5(-7,-3)\\\\ -------------------------------[/tex]
[tex]\bf A=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\ -------------------------------\\\\ A=\left(\cfrac{(2\cdot -2)+(5\cdot -7)}{5+2}\quad ,\quad \cfrac{(2\cdot 8)+(5\cdot -3)}{5+2}\right) \\\\\\ A=\left(\cfrac{-4-35}{7}~~,~~\cfrac{16-15}{7} \right)\implies A=\left( -\cfrac{39}{7}~~,~~\cfrac{1}{7} \right) \\\\\\ A=\left( -5\frac{4}{7}~~,~~\cfrac{1}{7} \right)[/tex]
fourteen less than three fourths of a number is negative eight
Answers
After solving it...
x = 8
Hope this helps
14+8 = 3/4x
22 = 3/4x
88 = 3x
88/3 = x
Write the equation of a line that includes the point (1, 5) and has a slope of 3 in standard form. 3x + y = 5 –3x + y = 5 3x + y = 2 –3x + y = 2
Answers
What is the slope of the line that contains the points (4,-1) and (-1,4)?
Answers
proof:
slope formula: Y2-Y1/X2-X1=Slope (M)
4,-1 will be our x1,y1 and -1,4 will be our x2,y2
plug in numbers into formula: 4-(-1)/ -1-4
simplify you get 5/-5
simplify again and your answer is -1!!!
If its wrong im sorry
Answer:
-1
Step-by-step explanation:
What is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –(x – 6) and passes through the point (−2, −2)?
Answers
[tex]\sf y-y_1=m(x-x_1)[/tex]
Where 'm' is the slope and (x1, y1) is a point on the line.
Perpendicular lines have opposite slopes. To get the opposite, we take the reciprocal and multiply it by -1.
[tex]\sf -1[/tex]
Reciprocal:
[tex]\sf -\dfrac{1}{1}\rightarrow -\dfrac{1}{1}\rightarrow -1[/tex]
Multiply by -1:
[tex]\sf 1[/tex]
We can plug this slope and the point into point-slope form, and then convert it to slope-intercept form.
[tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\sf y-(-2)=1(x-(-2))[/tex]
Negatives cancel out:
[tex]\sf y+2=1(x+2)[/tex]
Distribute 1 into the parenthesis:
[tex]\sf y+2=x+2[/tex]
Subtract 2 to both sides:
[tex]\boxed{\sf y=x}[/tex]
How do you do this? It's so confusing! Please help!
Answers
notice AB ⟂ BC , whilst ∡B = 30°.
now, if we run a perpendicular line from C to AB, it'll be a 90° angle at M, however ∡AMC has to be 105°, so it has to be slanted more towards A, like in the picture, and surely you already know which one is the shortest.
A poker hand consist of 5 cards?
a.find the total number of possible five card poker card hands.
b.find the number of ways in which one can king can be selected? c)find the number of ways in which four aces can be selected .
d.find the number of ways of getting four aces and one king.
Answers
In poker probability calculations, there are 2,598,960 possible five-card hands, various specific hand combinations such as those containing a king or four aces have their own probability, which can be determined using the formulas for combinations.
Calculations for Poker Probabilities
The subject of probability in a poker hand involves various combinations and permutations. Here's how the calculations are made:
Total number of five-card poker hands: The total number is calculated using combinations, as the order in which cards are drawn does not matter. This is given by the combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of available cards (52), and r is the number of cards drawn (5). Thus, there are 52! / (5!(52-5)!)= 2,598,960 possible hands.
Number of ways one king can be selected: There are four kings in a deck, so there are C(52, 5) - C(48, 5) ways to choose a hand with at least one king, as you subtract the number of hands without any kings from the total number of hands.
Number of ways four aces can be selected: There is only one way to choose all four aces, and then there are 48 remaining cards to choose the fifth card from, which gives 48 combinations.
Number of ways of getting four aces and one king: There are four kings to choose from and one specific combination of aces, so there are 4 ways to have a hand with four aces and one king.
If a line crosses the y-axis at (0,8) and has a slope of -1/8,what is the equation of the line?
A.y= 1/8x+8
B.y=-1/8x-8
C.y=8x-8
D.y=-1/8x+8
Please help me!!!!!!
Answers
the slope is always connected to the x, and "b" is the y axis point of the two coordinate pairs, so it would be minus eight if the coordinate pairs were (0, -8).
[tex]y = mx + b[/tex]
m= slope
b= y axis point of the two coordinate pairs
Answer:
d
Step-by-step explanation:
The table below represents the displacement of a bird from its nest as a function of time: time (hours) x displacement from nest (miles) y 0 12 1 20 2 28 3 36 4 44 part
a.what is the y-intercept of the function, and what does this tell you about the bird? part
b.calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. part
c.what would be the domain of the function if the bird continued to fly at this rate until it traveled 172 miles from the nest?
Answers
Part A: The y-intercept is the first value, or 12. That means that they bird is 12 miles from its nest when the time started.
Part B: The average rate of change is the slope. From 1 to 3 hours, the bird went from 20 to 36 or 16 miles. 16 miles in 2 hours is the same as 8 miles in 1 hour.
Part C: To find the extent of the domain, write and solve the following equation for 172 miles.
172 = 8x + 12
160 = 8x
20 = x
The domain will go up to 20 hours.
You and your friend are standing back-to-back. Your friend runs 10 feet forward and then 8 feet right. At the same time, you run 11 feet forward and then 12 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?
Answers
Will mark brainliest!!
The histogram shows the ages of cars sold at a car auction.
What percent of the cars was less than 20 years old or more than 40 years old?
Answers
I know not the correctness of my answer due to:
The Total was 8 to fit the criteria, the others older than 20 but younger than 40 are 12
(However I do not know how to calculate percentage, went to Google and got a percentage calculator to find what percentage 8 is to 12)
hElP!
A carpenter designs two cabinets: one in the shape of an oblique rectangular prism and one in the shape of a right rectangular prism. The volume of each cabinet is 4,608 cubic inches. The oblique rectangular prism is 48 inches tall and has an edge length of 64 inches. The right rectangular prism has a height of 48 inches. Which statements about the cabinets are true? CHECK ALL THAT APPLY
a. The cabinets have the same base area.
b.The base area of the oblique prism is smaller than the base area of the right prism.
c.The cabinets may have the same base dimensions.
(MORE DOWN BELOW),
Answers
Answer:
A- The cabinets have the same base area.
C- The cabinets may have the same base dimensions.
D- The cabinets may have different base dimensions
Step-by-step explanation:
Answer:
A. C. D.
Step-by-step explanation:
Exponential Growth/Decay Function
Hint/Tip:
Remember, the basic general exponential function form is: y = Abx In detail, b is written as (1-r) where r is the rate of growth or decay, so our detailed formula is: y = A(1-r)x
Always work with the rate as a decimal number, not as percentage. If the rate is given as percent (%), you will need to divide it by 100 to have the decimal form.
The value of a car is $21,500. It loses 12% of its value every year.
(a) Write a function that represents the value y (in dollars) of the car after x years.
(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
Answers
For this case what we should do is write the equation of exponential type.
We have then:
y = A (b) ^ x
Substituting the values:
y = 21500 (0.88) ^ x
Answer:
y = 21500 (0.88) ^ x
(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
We use the function found in part (a) and evaluate for x = 6.
We have then:
y = 21500 (0.88) ^ 6
y = 9985 $
Answer:
the value of the car after 6 years is:
y = 9985 $
Set operations including cardinality of power sets and listing the elements of a power set and finding the number of subsets of a given size. let u = {-1, 0, 1, 2, 3, 4, 6} , a = {-1, 1, 2, 3, 4} and b = {0, 2, 4, 6}. find
a.a u b,
b.a ∩ b,
c.b – a,
d.the power set of b and its cardinality
Answers
a [tex]\cup[/tex] b means the resulting set when a and b are merged, less duplicates.
a [tex]\cup[/tex] b={-1, 1, 2, 3, 4} [tex]\cup[/tex] {0, 2, 4, 6}
={-1,0,1,2,3,4,6}
b. a [tex]\cap[/tex] b
a [tex]\cap[/tex] b means the set of members which are common to both a and b.
a [tex]\cap[/tex] b={-1, 1, 2, 3, 4} [tex]\cap[/tex] {0, 2, 4, 6}
={2,4}
c. b-a
b-a is the set of members present in b but not in a.
{0, 2, 4, 6}-{-1, 1, 2, 3, 4}
={0,6}
d. Power set of b, its cardinality
Power set is the set of all possible combinations of elements.
There are 2^n members in the power set of x where n is the number of elements in the set x.
For example, power set of S={1,2} is {[tex]\phi[/tex],{1},{2},{1,2}}
The cardinality of S above is the number of elements in the set, therefore 2^2=4.
For b={0,2,4,6}
The power set is
{[tex]\phi[/tex],{0},{2},{4},{6},{0,2},{0,4},{0,6},{2,4},{2,6},{4,6},{0,2,4},{0,2,6},{0,4,6},{2,4,6},{0,2,4,6}}
for a total of 2^4=16 members in the power set.
Therefore the cardinality of the power set is 16.
The union of A and B is {-1, 0, 1, 2, 3, 4, 6}, the intersection is {2, 4}, and the difference B - A is {0, 6}. The power set of B contains 16 subsets.
Set Operations: Union, Intersection, Difference, and Power Sets
Let's solve the given problems step by step:
a. The union of sets A and B (A ∪ B)
A ∪ B represents all unique elements that are in either set A or set B.
Given: A = {-1, 1, 2, 3, 4} and B = {0, 2, 4, 6}
A ∪ B = {-1, 0, 1, 2, 3, 4, 6}
b. The intersection of sets A and B (A ∩ B)
A ∩ B represents all elements that are present in both sets A and B.
A ∩ B = {2, 4}
c. The difference of sets B and A (B - A)
B - A represents all elements that are in set B but not in set A.
B - A = {0, 6}
d. The power set of B and its cardinality
The power set of a set is the set of all its subsets, including the empty set and the set itself. If a set has n elements, its power set will contain 2^n subsets.
B = {0, 2, 4, 6}
The power set of B is: { {}, {0}, {2}, {4}, {6}, {0, 2}, {0, 4}, {0, 6}, {2, 4}, {2, 6}, {4, 6}, {0, 2, 4}, {0, 2, 6}, {0, 4, 6}, {2, 4, 6}, {0, 2, 4, 6} }
The cardinality of the power set of B is 2^4 = 16.
In summary:
A ∪ B = {-1, 0, 1, 2, 3, 4, 6}
A ∩ B = {2, 4}
B - A = {0, 6}
The power set of B has 16 elements.
PLEASE HELP ME ON THIS
THANK U
PLZ SHOW UR WORK
Answers
50,000 records
2013
50,000 × 1.1
55,000 records
2014
55,000 × 1.1
60,500 records
2015
60,500 × 1.1
66,550 records
2016
66,550 × 1.1
73,205 records
A rectangle is 1/2 feet long and 3/4 wide what is the area of rectangle
Answers
I assume you left out "ft" from the width, so the width is 3/4 ft.
A = LW = 1/2 ft * 3/4 ft = 3/8 ft^2
A = 1/2 × 3/4
A = 0.375 or 3/8
Suppose the line of best fit is being found for some data points that have an r-value of 0.876. If the standard deviation of the x-coordinates is 5.559, and the standard deviation of the y-coordinates is 7.163, what is the slope of the line to three decimal places?
Answers
Answer: 1.129
Step-by-step explanation:
In statistics, the slope of the line is given by :-
[tex]b=r\dfrac{\sigma_y}{\sigma_x}[/tex],
[tex]\text{where r is correlation coefficient,}\\\sigma_y\text{ is standard deviation of the y-coordinates,}\\\sigma_x\text{ is standard deviation of the x-coordinates,}[/tex]
[tex]\text{Given: }r=0.876\\\sigma_x=5.559\\\sigma_y=7.163[/tex]
Now, the slope of the line will be :-
[tex]b=0.876\times\dfrac{7.163}{5.559}\\\\\Rightarrow\ b =1.12876200756\approx1.129[/tex]
Hence, the lope of the line to three decimal places =1.129
What is the volume of a square pyramid with a base length of 6 cm and a height of 9 cm?
Enter your answer in the box.
cm³
Answers
Answer:
1/3 x base squared x height
Step-by-step explanation:
so yes 108 is correct.
Please Help!!!
The figure shows a line graph and two shaded triangles that are similar:
Which statement about the slope of the line is true? (5 points)
Select one:
a. It is fraction 1 over 2 throughout the line.
b. It is 2 throughout the line.
c. The slope from point O to point A is fraction 1 over 2 time the slope of the line from
point A to point B.
d. The slope from point O to point A is two times the slope of the line from point A to point B.
Answers
Looking at the first triangle, the rise is 2 and the run is 4. That gives us a slope of 2/4 = 1/2.
For the second triangle, the rise is 1 and the slope is 2. This gives us a slope of 1/2.
Any linear function will have the same slope throughout the entire line.
You and your friend are standing back-to-back. Your friend runs 16 feet forward and then 12 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?
Answers
784+9=x2
793=x2
28.1602556807=x
In triangle XYZ, the length of side XY is 24 mm and the length of side YZ is 34 mm. Which of the following could be the length side XZ?
A. 8 mm
B. 63 mm
C. 42 mm
D. 60 mm
Answers
34 mm - 24 mm = 10 mm
The length of side XZ must be greater than 10 mm.
24 mm + 34 mm = 58 mm
The length of side XZ must be less than 58 mm.
The only choice between 10 mm and 58 mm is 42 mm.
A warranty identification number for a certain product consists of a letter of the alphabet followed by four-digit number. How many possible identification numbers are there if the first digit of the four-digit number must be nonzero?,