Answer:
when x = 39.25, y = 2.75
when x = 2.75, x = 39.25
Step-by-step explanation:
use substitution method
x+y = 42 ------ (1)
xy = 108 ------ (2)
from (1) ,
x+y = 42
y = 42-x ------ (3)
substitute (3) into (2)
xy = 108
x( 42-x ) = 108
42x - x² = 108
-x² + 42x - 108 = 0
x² - 42x + 108 = 0
use the following formula to solve the value of x:
[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \\ ii) \: x = \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
a = 1
b = -42
c = 108
[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]x = \frac{ - ( - 42) + \sqrt{( - 42) {}^{2} - 4(1)(108)} }{2(1)} [/tex]
[tex]x = \frac{42 + \sqrt{1764 - 432} }{2} [/tex]
[tex]x = \frac{42 + \sqrt{1332} }{2} [/tex]
[tex]x = \frac{42 + 6 \sqrt{37} }{2} [/tex]
[tex]x = 21 + 3 \sqrt{37} [/tex]
[tex]x = 39.25[/tex]
[tex]ii) \: x \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]x = \frac{ - ( - 42) - \sqrt{( - 42) {}^{2} - 4(1)(108} }{2(1)} [/tex]
[tex]x = \frac{42 - \sqrt{1764 - 432} }{2} [/tex]
[tex]x = \frac{42 - \sqrt{1332} }{2} [/tex]
[tex]x = \frac{42 - 6 \sqrt{37} }{2} [/tex]
[tex]x = 21 - 3 \sqrt{37} [/tex]
[tex]x = 2.75[/tex]
the 2 values of x are x = 39.25 and x = 2.75
substitute x = 39.25 into (3)
y = 42-x
y = 42-39.25
y = 2.75
substitute x = 2.75 into (3)
y = 42-x
y = 42-2.75
y = 39.25
when x = 39.25, y = 2.75
when x = 2.75, x = 39.25
B is between A and C. If AB = 2x + 1, BC = x, and AC = 22. Find AB.
Answer:
15
Step-by-step explanation:
AB + BC = AC
2x + 1 + x = 22
3x + 1 = 22
3x = 22 -1
3x = 21
x = 21/3
x = 7
AB = 2*7 +1
= 14 + 1
= 15
The table below represents a linear function f(x) and the equation represents a function g(x):
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
(10 points)
Answer:
Step-by-step explanation:
Part A
for f(x) slope between points (-1,-6) and (1,0)
m= y2-y1/x2-x1 = -6-0/-1-1 = -6/-2= 3
for g(x) slope m=4 because we compare to equation y=mx+b the given equation g(x)=4x-5
The slope of f(x) is 3 and the slope g(x) is 4 so the line of g(x) is steeper
part B
The y intercept for g(x) is (0, -5)
The equation of f(x) can be found
y-y1 =m(x-x1) take any point for example point (1,0)
y-1 =3(x-0)
y=3x+1 so the y-intercept is at (0,1)
The y-intercept for f(x) is greater at y=1 then the one of g(x) at y=-5
A fireman's ladder leaning against a house makes an angle of 50° with the ground. How long is the ladder if the ladder is 8 feet from the foot of the house?
The ladder would be 12.4 feet hope that helps
HELP!! Who ever does all these problems gets a brainlist and 50 points
Answer:
760cm = 7.6m
2485m = 2.485km
3090g = 3.09kg
205ml = 0.205ml
It seems I only get 30 points, ah well.
Help PLEASE. 15 pts
Which equations illustrate the zero property of multiplication? Select ALL that apply.
[tex] \frac{1}{3} \times 3 - 3 = 4[/tex]
[tex] \frac{1}{2} + 2 - 2 = \frac{1}{2} [/tex]
[tex]0 \times \frac{1}{9} \times 9 = 0[/tex]
[tex]x - 5 + 5 = x[/tex]
[tex] \frac{1}{3}(9 + 3) = 3 + 1 [/tex]
Answer:
0* 1/9*9=0
Step-by-step explanation:
The zero property of multiplication states that any non-zero number multiplied by zero will equal zero.
it can't be the first one, since there's no zero in it, and the answer isn't zero
it can't be the second one since there's no multiplication illustrated.
The third one is an option, since there is a zero and it's being multiplied by two non-zero numbers, and the answer is 0
the fourth one isn't an option since there's no multiplication
the fifth one isn't an option since there is no 0's there.
hope this helps!
It takes Andre 4 minutes to swim 5 laps.
How many laps PER MINUTE is that? (round to two decimal places if needed)
can someone also show there work?
Find the value of x
please help asap!!!
Answer: 108
Step-by-step explanation:
x = 108
Whats the slope of (6,0) and (2,-2)
HELP!! (30 points) and brainlist
Answer:
5.5 feet is 66 inches. and 56.75 pounds is 908 ounces
Step-by-step explanation:
Hope this helped you!! Give brainliest
Here is a triangle with the height on the side of the triangle. Use the formula: (1/2)*(Base)*(Height) to find the area of the triangle at the left.
(If one square on the graph = one centimeter)
b = 10cm
h = 10cm
Area
[tex] = \frac{1}{2} \times b \times \: h[/tex]
[tex] = \frac{1}{2 } \times 10 \times 10[/tex]
[tex] = \frac{1}{2} \times 100[/tex]
[tex] = 50 {cm}^{2} [/tex]
PLEASE HELO ME I NEED HDLP PLEASE
Answer:
what's that 120 which angle is that
Step-by-step explanation:
Triangle AGB has Angle AGB = 120° and AG = GB. (given)
Since it is isosceles, x = (180° - 120°)/2 = 30°.
can someone plz help i need to graph it and identify the x-intercept
Answer:
(-7/2,0) is the x intercept
Step-by-step explanation:
1. y+3 = -6/7x
2. -3 -3 ....subtract 3 from both sides to isolate the variable y
y= =-6/7x -3 ....is your new equation
You graph it by putting your point on negative three and then counting 6 units down and 7 units right.
For the x intercept you set y to 0 and solve for x
0= -6/7x -3
+3 +3 ...to both sides
3= -6/7x .....divide both sides by -6/7
-7/2=x
put it in as a coordinate
Sarah said that 26÷8 is the same as/equal to 14÷4 and the answers are "3r2". What did Sarah do wrong? 5th grade math help fir my daughter. I think Sarah meant: 26÷8 is the same as or equal to 13÷4 instead of 14÷4 which is what she did wrong?
Answer:
Yes
Step-by-step explanation:
Yes, that is exactly what Sarah did wrong. Apparently, she tried to divide both the numerator and denominator in this problem by 2 (half) but divided the numerator incorrectly. 26 divided by 2 would equal 13 but Sarah mistakenly calculated it as 14 which would give her a totally different value when divided by the new denominator. If were to have divided correctly it would give her [tex]\frac{13}{4}[/tex] which is the same as [tex]\frac{26}{8}[/tex]
-2(-g + 5)
someone please explain how to simplify then combine like terms
Answer:
2g-10
Step-by-step explanation:
-2(-g+5) take the -2 and multiply each term in the ()
-2*-g= 2g Two negatives multiplied turns it into a positive number
-2*5= -10
The answer is 2g-10
Solve the system of equations. (1 point)
2x − 5y = 3
x − 3y = 1
(4, 1)
(5, 2)
(7, 2)
(9, 3)
Answer:
The answer is (4, 1)
Step-by-step explanation:
I hope this helps have a good day.
The equation for line p can be written as y = 1/4x + 3. Line q includes the point (-1, 5) and is
perpendicular to line p. What is the equation of line q?
Answer:
[tex]y=-4x+1[/tex]
Step-by-step explanation:
To get this, use the following steps:
1) Knowing that line q is perpendicular to the line p, the slope of line q must be the negative reciprocal of the slope of line p. Thus the slope is [tex]-(\frac{1}{4})^{-1} = -4[/tex]
2) To find the equation, plug in the point given:
[tex]5 = -4(-1) + b[/tex]
[tex]b = 1[/tex]
3) The equation of line q is thus:
[tex]y= -4x+1[/tex]
someone please help me answer question in attachment..
Answer:
135*
Step-by-step explanation:
trust me
How many apples are there in a bag if there is a total of nine pieces of fruit
Answer:
9
Step-by-step explanation:
if their nine pieces nine apples
hope im right!
A factory is going to hire 33 new employees. There are 79 applicants. Which
choice represents the ratio of new hires to applicants?
Answer:
33:79
Step-by-step explanation:
We are told that a factory is going to hire 33 new employees.
and the total applicants is 79
In this problem, we want to represent the situation as a ratio of new hires to applicants
Since the question says new hires to applicants
Hence, the ratio will be
33 to 79
or
33/79, we can simplify this as
33:79
^^ this is the last oneeee
Answer:
30 degrees
Step-by-step explanation:
So a complete circle consists of 360 degrees but we are trying to find what ADB equals so we are going to subtract BDC and ADC from 360:
BDC = 150
The graph does not say what ADC equals so we are going to look at the graph and see that ADC is half of the circle so we are going to divide 360 by 2:
360/2 = 180
So ADC equals 180, since we know what ADC and BDC equal we are going to add them together and then subtract them from 360:
180 + 150 = 330
360 - 330 = 30
So ADB = 30 degrees
Hope this helps!
Car A is traveling east at a steady speed of 45 miles per hour. After 2 hours, it is 100 miles east of Johnstown
Car B is traveling east on the same road. it’s distance east of Johnstown is represented by the graph.
Where were the two cars in relation to each other when they began traveling?
A. Car B was 10 miles east of car A
B. Car A was 45 miles east of car B
C. Car A was 10 miles east of car B
D. Car B was 40 miles east of car A
Answer:
The correct option is;
A. Car B was 10 miles east of car A
Step-by-step explanation:
The given parameters are;
The speed of car A = 45 miles per hour
The direction of car A = East
The distance of car B from Johnstown after 2 hours = 100 miles east
The direction of Car B = East
The distance of car B from Johnstown is given on the graph
Therefore, the initial distance of car A from Johnstown when car A began driving is given as follows;
The initial distance, east, of car A from Johnstown = 100 - 2 × 45 = 10
∴ The initial distance, east, of car A from Johnstown = 10 miles
From the graph, the initial distance, east, of car B from Johnstown = 20 miles
Therefore, car B was 10 miles east of car A
Answer:
Car B was 10 miles east of car A
Step-by-step explanation:
PLZ HELP PLZ PLZ PLZZZZZ
G(n)=-11*4^n complete the recursive formula of g(n) g(1) g(n)=g(n-1)
Answer:
-44
4
Step-by-step explanation:
Question 5
3 pts
A map has a scale of 2 inches = 3 miles. If two towns are nine inches apart on the map, how
far are they actually apart?
O 13.5 miles
O 6 miles
O 13.5 inches
O 54 miles
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A school group is planning a trip to Jacksonville, Florida. There are 29 people going on the trip. They have agreed to share the total cost of the trip equally. Let s equal each person’s share of the cost. What is each person’s share of the cost? Solve this problem any way you choose. bus cost 7,830$ the hotel cost 10,034$ the meal cost 812$ the event ticket cost 435$ the cost of eveyting is 19,111$
Answer:659
Step-by-step explanation:
Helppppppp pleaseeee
Answer:
-5
Step-by-step explanation:
a= -4 than 2 times-4. than be 8.and 4 square is -16. So it be 3+8-16 = -5
Answer:
27
Step-by-step explanation:
[tex]3-2a+a^2\\[/tex]
If a = -4 then just replace a with -4
[tex]3-2(-4)+(-4)^2\\3+8+16\\27[/tex]
Jill spent half of the money she saved to buy a video game. To earn more money her parents let her wash the car and do other chores for $20. How much money did she have saved if she now has $50.
VALID ANSWERS ONLY OR YOU GET REPORTED.
Answer:
Step-by-step explanation:
She has $50 and before she earn $20 had $50-$20=$30
so she had $60
payed for video game $30 now has $30
earn from parents $20 now has $50
If she would not bye the video game she would have had $80 saved
Daniel needs to order some new supplies for the restaurant where he works. The
restaurant needs at least 792 forks. There are currently 223 forks. If each set on sale
contains 15 forks, what is the minimum number of sets of forks Daniel should buy?
HELP ME PLEASE
Mr. Parke made snacks in separate gift bags. He gave one each to the 86 seventh grade students going on the field trip. Then he gave 17 bags to the students in Mrs. Mark's class for decorating the trophy cases. Next he gave 11 to the students in Mrs. Green's class for helping during the school play. Mr. Parke had 11 snacks left. How many snacks did he make?
Answer:
125 snacks
Step-by-step explanation:
just add every number
Answer:
125
Step-by-step explanation:
HELP ME PLEASE!!!
Martha states that –6 is a rational number. Which is a correct explanation for this statement?
The number –6 is the opposite of 6.
The number –6 is a negative integer.
The number –6 can be written as -6/1.
The number –6 is less than 0.