Answer:
1 and 7
Step-by-step explanation:
(x+4)(x-2) = x²+2x-8
set up proportion:
2x-3/ x²+2x-8 = 1/5
cross-multiply:
5(2x-3) = x²+2x-8
10x-15 = x²+2x-8
Combine Like Terms:
x²-8x+7
Factor:
(x-7)(x-1)
set each factor equal to zero and solve: x = 1, x = 7
Answer:
[tex] \frac{(2x - 3)}{(x + 4)(x - 2)} = \frac{1}{5} \\ \frac{2x - 3}{x {}^{2} - 2x + 4x - 8} = \frac{1}{5} \\ x {}^{2} - 2x + 4x - 8 = 5(2x - 3) \\ x {}^{2} + 2x - 8 = 10x - 15 \\ x {}^{2} + 2x - 10x = - 15 + 8 \\ x { }^{2} - 8x = - 7 \\ x {}^{2} - 8x + 7 = 0 \\ x {}^{2} - x - 7x + 7 = 0 \\ x(x - 1) + 7(x - 1) \\ x + 7 = 0 \\ x = - 7or \\ x - 1 = 0 \\ x = 1[/tex]
Step-by-step explanation:
x=7 or x=1
It is given that y varies inversely as x^2. If x is decreased by 50%, find the percentage change in y.
Answer:
300%
Step-by-step explanation:
Given
[tex]y\ \alpha\ \frac{1}{x^2}[/tex]
Required
Find the percentage change in y when x decreased by 50%
First, convert to equation
[tex]y\ = \ \frac{k}{x^2}[/tex]
Where k is the constant of proportionality
When x decreased by 50%
[tex]Y = \frac{k}{(x - 0.5x)^2}[/tex]
[tex]Y = \frac{k}{(0.5x)^2}[/tex]
[tex]Y = \frac{k}{0.25x^2}[/tex]
Expand
[tex]Y = \frac{1}{0.25} * \frac{k}{x^2}[/tex]
Substitute [tex]\frac{k}{x^2}[/tex] for y
[tex]Y = \frac{1}{0.25} * y[/tex]
[tex]Y = 4 * y[/tex]
[tex]Y = 4 y[/tex]
The percentage change is then calculated as:
[tex]\%Change = \frac{Y - y}{y} * 100\%[/tex]
[tex]\%Change = \frac{4y - y}{y} * 100\%[/tex]
[tex]\%Change = \frac{3y}{y} * 100\%[/tex]
[tex]\%Change = 3 * 100\%[/tex]
[tex]\%Change = 300\%[/tex]
The percentage in y is 300%
From the calculation, the percentage change in y is 300%.
From the statement of the question; y α 1/x^2 so introducing the constant of proportionality, we have; y =k/x^2 so k = x^2y.
We are then told that x is decreased by 50% hence;
Y = k/(x - 0.25x)^2
Y = k/(0.5x)^2
Y = 1/0.25 k/x^2
But k/x^2 = y so;
Y = 1/0.25 y
Y = 4y
Change = 4y -y/y * 100/1
= 300%
Learn more about percentage change: https://brainly.com/question/15308590
Help plz!
The Corresponding Angles Conjecture states that if two
parallel lines are cut by a transversal, the corresponding
angles are congruent. The picture below shows this
relationship
Answer:
B
Step-by-step explanation:
Corresponding angles form a sideways U when you connect the angles.
b is the only one that does that.
1 and 4 are consecutive angles.
1 and 3 are vertical angles
4 and 3 are linear pair angles.
What is the value of x in reduced radical form? (us sqrt)
Answer:
sin theta= p/h
here, 40√3/x=x sin 60
40√3/x=x √3/2
40/x= x/2
x^2=80
=√80=4√5
To create a pattern with Legos, Jerry uses 5 green Legos for every 3 blue Legos. If he used 35 green Legos in the pattern, what is the TOTAL amount of Legos he used?
A.43 legos in all
B.8 legos in all
C.56 legos in all
D.21 legos in all
Answer:
56 legos in all
Step-by-step explanation:
35/5=7
7*3=21
21+35=56
Answer:
well i have legos in rl so i think the answer is C. or 56 legos in all
Step-by-step explanation:
how 2 do?
(n)(n+7)(n+8)
Answer:
[tex]n^{3} + 15n^{2} + 56n[/tex]
Step-by-step explanation:
First FOIL (n + 7)(n + 8) and then distribute n
(n + 7)(n + 8) = [tex]n^{2} +15n + 56[/tex]
n ([tex]n^{2} +15n + 56[/tex])
= [tex]n^{3} + 15n^{2} + 56n[/tex]
In a exam 90% students passed.if 15 students failed,find the number of students appeared in the examination?
Answer:
150
Step-by-step explanation:
10%=15
100%=150
15 x 10=150
to check find 90% of 150 which is 135
150-135=15
Find the missing angle.
Answer:
90°
Step-by-step explanation:
40+50+x=180
x=90
please help! this is a huge chunk of my grade!!
Answer:
r=8Step-by-step explanation:
3r+4+8r-2 = 90
11r +2 = 90
11r= 88
r= 8In ΔPQR, the measure of ∠R=90°, the measure of ∠P=53°, and QR = 17 feet. Find the length of PQ to the nearest tenth of a foot.
Answer:
21.2863≈21.3 feet
Step-by-step explanation:
Answer:
21.3
Step-by-step explanation:
Lydia is an architect. She has to design a courtyard garden inside a new hotel. On her blueprint, which is 1/20 the size of the actual garden, the width of the garden is 36 inches. What is the width of the actual garden?
Answer:
720 inches
Step-by-step explanation:
On her blueprint, which is 1/20 the size of the actual garden
the width of the garden is 36 inches.
What is the width of the actual garden?
Let width of the actual garden = x
1/20 of x = 36
1/20 * x = 36
x = 36 ÷ 1/20
x = 36 * 20/1
x = 720
x = 720 inches
The width of the actual garden = 720 inches
I really need help with a thing for math if yall can help I would appreciate it. If yall know this comment down below and tell me the answer
Answer:
27
Step-by-step explanation:
3/5of 45 is basically what you are looking for and it in itself is the equation you have to solve
3/5 is 3 divided by and "of" is basically multiply by 45
3/5*45
.6*45
27
WHat is the answer to number 2
Answer:
My best guess C im pretty sure.
In 4 minutes, a conveyor belt moves 800 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long it takes to move the cans to the storage area.
Answer:
It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.
Step-by-step explanation:
Given - In 4 minutes, a conveyor belt moves 800 pounds of recyclable
aluminum from the delivery truck to a storage area. A smaller belt
moves the same quantity of cans the same distance in 6 minutes.
To find - If both belts are used, find how long it takes to move the cans
to the storage area.
Proof -
Given that,
Larger belt take 4 minutes to transfer the aluminium from delivery truck to storage area.
⇒ Time taken by Larger belt = 4 min/ shifting
Also,
Smaller belt take 6 minutes to transfer the aluminium from delivery truck to storage area.
⇒ Time taken by Smaller belt = 6 min/ shifting
Now,
As we know that Time is inversely proportional to time, so
Rate of Larger Belt = [tex]\frac{1}{4}[/tex] shifting/min
Rate of Smaller Belt = [tex]\frac{1}{6}[/tex] shifting/min
Now,
Let us assume that , if both belts used then,
Total time taken = x min/shifting
Then, Rate = [tex]\frac{1}{x}[/tex] shifting/min
Now,
[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{x}[/tex]
⇒[tex]\frac{6 + 4}{24} = \frac{1}{x}[/tex]
⇒[tex]\frac{10}{24} = \frac{1}{x}[/tex]
⇒10x = 24
⇒x = [tex]\frac{24}{10}[/tex] = 2.4 minutes
∴ we get
It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.
Add: 2 2/3 + 3 1/12 PLEASE HURRY IM TIMED AND I WILL BE GROUNDED IF I FAIL BECAUSE I FAILED LAST TIME SO PLEASE HURRY AND HELP MEEEEE
Answer: 23/4 is you answer!!
Step-by-step explanation:
Answer: 5 3/4
Step-by-step explanation: I put them in the same denominator to add them
i don’t understand how to do this and i need help!!
Answer:
x = 26
Step-by-step explanation:
6x + 6x + (x-2) + (x-2) = 360
14x - 4 = 360
14x = 364
x = 26
6(26) = 156
(26 - 2) = 24
A Y U D E N P O R F A :(
Answer:
x=2
Step-by-step explanation:
Primero, necesitamos calcular <<a>>
Sabemos que AD=BC y AB=CD porque lados opuestos congruentes
Entonces, vamos a calcular <<a>>.
Usamos AD y BC
2a-1=4a-15
suma 15 a ambos lados
2a+14=4
añada 2 en ambos lados
14=2a
divida
7=a
Ahora, usamos esta información para calcular <<x>>
Usamos CD=AB
2a-8=4x-2
pero sabemos que <<a>> es 7
entonces:
14-8=4x-2
6=4x-2
8=4x
2=x
<<x>> es 2
(¡lo siento mi español no es perfecto!
A culture of bacteria has an initial population of 7100 bacteria and doubles every 2
hours. Using the formula P+ = Po · 2ả, where P is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 15 hours, to the nearest whole number?
Answer:
Pt=1285237.2855≈ 1285237
YOUR WELCOME :)
Camden is deciding between two parking garages. Garage A charges an initial fee of
$12 to park plus $4 per hour. Garage B charges an initial fee of $8 to park plus $5 per
hour. Let A represent the amount Garage A would charge if Camden parks for t
hours, and let B represent the amount Garage B would charge if Camden parks for t
hours. Write an equation for each situation, in terms of t, and determine the hours
parked, t, that would make the cost of each garage the same.
Answer:
4 hours
Step-by-step explanation:
A = 12 + 4t
B = 8 + 5t
12 + 4t = 8 + 5t
t = 4
The cost of each garage would be the same when Camden parked the car for 4 hours
Will mark brainliest and give thirteen points explanation
Answer:
geyser =groundwater
glacier = freshwater
lake=freshwater
ocean=salt water
Step-by-step explanation:
Which is the graph of y= 2x-3?
Answer:
(A:
Step-by-step explanation:
EXAMPLE:
in Slope Intercept form, the letter x determines the slope of the line, where 0 makes the line horizontal and 1 makes the line at a 45 degree angle, in this case to go from x to x plus 1 you would climb y two times, so it takes two units to go one unit to the right, so x is multiplied by 2
the addition at the end of the formula resembles how high up or down the line crosses the y axis, if the number is positive, then the line crosses that amount higher then 0, if it were a negative number, it would cross that much lower
hope this makes sence, dont worry, once you understand how slope intercept form works, you will never forget it, good luck with ur studies :)
MEGA CREDITS to MisterZeng for double checking our work, thx m8 :D
If a =3, b = 2 and c = 5, solve the following algebraic expressions: (3 marks)
a) 3c + 5 - b
b) b(4 - 2) + c
c) 4a - (2c)
Answer:
A) 18
B)9
C)-2
Step-by-step explanation:
Replace the a,b or c with the give number. So let’s say it’s says 2 + a. It would be 2+3.
Which of these is the best approximation of
5
to the nearest hundredth?
OA) 0.17
OB) 0.75
OC) 0.83
OD) 1.20
Answer:
oc)0.83
Step-by-step explanation:
have a good day!!!
someone plzz help me i don't know if its right I'm lost out of time
Answer:
12. 30
13. 3
Step-by-step explanation:
The cost of the circular carpet, $C, varies as the square of the radius,
r metres. If C = 200 when r= 2
Find the cost of the circular carpet when r= 3
Answer:
$450
Step-by-step explanation:
C = k[tex]r^{2}[/tex]
200 = k([tex]2^{2}[/tex]) = 4k
k = 50
C = 50[tex]r^{2}[/tex] = 50([tex]3^{2}[/tex]) = 50(9) = $450
what is the product of 3/7 and 3/8?
Answer:
9/56
Step-by-step explanation:
..................
A fully loaded truck weighed 10 3/5 tons. After unloading, the truck weighed 3 2/3 tons. What was the weight of the load?
Answer:
14
Step-by-step explanation:
A fully loaded truck weighs 10 3/5 tons
After unloading the truck weighed 3 2/3 tons
Therefore the weight of the load can be calculated as follows
= 10 3/5 - 3 2/3
= 53/5 - 11/3
= 265-55/15
= 210/15
= 14
Hence the weight of the load 14
Divide R300 000 between Leona and Janet in the ratio 3:2.
Answer:
let the ratio be in x
a/q. 3x + 2x = 300000
5x = 300000
x = 300000/5
x= 60000
Leona = 60000*3 = 180000
Janet = 60000*2 = 120000
hope it helps
find the surface area of the triangular prism
Answer:
608 ft²
Step-by-step explanation:
1) Find the area of the bases
[tex]A=\frac{1}{2} bh[/tex] where b is the base length and h is the height
Plug in b and h
[tex]A=\frac{1}{2} (12)(8)\\A=48[/tex]
Multiply the answer by 2 (because there are 2 bases)
A=96
Therefore, the area of the two bases is 96 ft².
2) Find the area of the two sides facing up
[tex]A=lw[/tex] where l is the length and w is the width
Plug in l and w
[tex]A=10*16\\A=160[/tex]
Multiply the answer by 2 (because there are 2 sides)
A=320
Therefore, the area of these two sides is 320 ft².
3) Find the area of the bottom side
[tex]A=lw[/tex] where l is the length and w is the width
Plug in l and w
[tex]A=12*16\\A=192[/tex]
Therefore, the area of this side is 192 ft².
4) Add all the areas together
96 ft² + 320 ft² + 192 ft²
= 608 ft²
Therefore, the surface area of the triangular prism is 608 ft².
I hope this helps!
Answer:
608
Step-by-step explanation:
first off you have to find the area of the base
the base is 16 by 12 feet.
so you multiply them and you get
16*12=192 you will have to come back later for this number
next, you find the two outsides of the triangular prism.
they are 10 by 16
10*16=160 and there are two of them so you double it and get 320
now save the 320 too with the 192
now we are going to find the triangles
the formula for an area of a triangle is A=1/2h*w
so we plug in the height which is 8 and the width which is 12
A=1/2(8)*(12)
Simplify
A=48 once again there are two of them so we double it to make it 96
now take all your saved numbers and add them all up
96+320+192
this should give you an answer of 608
hope this helps! have a nice day:)
Find f(5) for f(x)=1/4 (2)^x
f(5) = 1/4(2)^5
f(5) = 1/4 (32)
f(5) = 8
answer
A. 8
Is this a function ? :)
Answer:
yes
Step-by-step explanation:
Hey There!
So if you didn't know in order for it to be a function none of the x values can repeat
In the given relation none of the x values repeat, or each input has a different output therefore it is a function