Please help
solve the system of equations
Answer:
(x, y) = ( 5, 6)
(x, y) = ( - 1, 0)
Step-by-step explanation:
[tex] \begin{cases} y + x^2 - 5x = 6\\\\ y - x = 1\implies y = x + 1\end{cases} [/tex]
Plug [tex] y = x +1 [/tex] in the equation [tex] y + x^2 - 5x = 6[/tex] we find:
[tex] x + 1 + x^2 - 5x = 6[/tex]
[tex] x^2 - 4x - 5=0[/tex]
[tex] x^2 - 5x +x- 5=0[/tex]
[tex] x(x - 5) +1(x- 5)=0[/tex]
[tex] (x - 5) (x+1)=0[/tex]
[tex] (x - 5) =0, \: (x+1)=0[/tex]
[tex] x =5, \: x=-1[/tex]
[tex] When \:x =5 \implies y =5+1=6 [/tex]
(x, y) = ( 5, 6)
[tex] When \:x =-1 \implies y =-1+1=0 [/tex]
(x, y) = ( - 1, 0)
the graph shows the function y=3x-1. What are the cordinates of intercepts
Answer:
[tex]y \: intercept : when \: x = 0 \\ y = (3 \times 0) - 1 = - 1 \\ = > (0, - 1) \\ x \: intercept : when \: y = 0 \\ 0 = 3x - 1 \\ x = \frac{1}{3} \\ = > ( \frac{1}{3} ,0) \\ intercepts : (0, - 1) \: and \: ( \frac{1}{3} ,0)[/tex]
The volume of this cylinder is 16,328 cubic millimeters. What is the height?
Answer: 13
Step-by-step explanation:
Answer:
Step-by-step explanation:
Givens
r = 20 mm
Volume = 16328
h = ?
Formula
V = pi * r^2 * h
Solution
16328 = 3.14 * 20^2 * h
16328 = 3.14 * 400 * h
h = 16328/(3.14 * 400)
h = 16328 / 1256
h = 13
LOOKS EASY !! NO FILES/LINKS THX
Answer:
16
Step-by-step explanation:
Comment if you want explanation
Answer: C. 16
Step-by-step explanation: multiply 12 and 16 to get 192. then subtract 192 to 6 to get 186.
Find the surface area. Show ALL your work!
Your aunt has baked 80 cookies, and she gave you 28 to take home with you. What percent of the cookies did she give to you? What percent of the cookies did she keep?
REMEMBER THAT THE RISE TESTS DO NOT GO TOWARDS YOUR GRADE, THEY ARE ONLY FOR THE SHOOLS TO SEE HOW WELL THEY ARE TEACHING YOU.
Remember that the Rise tests are only for your state. Different states have different tests. My state has the Peaks test.
Which set of ordered pairs is included in this relation?
A {(-5, 4), (-3, 2), (2, -1), (3, 0)}
B {(-4, 1), (-2, -5), (1, -2), (5, 2)}
C {(-3, -2), (0, 3), (1, -2), (4, 1)]
D {(-2,-5), (-1, 4), (2, -1), (3, 0)}
find x to the nearest 10th help pls
Answer:
5.9
Step-by-step explanation:
Find the measure of angle N
Help
Answer:
direct answer 20
Step-by-step explanation:
The function N(t) = 100e^−0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest?
Options:
A. [1,10] B. [10,20] C. [15,25] D. [1,30]
Answer:
A. [1,10]
Step-by-step explanation:
Given
[tex]N(t) = 100e^{-0.023t}[/tex]
Required
Interval with the fastest rate of decay
The rate of change over [a,b] is calculated as:
[tex]Rate = \frac{N(b) - N(a)}{b - a}[/tex]
So, we have:
A. [1,10]
[tex]Rate = \frac{N(10)-N(1)}{10 - 1}[/tex]
[tex]Rate = \frac{N(10)-N(1)}{9}[/tex]
Calculate N(10) and N(1)
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{79.45-97.73}{9} = \frac{-18.28}{9} = -2.03[/tex]
B. [10,20]
[tex]Rate = \frac{N(20)-N(10)}{20 - 10}[/tex]
[tex]Rate = \frac{N(20)-N(10)}{10}[/tex]
Calculate N(20) and N(10)
[tex]N(20) = 100e^{-0.023*20} = 100e^{-0.46} = 63.13[/tex]
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
So:
[tex]Rate = \frac{63.13 - 79.45}{10} = \frac{-16.32}{10} = -1.632[/tex]
C. [15,25]
[tex]Rate = \frac{N(25)-N(15)}{25 - 15}[/tex]
[tex]Rate = \frac{N(25)-N(15)}{20}[/tex]
Calculate N(25) and N(15)
[tex]N(25) = 100e^{-0.023*25} = 100e^{-0.575} = 56.27[/tex]
[tex]N(15) = 100e^{-0.023*15} = 100e^{-0.345} = 70.82[/tex]
So:
[tex]Rate = \frac{56.27 - 70.82}{10} = \frac{-14.55}{10} = -1.455[/tex]
D. [1,30]
[tex]Rate = \frac{N(30)-N(1)}{30 - 1}[/tex]
[tex]Rate = \frac{N(30)-N(1)}{29}[/tex]
Calculate N(30) and N(1)
[tex]N(30) = 100e^{-0.023*30} = 100e^{-0.69} = 50.16[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{50.16 - 97.73}{29} = \frac{-47.57}{29} = -1.64[/tex]
By comparing the values of the calculated rates,
-2.03 is the smallest, in other words; the fastest rate
Hence, the interval [1,10] has the fastest rate of decay
The required average rate of change is the fastest on [tex][1,10][/tex].
The average rate of change :The formula for the average rate of change on the interval [tex][a,b][/tex] is,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{b-a}[/tex]
Now, applying the given function into the above function is,
Now, [tex]a=1,b=10[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{10-1} =-2.03[/tex]
Now, [tex]a=10,b=20[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{20-10} =-1.6325[/tex]
Now, [tex]a=15,b=25[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{25-15} =-1.455[/tex]
Now, [tex]a=1,b=30[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{30-1} =-1.64[/tex]
So the average rate of change is fastest on [tex][1,10][/tex]
Learn more about the topic of the average rate of change:
https://brainly.com/question/20884505
NEED HELP ASAP!!! Which of the following shows the prime factorization of 72 using exponential notation?
A) 8x9
B)2^2 x 3^2
C)2 x 6^2
D)2^3 x 3^2
Answer:
D)2^3 x 3^2
Step-by-step explanation:
2 x 2 x 2 = 8
3 x 3 = 9
8 x 9 = 72
mike is training to run a marathon. currently, he can run 4 miles in 44 minutes. if he maintains this running speed, how long will it take him to run 10 miles?
Answer:
110 minutes or 1 hour 50 minutes
Step-by-step explanation:
44 divided into 4 since we want to find out how much time it takes to run 1 mile, so 44 divided into 4 is 11
then simply multiply 11 with 10 and the answer is 110
: )
plsssssssssssssssssssssssssssssssssss help
Answer:
m=10
n=12
Step-by-step explanation:
[tex]\frac{1}{5} m-\frac{1}{6} n=0\\m=\frac{5}{6} n\\5 \times \frac{5}{6} n-4n=2\\25n-24n=12\\n=12\\m=\frac{5}{6} \times 12=10[/tex]
125
21
Find the value of the missing angle
Answer:
146°.................plz mark me brainliest
La montaña más alta del mundo es Everest cuya altura es de 8.848m y la altura de la segunda montaña más alta es de 2hm 3dam y 7m menos ¿Cuantos metros de altura tiene la segunda montaña más alta del mundo
Answer:
La segunda montaña más alta del mundo tiene 8611 metros.
Step-by-step explanation:
La montaña más alta del mundo es Everest cuya altura es de 8.848m.
La altura de la segunda montaña más alta es de 2hm 3dam y 7m menos. Para calcular la altura que tiene la segunda montaña más alta del mundo, debes realizar primero un cambio de unidades sabiendo que
1 hm= 100 m1 dam= 10 mEntonces podes aplicar las siguientes reglas de tres simple:
Si 1 hm equivale a 100 m, 2 hm equivale a ¿Cuántos metros?
[tex]metros=\frac{2 hm*100 m}{1 hm}[/tex]
metros= 200
Si 1 dam equivale a 10 m, 3 dam equivale a ¿Cuántos metros?
[tex]metros=\frac{3 dam*10 m}{1 dam}[/tex]
metros= 30
Entonces, la altura de la segunda montaña más alta es de 200 m+30 m+ 7 m menos que el Everest. Esto es, 237 metros menos que la montaña más alta del mundo. Entonces:
8848 metros - 237 metros= 8611 metros
La segunda montaña más alta del mundo tiene 8611 metros.
The Wheelers’ bill at a restaurant is $63.00. How much total money is Mr. Wheelers' lunch if he plans to tip 15%?
asap besties
we know that
when you want to figure out a tip, you take your total bill and multiply it by the percentage you would like to tip them
so
15%=15/100------> 0.15
$63*0.15=$9.45
the answer is
$9.45
A plane is at cruising altitude of 10,200 feet. If the angle of depression to the run way is 18 degrees, what is the distance, to the nearest foot, from the plane to the run way
Answer: [tex]33,007.9\ ft[/tex]
Step-by-step explanation:
Given
The plane is cruising at an altitude of [tex]h=10,200\ ft[/tex]
The angle of depression is [tex]\theta=18^{\circ}[/tex]
Suppose the distance of the plane to the runway is x
from figure
[tex]\Rightarrow \sin 18^{\circ}=\dfrac{h}{x}\\\\\Rightarrow \sin 18^{\circ}=\dfrac{10,200}{x}\\\\\Rightarrow x=33,007.9\ ft[/tex]
Solve the system of equations. 2y-y=5 and 3x+2y=4
Answer:
Step-by-step explanation:
Answer:
y=5 x=-2
Step-by-step explanation:
pls help asap will make brainliest
Answer:
,,,,,,,,,,,,,,,,,,,,
A bird is 50 feet above sea level, a fish is swimming 23 feet below sea level. What's the distance between the bird and the fish
Answer:
73 feet
Step-by-step explanation:
50 + 23 = 73 feet
Write an equation equivalent to 0.127
Answer:
127x10^-3
Step-by-step explanation:
0.127=
[tex]127 \times {10}^{ - 3} [/tex]
The density of an object is equal to the quotient of its mass, and volume. An object has a density of 10g per liter and a volume of 40 liters. What is its mass in grams.
Answer:
400 grams
Step-by-step explanation:
If the equation is density = mass / volume, fill it out to find mass
10 = x / 40
400 = x
x = 400 g
What is the point-slope form of a line with slope 2 that contains the point
(1,3)?
Answer:
(y-3) = 2(x-1)
Step-by-step explanation:
Point slope form is
(y-y1) = m(x-x1) where m is the slope and (x1,y1) is a point on the line
(y-3) = 2(x-1)
A pair of jeans regularly sells for $24.00. They are on sale for 25% off. What is the sale price of the jeans.
Answer:
24 x 25/100 = 6
of means multiplication so you are multiplying the percent to the regular price. Always consider cent as a hundred and a percent out of 100 in fractions.
Answer:
18 dollars
Step-by-step explanation:
half of 24 is 12 and half of that is 6 so 24-6=18 :)
sorry for the color yellow
Answer:
I believe it's the first option.
-2 (7– 5x – 3) = -2(7 + -5x x +
-14 +
10 х +
=
-14 +
10 х
+
10 х
Answer:
Step-by-step explanation:
make the question clearer homie urs makes no sense
whts 5/8 - 2/4
plz help will mark brainliest
and i will give 30 points
Answer:
5/8 - 2/4 = 1/8
(Hope this helps! Btw, I answered first. Brainliest please! :D)
find the original price of a pair of gloves that is 28$ after a 30% discount?
Answer:
$40
Step-by-step explanation:
Find the original price by dividing 28 by 0.7
28/0.7
= 40
So, the original price was $40
8/9÷3= 7/8 1/5 8/27 2/3