By solving given equation and then finding discriminant we get that this system of equations have 2 solutions
What is system of equations?Collection of two or more equations with a same set of unknowns is called system of equations.
Given equation
[tex]$$y=-2 x+2\ \ ...(1)\\\\y=x^{2}-3 x$$\ \ \ ...(2)[/tex]
From equation (1) and (2)
[tex]x^{2}-3 x=-2 x+2\\\\x^{2}-3 x+2 x-2=0\\\\x^{2}-x-2=0[/tex]
This is a quadratic equation
So discriminant
[tex]D=b^2-4ac[/tex]
[tex]D=(-1)^2-4(1)(-2)\\D=1+8\\D=9[/tex]
As D is >0 so we will get two values of x
and two values of y corresponding to values of x
By solving given equation and then finding discriminant we get that this system of equations have 2 solutions
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n=3;
-3 and 9 + 2i are zeros;
f(2)=265
Answer:
6 inches wide and a row of 7 stamps how wide is each stamp
Which of the following lists is in order from smallest to largest?
2/11, 0.1, 1/9, 1.1%
1/9, 0.1, 1.1%, 2/11
1.1%, 0.1, 1/9, 2/11
0.1, 1/9, 2/11, 1.1%
Answer:
D because 1.1% is the smallest percent of them all
Find the slope of intercept of the line that passes through (-3,-5) and has a slope of 1/3
Consider the intial value problem 2ty' = 4y, y(1) = -2.
Answer:
y+-2t^2
Step-by-step explanation:
Solve the inequality for x. 1/2 x − 2 > 22
A) x > 12
B) x > 48
C) x > −12
D) x > −48
B is correct
1/2x-2>22
Remember 1/2=0.5
We write the equation as
0.5x-2 >22
Collect like terms
0.5x > 22+2
0.5x>24
Divide through by 0.5
X>24/0.5
X>48
Option b
Answer:
B x > 48
Step-by-step explanation:
1/2x -2 >22
Mulitply both sides of the inequality by 2
x - 4 > 44
Move the constant to the right
x > 44+4
Add the numbers
x>48
The internal dimensions of a fuel can
are:
10 cm by 20 cm by 25 cm.
What is its capacity in litres?
The capacity of this fuel can is equal to 5 liters.
Given the following data:
Length = 10 cm.Width = 20 cm.Height = 25 cm.To calculate the capacity of this fuel can in litres:
How to calculate the capacity of the fuel can.In order to calculate the capacity of this fuel can, we would determine its volume by using this formula:
[tex]Volume = length \times breadth \times height[/tex]
Substituting the given parameters into the formula, we have;
[tex]Volume = 10 \times 20 \times 25[/tex]
Volume = 5,000 [tex]cm^3[/tex].
In liters:
1 [tex]cm^3[/tex] = 0.001 liters.
5000 [tex]cm^3[/tex] = 5 liters.
Capacity = 5 liters.
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Graph this function:
y + 3 = -5(x + 8)
Click to select points on the graph.
A boat is tracking the depths of four divers, as recorded below in the chart. Which diver is farthest from the surface? Audrey What is the depth of the shallowest diver? −10 meters. What is the distance between Steve Z. And Audrey? −53 meters. There is a GPS buoy for fishermen located 30 meters below the surface. How far is Jacques from the buoy? 48 meters
Answer:
Which diver is farthest from the surface? Dave
What is the depth of the shallowest diver? 12.67
What is the distance between Steve Z. and Audrey? 51
There is a GPS buoy for fishermen located 30 meters below the surface. How far is Jacques from the buoy? 1072
Step-by-step explanation:
by solving for v you have to divide 1072 by 12.67 and you get 84.6093133386 so you multiply 51 by 84.6093133386and you get 4315.07498027so you answer is 4315.07498027
(04.03 MC)
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 8(1.05)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent? (4 points)
(10 points)
Answer:
A) 0 ≤ n ≤ 7
B) initial height of plant = 8 cm
C) average rate of change = 0.475 cm/day.
Plant grew an average of 0.475 cm per day from day 2 to day 6
Step-by-step explanation:
[tex]f(n)=8(1.05)^n[/tex]
Part A
Given height = 11.26 cm
[tex]\implies 8(1.05)^n=11.26[/tex]
[tex]\implies(1.05)^n=\dfrac{11.26}{8}[/tex]
[tex]\implies(1.05)^n=1.4075[/tex]
Taking natural logs:
[tex]\implies \ln(1.05)^n=\ln(1.4075)[/tex]
[tex]\implies n\ln(1.05)=\ln(1.4075)[/tex]
[tex]\implies n=\dfrac{\ln(1.4075)}{\ln(1.05)}[/tex]
[tex]\implies n=7.005819448[/tex]
[tex]\implies n \approx7[/tex]
Therefore, the scientist concluded his study after 7 days, so the domain is 0 ≤ n ≤ 7
Part B
y-intercept is when the curve intersects the y-axis (when n = 0):
[tex]\implies f(0)=8(1.05)&^0=8\times1=8[/tex]
The y-intercept represents the initial height of the plant, which is 8 cm
Part C
Rate of change = change in y ÷ change in x
⇒ rate of change = change in f(n) ÷ change in n
[tex]\implies f(2)=8(1.05)^2=8.82[/tex]
[tex]\implies f(6)=8(1.05)^6=10.72076513...[/tex]
[tex]\implies \textsf{rate of change} \ =\dfrac{f(6)-f(2)}{6-2}=0.4751912813...[/tex]
So the average rate of change was 0.475 cm/day. This indicates that the plant grew an average of 0.475 cm per day from day 2 to day 6 (over a period of 4 days).
ETA: please see attached graph. The gray dotted curve is the function, and the black solid curve is the function with the restricted domain of 0≤n≤7 since the study took 7 days.
Solve the system of equations y = 6x -7
y = 3x + 11
The solution of the given equation will be y = 29 and x = 6.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If they both are equal to y, they must be equal to each other, therefore,
6x-7 = 3x+11
3x = 18
x=6
Y = 6x - 7
y = 6 x 6 - 7
y = 36 - 7
y = 29
Therefore the solution of the given equation will be y = 29 and x = 6.
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3 times 1 times 5/3 pleaseeeeeee helpppp
Answer:
5
Step-by-step explanation:
3*1*5/3=5
Classify Angle 5 & Angle 6 by choosing the correct term from the choices below.
A) complementary
B) vertical
C) adjacent
D) supplementary
Answer:
Vertical is the answer.
Step-by-step explanation:
The total bill for the drinks and pizza comes out to be $17.28. How much should each person pay if they are to share the total bill equally among the three of them?
pls help yall are soo smart
Answer:
5.76
Step-by-step explanation:
17.28/3
Select the correct answer. A square field has an area of 10 square miles. What is the approximate length, to the nearest thousandth, of one side of this field? A. 2. 5 miles B. 3 miles C. 3. 162 miles D. 3. 612 miles.
The approximate length, to the nearest thousandth, of one side of this field is 3.162 miles. Then the correct option is C.
What is a square?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a square, opposite sides are parallel and all sides are equal and each angle is 90 degrees. And its diagonals are also equal and intersect at mid-point at right-angle.
A square field has an area of 10 square miles.
Let the side of the square be x.
We know that the area of the square will be
[tex]\rm (Side)^2 = Area[/tex]
Then we have
[tex]\rm x^2 = 10\\\\\rm x \ = \sqrt{10}\\\\\rm x \ = 3.162[/tex]
The approximate length, to the nearest thousandth, of one side of this field is 3.162 miles. Then the correct option is C.
More about the square link is given below.
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PLEASE SOLVE ASAP I WILL CROWN BRAINLIST
B
To find the area you multiply width times height, here for the bigger rectangle, to find the area you multiply 7*6 and then add that with 6 * x because those are the width and height of the smaller rectangle.
Second part
I believe that Wiliam chose C because he accidentally thought that adding everything was correct. He added 7+6 to get 13 for the bigger rectangle and then for the smaller rectangle decided that to find the area you would add 6 and x.
Answer:
Step-by-step explanation:
a, b and d all represent the combined area of the gardens
(6*7) + (6*x) is equivalent to 6(7+x) and 42 + 6x
Check:
(6*7) + (6*x)
42 + 6x
6(7+x)
42 + 6x
42 + 6x
William chose C because he added the length and width of the vegetable garden (7 + 6 = 13), and then added the length and width of the flower garden (6 + x = 6 + x).
Hope this helps!
What is the value of (32)4 ?
Answer:
128
Step-by-step explanation:
15×30
Select each correct answer.
There were 30 people in a room. One-fifth of the people had blue eyes. How many people had blue eyes?
Evan's mother drove 30 miles on Wednesday and another 15 mile on Wednesday. How many miles did she drive in all?
Jada had 30 crayons. She lost 15 of the crayons. How many crayons does she have left?
Amelie read 30 pages of a book. She read 15 of the pages on Monday. How many pages did she read on Monday?
Answer:
6 people had blue eyes
45 miles
15 crayons
15 pages
Step-by-step explanation:
Q: There were 30 people in a room. One-fifth of the people had blue eyes. How many people had blue eyes.
A: total number of people x 1/5 = 30 x 1/5 = 6
Q: Evan's mother drove 30 miles on Wednesday and another 15 mile on Wednesday. How many miles did she drive in all?
A: total miles = 30 + 15 = 45 miles
Q: Jada had 30 crayons. She lost 15 of the crayons. How many crayons does she have left?
A: total number of crayons - number lost = 30 - 15 = 15 crayons left
Q: Amelie read 30 pages of a book. She read 15 of the pages on Monday. How many pages did she read on Monday?
A: 15 pages, as the question states "She read 15 of the pages on Monday"
ANSWER:
450
6 of them had Blue eyes
Evan's mother drove 45 miles in total.
Jada had 15 crayons left
Amelie read 15 pages on monday.
Dolores spent $13.00 of the $20.00 in her wallet. Which decimal represents the fraction of the $20.00 Dolores spent? Answer in a complete paragraph
Answer:
0.65 can I have branliest please?
A university has 39,930 students. in a random sample of 270 students, 18 speak three or more languages. predict the number of students at the university who speak three or more languages.
Answer:
65 students speak 3 or more languages
Step-by-step explanation:
HELP ME QUICKLY LLEASE IM BEGGING ANYONE ESS
Which source is the most credible?
A. New guidelines from the government about how much sugar
people should eat
B. A report by the sugar industry saying sugar can be a safe and
healthy part of people's diets
C. An article from 2001 stating that diets high in fat are more harmful
than diets high in sugar
D. A blog by someone who worked hard to remove sugar from her
diet and now feels much more energetic
Step-by-step explanation:
Option C. Even though it's not Mathematics
Answer:
A. It's new, so it's recent and probably more applicable
Daniel is able to land his backflip 60% of the time. He tells his friend that in his next 5 backflips, he will land more than 3 of them. To estimate the probability of this happening, Daniel uses a computer to randomly select 5 numbers from 1 through 5. He lets 1 through 3 represent landing his backflip and 4 and 5 represent not landing it. He repeats this for a total of 22 trials and records the results in the table below. 43113 43323 21245 53154 11545 44511 45221 14221 11123 55131 24535 35133 21454 41314 55242 52214 53542 15231 31244 54541 31415 52522 What is the best estimate, based on this simulation, of the probability that in his next 5 backflips Daniel will land more than 3 of them? 27% 39% 41% 68%.
The best estimate, based on this simulation, of the probability that in his next 5 backflips Daniel will land more than 3 of them is 27%.
Given
Daniel is able to land his backflip 60% of the time.
He tells his friend that in his next 5 backflips, he will land more than 3 of them.
Daniel uses a computer to randomly select 5 numbers from 1 through 5. He lets 1 through 3 represent landing his backflip and 4 and 5 represent not landing it.
He repeats this for a total of 22 trials and records the results in the table below.
43113 43323 21245 53154 11545 44511 45221 14221 11123 55131 24535
35133 21454 41314 55242 52214 53542 15231 31244 54541 31415 52522
Probability;Probability is defined as the number of trials in which he landed more than three times/Total number of trials.
Let, p denotes the probability of an event.
The best estimate, based on this simulation, of the probability, that in his next 5 backflips Daniel will land more than 3 of them is;
[tex]\rm Probability=\dfrac{6}{22} \times 100\\\\Probability =\dfrac{600}{22}\\\\Probability=27[/tex]
Hence, the best estimate, based on this simulation, of the probability that in his next 5 backflips Daniel will land more than 3 of them is 27%.
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Pls hurry ASAP! U will get Brainly
Answer:
- 9 and 28
Step-by-step explanation:
substitute the given values for x, y, z into the expressions
1
- (3 - 2) - 4(3 + 1) + 1 + (2(3) + 2)
= - 1 - 4(4) + 1 + 6 + 2
= - 1 - 16 + 9
= - 17 + 9
= - 8
2
4(2) - 6(- 3 + 1²) + 4(2)
= 8 - 6(- 3 + 1) + 8
= 8 - 6(- 2) + 8
= 8 + 12 + 8
= 28
Answer:
-8 28Step-by-step explanation:
You want to evaluate these expressions when (x, y, z) = (3, 2, 1).
-(x -y) -4(x +z) +z +(2x +y)4y -6(-x +z²) +4ySimplifyWe find it easier to evaluate the expression when it is simplified to a form that minimizes that amount arithmetic we need to do. So, our evaluation does that first. Then the corresponding values are put where the variables are in the expression, and the arithmetic is carried out.
1.Simplifying, we find the sum to be ...
-x +y -4x -4z +z +2x +y = x(-1-4+2) +y(1+1) +z(-4+1)
= -3x +2y -3z = 2y -3(x +z)
= 2(2) -3(3 +1) = 4 -12
= -8
2.Simplifying, we find the sum to be ...
4y +6x -6z² +4y
= 6x +8y -6z²
= 6(x -z²) +8y
= 6(3 -1²) +8(2) = 12 +16
= 28
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Are the 2 triangles similar? how do you know?
Answer:
Yes
Step-by-step explanation:
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar
I need help with number 19
Answer:
Step-by-step explanation:
A tangent to a circle always meets a diagonal of a circle at right angles.
w = 90
What’s the answer?????
Answer:
324
Step-by-step explanation:
a
2
a
1
=
12
4
=
3
a
3
a
2
=
36
12
=
3
⇒
common ratio
=
r
=
3
and first term
=
a
1
=
4
no: of terms
=
n
=
9
Sum of geometric series is given by
S
u
m
=
a
1
(
1
−
r
n
)
1
−
r
⇒
S
u
m
=
4
(
1
−
3
9
)
1
−
3
=
4
(
1
−
19683
)
−
2
=
−
2
(
−
19682
)
=
324
Solve this multistep equation: 3x+20 = x + 30
Answer:
x=5
Step-by-step explanation:
Subtract 20
from both sides of the equation
2
Simplify
Subtract the numbers
Subtract the numbers
3
Subtract x
from both sides of the equation
Answer:
X = 5
Step-by-step explanation:
To solve for x, you need to get x to one side and everything else to the other side.
3x+20=x+30
Since there is only one positive x on the right, we can subtract it from both sides. This moves it over.
2x+20=30
Since there is a +20 on the same side we put our x, we need to subtract it from both sides to move it over.
2x = 10
Now x is being multiplied by 2. To get rid of it, we divide both sides by 2.
x = 5
A car costs $25,750.00 and depletes in value by 20% per year. How much would the car be worth after 5 years?
A) $5,150
B) $8,437.76
C) $8,240
D) $20,600
Answer : B
First year : 25750 x 80% = 20600
Second year : 20600 x 80% = 16480
Third year : 16480 x 80% = 13184
Fourth year : 13184 x 80% = 10547.2
Fifth year : 10547.2 x 80% = 8437.76
I need help on 8 9 and 10
9. x + (y - 3 - 4x + 2( 3x - (-y - 1) + 2y) - 3x)
= x + (y - 3 - 4x + 2 (3x + y - 1) + 2y - 3x)
= x + (y - 3 - 4x + 6x + 2y - 2 + 2y - 3x)
= (x - 4x + 6x - 3x) + (y + 2y + 2y) - (3+2)
= 0 + 5y - 5
= 5y - 5 (or simplified as 5(y-1)
10. 6 + (-a -3(b + 6(a - b)+4a) - 2b)
= 6 + (-a - 3(b + 6a - 6b + 4a) -2b)
= 6 + (-a - 3b + 18a - 18b + 12a - 2b)
= 6 + (-a + 18a + 12a) + (-3b - 18b - 2b)
= 6 + 29a - 23b
Lmk if it's wrong, I'll try to edit it.
If the square root of x square + nine equal to x +1 solve for x
Answer:
Simplify square root of x^2-9
√
x
2
−
9
Rewrite
9
as
3
2
.
√
x
2
−
3
2
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
x
and
b
=
3
.
√
(
x
+
3
)
(
x
−
3
)
Please help!!!
Please answer two of these questions and I’ll give 20 points!!
12. In a Fibonacci sequence, every term (except the first two) is the sum of the two
preceding terms. For example, 1, 1, 2, 3, 5, 8, 13, 21, ... is a Fibonacci sequence.
Find the sixteenth term of a Fibonacci sequence whose first two terms are -3 and 9.
13. If you buy 31 floops, the total cost will be less than 40$. But if you buy 32 floops, the total cost will be more than 41$. Assuming these prices do not involve tax, what is the cost of one floop?
12. If the first two terms of the sequence are -3 and 9, the next few terms are
-3 + 9 = 6
9 + 6 = 15
6 + 15 = 21
15 + 21 = 36
and so on. Continuing in this way, you'd find the 16th term to be 4359.
13. Let x be the cost of 1 floop.
31 floops cost less than $40, so 31x < 40 or x < 40/31.
32 floops cost more than $41, so 32x > 41 or x > 41/32.
Equivalently,
41/32 < x < 40/31
and
41/32 ≈ 1.28125
40/31 ≈ 1.29032
which means x = $1.29.
