Answers
Since both of these equations have y isolated, we can set them equal to each other:
2x=x²-3
We want all of the variables on one side, so subtract 2x:
2x-2x = x²-3-2x
0=x²-3-2x
Write the quadratic in standard form:
0=x²-2x-3
This is easily factorable, as there are factors of -3 that will sum to -2. -3(1)=-3 and -3+1=-2:
0=(x-3)(x+1)
Using the zero product property we know that either x-3=0 or x+1=0; therefore x=3 or x=-1.
Substituting this into the first equation (it is simpler):
y=2(3) = 6
y=2(-1)=-2
Therefore the coordinates are (3, 6) and (-1, -2).
Answer:
(x1, y1)=(-1, -2)
(x2, y2)=(3, 6)
Step-by-step explanation:
y=2x
y=x^2-3
Since both of the expressions 2x and x^2-3 are equal to y, set them equal to each other forming an equation in x
2x=x^2-3
solve the equation for x
x=-1
x=3
Substitute the given value of x into the equation y=2x
y=2 x (-1)
x=3 y=2 x 3
Solve the equation for y
y=-2
y=2 x 3 y=6
The possible solutions of the system are the ordered pairs (x, y)
(x1, y1)=(-1, -2)
(x2, y2)=(3, 6)
Check if the given ordered pairs are the solutions of the system of equations
-2=2x(-1)
-2=(-1)^2-3
6=2x3
6=3^2-3
Simplify the equalities
-2=-2
-2=-2
6=2x3
6=3^2-3
-2=-2
-2=-2
6=6
6=6
Since all of the equalites are true, the ordered pairs are the solution of the system
(x1, y1)=(-1, -2)
(x2, y2)=(3, 6)
Related Questions
Justin is working with a microscope that magnifies objects to 175 times their actual size.
Part A
Enter a number in each box to determine the scale factor for the microscope.
Part B
The diameter of an amoeba cell is 0.30 millimeter. How big will the cell appear to Justin under the microscope?
millimeters
Part C
What is the percent increase of the area of the amoeba cell under the microscope?
%
Answers
Answer:
Part A
Scale factor
= 1 : 175
Part B
52.5 mm
Part C
99.4%
Step-by-step explanation:
Justin is working with a microscope that magnifies objects to 175 times their actual size.
Part A
Enter a number in each box to determine the scale factor for the microscope.
= 1 : 175
Part B
The diameter of an amoeba cell is 0.30 millimeter. How big will the cell appear to Justin under the microscope?
Scale factor =
1 : 175
Diameter of the Amoeba cell = 0.3mm
1mm = 175 mm
0.3mm = x
Cross Multiply
x = 0.3 × 175
x = 52.5 mm
Part C
What is the percent increase of the area of the amoeba cell under the microscope?
Increase = 52.5 mm - 0.3mm
= 52.2 mm
Percent increase
= 52.2/52.5 × 100
= 99.4%
A type of electric car can travel 5 on 1 kilowatt hour of electricity. How many kilowatt hours of electricity would it take Helen to drive her electric car to her aunts house and back? Helen lives 70 miles from her aunt.
Answers
Answer:
28 kwh
Step-by-step explanation:
given that the care can travel 5 miles on 1 kwh, i.e
5 miles travelled -----> uses 1 kwh
hence to find the unit rate:
1 mile travelled ----> Uses 1 kwh ÷ 5 = 1/5 kwh
We are also given that Helen lives 70 miles away from her aunt.
Hence a return trip (i.e "to aunts house and back"), will be 70 x 2 = 140 miles
using the unit rate that we found above, we can find the number of kwh that is used to travel 140 miles
140 miles = 140 miles x unit rate
= 140 x 1/5
= 28 kwh
Which statement best describes the area of Triangle ABC shown below? A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 6, vertex B is on ordered pair 6 and 1, and the vertex C is on ordered pair 2 and 1. It is twice the area of a rectangle of length 4 units and width 5 units. It is one-half the area of a rectangle of length 4 units and width 5 units. Correct Answer It is twice the area of a square of side length 5 units. It is one-half the area of a square of side length 5 units.
Answers
Answer:
The answer would be... It is one-half the area of a rectangle of length 4 units and width 5 units.
Step-by-step explanation:
Answer:
1 half rectangle
Step-by-step explanation:
will give brainliest for right answer
Answers
Answer:
radius-5mm
diameter-10mm
circumference- 31.42mm
Classify the quadrilateral then find the values of the variable (s) PLS HELPPP
im stuck
Answers
Answer:
basic math?
pre algebra?
algebra?
trigonometry?
pre calculus?
or
calculus?
5c -4c +с - 3с
Help please
Answers
Answer:
cannot factor
Step-by-step explanation:
Because they cannot be factored in any other way, we say that they cannot be factored.
Answer:
-2c
Step-by-step explanation:
5c -4c +с - 3с
-1c+c-3c
c-3c
-2c
A data set consists of 2, 2, 3, 4, 5, 5, and 7. Then, 20 is added to the data set. The new value will have little effect on the , but it will raise the significantly.
Answers
Answer:
Median; mean.
Step-by-step explanation:
A data set consists of 2, 2, 3, 4, 5, 5, and 7. Then, 20 is added to the data set. The new value will have little effect on the median, but it will raise the mean significantly.
Let's find the median and mean from the original data;
x = 2, 2, 3, 4, 5, 5, 7.
F(x) = 2 + 2 + 3 + 4 + 5 + 5 + 7
F(x) = 28
[tex] Mean = \frac {F(x)}{7} [/tex]
[tex] Mean = \frac {28}{7} [/tex]
Mean = 4
Median is the middle number of a sorted array of numbers.
Median = 4
Now, let's find the median and mean from the new data;
x = 2, 2, 3, 4, 5, 5, 7, 20.
F(x) = 2 + 2 + 3 + 4 + 5 + 5 + 7 + 20
F(x) = 48
[tex] Mean = \frac {48}{6} [/tex]
Mean = 8
[tex] Median = \frac {4 + 5}{2} [/tex]
Median = 4.5
Therefore, the median increased from 4 to 4.5 while the mean increased significantly from 4 to 8.
Solve each system by elimination.
- 6r – 6y = -18
-5r + 8y = 24
Answers
Answer:
Step-by-step explanation:
30r + 30y = 90
-30r + 48y= 144
78y = 234
y = 3
-6r - 6(3) = -18
-6r - 18 = -18
-6r = 0
r = 0
(0, 3)
Please Help!!!
Find the value of x.
B
8
4
С
N
D
X
x = [?]
Enter
Answers
Answer:
x = 3
Step-by-step explanation:
This answer will be about a day late, but I hope you can take something from it.
The scale factor is 6:8, or 3:4.
3/4 × 4 = 3
OR: Set Up A Proportion:
[tex] \frac{6}{x} \times \frac{8}{4} [/tex]
cross-mutliply
8x = 24
x = 3
Easy question.
You love the power you feel behind the wheel, and you want to see what it feels like to drive fast. You get your chance while driving alone
in the car. The speed limit is 55 mph, but there's no traffic on the road. What will you do?
Answers
I would continue to follow the speed limit in order to minimise any risk brought on by the unexpected arrival of any object on the road.
Give brief account on speed and road safety?Many aspects of people's speed behaviour are also influenced by their personalities, such as their desire for thrills, propensity for aggression, and chaotic lifestyles. Because they believe they need to drive faster to make up for their poor time, speeders can be especially pressed for time.
By using the following defensive driving strategies, you can lower your risk of driving:
Put safety firstBe aware of your surroundings - be carefulDo not rely on other driversFollow the 3-4 second rulePlease slow downHave an escape routeEliminate distractionsTo know more about speed, visit:
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not sure how to use a ruler like you know how they have the
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-
-
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----
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-
-
-
----
lik what do thos little lines mean. and what is there fraction
Answers
PLEASE HELP!!! WILL MARK BRAINLIEST!!!
Name each transformation correctly as a Translation, Dilation, or Reflection.
WILL MARK BRAINLIEST IF CORRECT!!!!!!
Answers
Answer:
Translation:
6 and 12Dilation:
1, 2, 4, 5, 11, 13, 14, 15, 16Reflection:
3, 11, 13, note 11 and 13 have both dilation and reflection Arrange the following in order from strong negative to strong positive.
Answers
Step-by-step explanation: It would be D - C
classify the polynomial
2x^5-3x^2-6
Answers
Answer:
A polynomial is a combination of terms separated by + or − signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms
Step-by-step explanation:
which most likely indicates a chemical change has occurred?
Answers
Oceanside Bike Rental Shop charges a $14 fixed fee plus $8 an hour for renting a bike. Tim paid
$86 to rent a bike. How many hours did he rent the bike? Write and solve an algebraic equation to
find the answer. Be sure to identify your variable. (7.EE.4)
Answers
Answer:
10.75 hours
Step-by-step explanation:
h= Hours 86divided by 8 = h= 10.75
the measure of the angles in a heptagon measure 95 107 132 138 145 and 158 what is the measure of the 7th angle
Answers
Answer:
ANSWER:123
Step-by-step its very simple its puttin x+11 is how u get ur answer by adding the numbers close to that one angle
The measure of the seventh angle in the heptagon is 125 degrees.
What is Polygon?A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
We are given the measures of six angles in the heptagon, which are:
95, 107, 132, 138, 145, and 158 degrees
Sum of angles in Heptagon is 900 degrees.
To find the measure of the seventh angle, we can subtract the sum of the six known angles from the sum of all the angles in the heptagon:
Measure of the seventh angle = Sum of angles - Sum of known angles
Measure of the seventh angle = 900 degrees - (95 + 107 + 132 + 138 + 145 + 158) degrees
Measure of the seventh angle = 900 degrees - 775 degrees
Measure of the seventh angle = 125 degrees
Therefore, the measure of the seventh angle in the heptagon is 125 degrees.
To learn more on Polygons click:
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3m-19=14
what it be???
Answers
Answer:
m=11
Step-by-step explanation:
Add 19 to both sides.
3m−19+19=14+19
3m=33
Divide both sides by 3.
3m/3=33/3
m=11
Answer:
m=11
Step-by-step explanation:
We want to isolate m on the left side of the equation.
3m-19=14; add 19 to both sides, now you have:
3m=33; divide 33 by 3:
m=11
The crew is taking 80 liters of water. There are 4 people on the crew. How many milliliters of water does each person get?
Answers
Answer:
Each people get 20,000 mili-litres of water.
Step-by-step explanation:
As , we know that
1 litre = 1000 mili-litre
As we have 80 litre of water
⇒ 80 litres = 80×1000 mili-litres
= 80,000 mili-litres
⇒ 80 litres = 80,000 mili-litres
∴ we have
Total water available in the crew = 80,000 mili-litres
As , there are 4 people in the crew
Let each people consume x mili-litre
⇒4x = 80,000 mili-litres
⇒x = [tex]\frac{80,000}{4} = 20,000[/tex] mili-litres
∴ we get
Each people gets 20,000 mili-litres of water.
Rewrite in simplest terms: 8(-10r - 9) + 9r
Answers
Answer:
-2
Step-by-step explanation:
you answer the brackets first then add 9 then add 8
Is the function linear or non linear?
Answers
Answer:
The function Has to Be Linear.
Step-by-step explanation:
The reason why the function has to be linear is because even though there is a slight curve the rest of the line is straight.
You need to look at the direction the line is pointing. Now say it was a line that had all kinds of wavey curves and loops that would be nonlinear.
I hope this helps you out. Let me know if linear is the correct answer, because if it isn't then that Assessment is crazy.
You have a Good day.
Signed, Coolnewman06
Can you help me out with this math problem? Please Simplify: (4 – 5) – (13 – 18 + 2). Show your work on how you got it.
(a) -1,
(b) –2,
(c) 1,
(d) 2.
Answers
Answer:
2
Step-by-step explanation:
(4-5)-(13-18+2)
=-1-(13-18+2)
=-1-(-5+2)
=-1(-3)
=2
please help me!!!!! urgent!!!!
Answers
Answer:
It is d it is a scalene
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
What is the complement of 45?
Answers
Answer:
45°
Step-by-step explanation:
If sum of two angles is 90° , then they are called complementary angles.
Complement of 45 = 90 - 45 = 45
state if polygons are similar
Answers
Can you help me plz.
Answers
Answer:1.885 miles
Step-by-step explanation:Do 0.58 times 3.25 which gives you 1.885.
Hope it helps :)
Answer:
1.885
Step-by-step explanation:
Mutiply 0.58 which is the miles per lap by 3.25 which are the number of laps Jessica walked
0.58*3.25=1.885
Andrew calculates that 40% of 50% of x is equal to 20% of 30% of y where x ≠ 0
which of the following is true
a) y equals 2x/3
b) y equals 4x/3
c) y equals 2x
d) y equals 8x/3
e) y equals 10x/3
Answers
1468
33
6
5
Step-by-step explanation:
1537825227
2382
Answer:
y=10x/3
Step-by-step explanation:
1a) simplify (8x)^2
Answers
Answer:
[tex] 64 {x}^{2} [/tex]
Step-by-step explanation:
[tex] {(8x)}^{2} = {8}^{2} . {x}^{2} = 64 {x}^{2} [/tex]
Aisha types 3/5 of a paragraph in 2/3 minute. If she continues at the same rate, what fraction of a paragraph can Aisha complete in 1 minute?
Answers
She competes 9/10 of a paragraph per minute.
Aisha complete 9/ 10 of a Paragraph in 1 minute.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Aisha types 3/5 of a paragraph in 2/3 minute.
So, In one minute she types
= 3/5 ÷ ( 2/3)
= 3/5 x 3/2
= 9/ 10 Paragraph
Learn more about fraction here:
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What proportion can be used when there is a %, the word "is" and the "of" in a problem?
Answers
Answer:
C. is / of = % / 100Step-by-step explanation:
We can interpret this as:
x% of y is zCalculation is:
x*y/ 100 = zTranslate this into the given format:
% * of / 100 = is ⇒ % / 100 = is / ofThis matches option C