sylvie finds the solution to the system of equations by graphing.
y=2/3x+1 and y=-2/3x-1
which graph shows the solution to sylvie’s system of equations?
a) graph 1
b) graph 2
c) graph 3
d) graph 4
Answers
Point 3,3 satisfies y=2/3x+1
Answer:
solution is (-1.5,0)
Graph 3
Step-by-step explanation:
[tex]y=\frac{2}{3}x+1[/tex]and [tex]y=-\frac{2}{3}x-1[/tex]
In the first equation [tex]y=\frac{2}{3}x+1[/tex]
slope = 2/3 and y intercept is 1
Lets start with graphing y intercept +1
then we slope , move 2 units up and 3 units to the right. stop at (3,3)
Now we graph the second equation
[tex]y=-\frac{2}{3}x-1[/tex]
slope = -2/3 and y intercept is -1
Lets start with graphing y intercept -1
then we slope , move 2 units down and 3 units to the right. stop at (3,-3)
both graph intersects at a point (-1.5,0)
Related Questions
Two angles that are complementary __________ form a right angle. 2. angles with a common side and a common vertex ______ form a linear pair. 3. two angles that are supplementary are _______ complementary.
Answers
if an angle is acute then its measure is 30 degrees true or false
Answers
An acute angle is any angle less than 90 degrees, and while 30 degrees is an example of an acute angle, it is not accurate to say that all acute angles must be 30 degrees.
Explanation:The statement 'If an angle is acute then its measure is 30 degrees' is false. An acute angle is defined as any angle that is less than 90 degrees. While 30 degrees is indeed an example of an acute angle, an acute angle can be any value less than 90 degrees. For example, 45 degrees, 20 degrees, or 1 degree are also acute angles. Therefore, it is not accurate to say that an acute angle must be 30 degrees.
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What is the difference between 3/7 and 1/14
Answers
3/7 = 6/14
6/14 - 1/14 = 5/14
hope this helps
The width of a poster is 4/5 of its length, It takes 36 ft. of metal framing to frame the poster. Find the dimensions of the poster.
Answers
If EG=40 and point F is 2/5 of the way between E and G, find the value FG.
The drawing is not to scale.
a. 32
b. 20
c. 16
d. 24
Answers
Point F (EF) = 2/5
EF = 2/5 × 40
EF = 16
EF + FG = EG
16 + FG = 40
FG = 24
d. 24
Roger can run one mile in 10 minutes. jeff can run one mile in 8 minutes. if jeff gives roger a 1 minute head start, how long will it take before jeff catches up to roger? how far will each have run?
Answers
Oranges are on sale for $1.59 per pound. Write a funtion as a standard equation and in a funtion notation.
Answers
f(x) = 1.59x
Help please pre calculus
Answers
put 7.6*10^-1 into the equation to get:
10log(1/7.6*10^-4) = 31.19
3.Cornelia spends 2 2/3 hours studying for her big science test. She spent 2/3 of an hour finishing her writing assignment and 1/4 of an hour playing outside. How much time did she spend overall on the three activities?
Answers
8/3 + 2/3 + 1/4 =
10/3 + 1/4 =
40/12 + 3/12 =
43/12 =
3 7/12 hrs <===
Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms. f(x) = (3x + 2)(−6x − 3)
A) quadratic function; quadratic term: 6x^2; linear term: 24x; constant term: −6
B) linear function; linear term: −21x; constant term: −6
C) quadratic function; quadratic term: −18x^2; linear term: −21x; constant term: −6
D) linear function; linear term: −18x^2; constant term: −6
Answers
Answer:
The correct Option is C). quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6
Step-by-step explanation:
Given : f(x) = (3x + 2)(-6x - 3)
Now, f(x) = -18x² -9x -12x - 6
⇒ f(x) = -18x² - 21x - 6
Now, since the highest degree of the given function f(x) is 2 so the function f(x) is quadratic.
Now, quadratic term is one which has highest power x = 2 So, quadratic term = -18x²
Linear term is one which has power x = 1 So, linear term = -21x
Constant term is one which has power of x = 0. So, constant term = -6
Hence, The correct Option is C). quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6
Find two positive numbers such that the sum of one and the square of the other is 200 and whose product is a maximum.
Answers
The scale on a map indicates that 1 inch corresponds to an actual distance of 95 miles. two cities are 4.5 inches apart on the map. what is the actual distance between the two cities?
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In Indianapolis, the Market Tower has 2/3 as many stories as the Chase Tower. If the Market Tower has 32 stories, how many stories does the Chase Tower have?
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What is the class rank if someone has the 40th best GPA in his class of 600?
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1. The equation of a circle is x ^2 + y ^2 – 4 x + 2 y = 11 .
What are the coordinates of the center of the circle?
Question 1 options
(2, –1)
(4, –2)
(–4, 2)
(–2, 1)
2. What is the equation of the circle with center (4, -3) and radius 2?
Question 2 options:
(x + 4)^2 + (y – 3)^2 = 4
(x + 4)^2 – (y – 3)^4 = 4
(x – 4)^2 + (y + 3)^2 = 2
(x – 4)^2 + (y + 3)^2 = 4
3. What is the equation of this circle? (has picture)
(x – 2)^2 + (y – 7)^2 = ½
(x + 2)^2 + (y + 7)^2 = ¼
(x + 7)^2 + (y + 2)^2 = ¼
(x + 2)^2 + (y + 7)^2 = ½
4. What are the center and radius of the circle described by the equation x2 + y2 – 18x + 12y + 68 = 0?
Question 4 options:
Center (-9, 6); radius 7
Center (9, -6); radius 7
Center (-6, 9); radius 7
Center (6, -9); radius 7
5. Select the equation of a circle with center (-3, 7) and radius 5.
Question 5 options:
(x - 3)^2 + (y + 7)^2 = 25
(x + 3)^2 + (y - 7)^2 = 25
(x + 3) + (y - 7) = 25
(x - 3) + (y + 7) = 25
Answers
x^2 + y^2 - 4x + 2y = 11
x^2 - 4x + y^2 + 2y = 11
(x^2 - 4x) + (y^2 + 2y) = 11
(x^2 - 4x + 4) + (y^2 + 2y) = 11 + 4
(x - 2)^2 + (y^2 + 2y) = 15
(x - 2)^2 + (y^2 + 2y + 1) = 15+1
(x - 2)^2 + (y + 1)^2 = 16
The equation
(x - 2)^2 + (y + 1)^2 = 16
can be written as
(x - 2)^2 + (y - (-1))^2 = 4^2
which is in the form
(x-h)^2 + (y-k)^2 = r^2
where,
center = (h,k) = (2,-1)
radius = r = 4
Answer: Choice A) (2,-1)
====================================================
Problem 2
Given Center = (h,k) = (4,-3)
h = 4, k = -3
Given Radius = r = 2
(x-h)^2 + (y-k)^2 = r^2
(x-4)^2 + (y-(-3))^2 = 2^2
(x-4)^2 + (y+3)^2 = 4
Answer is choice D
====================================================
Problem 3
Based on the picture, the center is (-2,-7)
(h,k) = (-2,-7)
h = -2
k = -7
Each tick mark is 1/2 a unit. The distance from the red center to the outer edge of the circle is 1 tick or 1/2 a unit. The radius is 1/2 a unit. So r = 1/2 and r^2 = (1/2)^2 = 1/4
(x-h)^2 + (y-k)^2 = r^2
(x-(-2))^2 + (y-(-7))^2 = (1/2)^2
(x+2)^2 + (y+7)^2 = 1/4
Answer is choice B
====================================================
Problem 4
x^2 + y^2 - 18x + 12y + 68 = 0
(x^2 - 18x) + (y^2 + 12y) + 68 = 0
(x^2 - 18x + 0) + (y^2 + 12y + 0) + 68 = 0
(x^2 - 18x + 81 - 81) + (y^2 + 12y + 36 - 36) + 68 = 0
(x^2 - 18x + 81) - 81 + (y^2 + 12y + 36) - 36 + 68 = 0
(x - 9)^2 + (y + 6)^2 - 81 - 36 + 68 = 0
(x - 9)^2 + (y + 6)^2 - 49 = 0
(x - 9)^2 + (y + 6)^2 = 49
(x - 9)^2 + (y - (-6))^2 = 7^2
The center is (9,-6) and the radius is 7
====================================================
Problem 5
Center = (h,k) = (-3,7)
Radius = r = 5
(x-h)^2 + (y-k)^2 = r^2
(x-(-3))^2 + (y-7)^2 = 5^2
(x+3)^2 + (y-7)^2 = 25
Answer is choice B
he formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
A=1/2 h(a+b)
Solve for h.
Answers
A=1/2h(a+b)
2A=1h(a+b)
2A/a+b=h
Hope I helped :)
The first three numbers in sequence are 1, 4, and 9. Marie determined that the fourth number in the sequence is 16. Marie’s rule involved multiplication. What rule did she use to determine the fourth number in the sequence? Specific please
Answers
1² = 1
2² = 4
3² = 9,
then 4² = 16 and son and so forth
the ordered pair (2 36) is a solution to which equation(s)
A. y=2x^2
B. y=(3x)^2
C. y=7x^2+2
D. y=(x+4)^2
Answers
(2, 36) → x = 2, y = 36
Substitute the value of x and y to the equations of the functions:
A. y = 2x^2
36 = 2(2)^2 → 36 = 8 FALSE
B. y = (3x)^2
36 = (3 · 2)^2 → 36 = 6^2 → 36 = 36 CORRECT
C. y = 7x^2 + 2
36 = 7(2)^2 + 2 → 36 = 7 · 4 + 2 → 36 = 30 FALSE
D. y = (x + 4)^2
36 = (2 + 4)^2 → 36 = 6^2 → 36 = 36 CORRECT
Answer: B. y = (3x)^2 and D. (x + 4)^2
What is the distance between points A and B?
___ units
Answers
we know that
the distance's formula between two points is equal to
[tex]d=\left|xB-xA\right|[/tex]
substitute
[tex]d=\left|1-(-5)\right|[/tex]
[tex]d=6\ units[/tex]
therefore
the answer is
[tex]6\ units[/tex]
The distance between two point [tex]A{\text{ and }}B[/tex] is [tex]\boxed{{\mathbf{6 units}}}[/tex].
Further explanation:
The distance between two points is the modulus of difference of the given two points.
The distance between two points can be found by the distance formula as,
[tex]\left| {B - A} \right|[/tex]
Here, [tex]A{\text{ and }}B[/tex] are the points on the number line.
The distance cannot be negative therefore modulus is applied in the formula.
Step by step explanation:
Step 1:
First we determine the points from the given number line.
It can be observed from the given number line that there are two points one is on the left side of the origin and the second is right side of the origin.
The point [tex]A[/tex] is [tex]- 5[/tex] and the point [tex]B[/tex] is 1.
Step 2:
Now use the distance formula to obtain the distance between the two points [tex]A{\text{ and }}B[/tex].
Here, the value of A is [tex]-5[/tex] and B is 1.
Substitute the value of [tex]A{\text{ and }}B[/tex] to obtain the distance as,
[tex]\begin{aligned}d&= \left| {B - A} \right| \\&= \left| {1 - \left( { - 5} \right)} \right|\\&= 6{\text{ units}}\\\end{aligned}[/tex]
Therefore, the distance between two point [tex]A{\text{ and }}B[/tex] is [tex]6{\text{ units}}[/tex].
Learn more:
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Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Number line
Keywords: Integers, distance, point, number line, units, measurement, origin, negative numbers, positive numbers, right side, left side, difference.
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
14.6 units
15.5 units
21.0 units
21.6 units
Answers
Right side: This is easiest since it's a vertical line - it's 7 units long.
Top side: If you look carefully, this side is really the hypotenuse of a triangle that is 1 unit tall and 6 units long. Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be 1^2 + 6^2 = c^2 --> c = 6.1
Left side: just like the top side, this side is the hypotenuse of a triangle that is 6 units tall and 6 units long. Pythagoras again: 6^2 + 6^2 = c^2 --> c = 8.5
Add these three numbers to get the perimeter: 7 + 6.1 + 8.5 = 21.6
A prism is named for the shape of its bases.
True
False
Answers
Wikipedia says "Prisms are named for their bases, so a prism with a pentagonal base is called a pentagonal prism."
https://en.wikipedia.org/wiki/Prism_(geometry)
true
Step-by-step explanation:
Hope is helps and good luck
Evaluate ab for a = 2 3/4 and b = 4/5
A. 1 1/15
B. 8/15
C. 2 1/5
D. 2/3
Answers
what is the mass of an object that has a force of 100 Newtons and acceleration of 25 m/s2
Answers
m=F/a
m=100/25=4 kg
Mass of an object is 4 kg
By the end of the school year, Terry had passed 80% of his science tests. If Terry failed 4 science tests, how many science tests did Terry pass?
Answers
In this case, x = 16 tests passed.
Answer: Terry passed 16 science tests.
Step-by-step explanation: Given that by the end of the school year, Terry had passed 80% of his science tests and Terry failed 4 science tests.
We are to find the number of science tests that Terry passed.
Let x represents the total number of science tests that Terry appeared in.
Since he failed 4 science tests, so the number of science tests that Terry passes is given by
[tex](x-4).[/tex]
Since he passed 80% of his tests, so we get
[tex]80\%\times x=x-4\\\\\\\Rightarrow \dfrac{80}{100}\times x=x-4\\\\\\\Rightarrow \dfrac{4}{5}\times x=x-4\\\\\Rightarrow 4x=5x-20\\\\\Rightarrow 5x-4x=20\\\\\Rightarrow x=20.[/tex]
So, total number of science tests = 20.
Therefore, the number of science tests that Terry passed is given by
[tex]n=20-4=16.[/tex]
Thus, Terry passed 16 science tests.
Twenty-five members of the eighth grade class at Park Center Middle School are going to a museum and then to lunch. Each student must pay an entrance fee to the museum and $7.25 for lunch. The total cost for the trip is $443.75. What is the entrance fee for one student?
Answers
1) the cost for lunch, which is given as a rate per student: $7.25/student
2) the cost for the trip which is $443.75 to be divided by the 25 students, so it is $443.75 / 25 = $17.75/student
Now, you can add up those two costs per student to have the total cost per student:
$7.25 + $17.75 = $25.00/student
Answer: $25.00
Answer: $17.75
Step-by-step explanation: $443.75 / 25 = $17.75
One car rental company charges $30 per day plus $0.25 per mile driven. a car company charges $40 per day plus $0.10 per mile driven. how many miles must you drive for a one-day rental at the second company to be less expensive than the same rental at the first company? write an inequality to solve.
Answers
let's say x is the miles you drive for a day
the first company's rental charge= $30+$0.25x
the second company's rental charge= $40+$0.10x
Calculate what the x is when two equations are equal to each other:
$30+$0.25x=$40+$0.10x
$0.25x-$0.10x=$40-$30
$0.15x=$10
x=$10/$0.15
x=66.667 miles
at least 66.667 miles. I am not sure though. I'm a little bit tired today, so you might want to check it yourself.
Answer:
66.667 miles
Step-by-step explanation:
Given: One car rental company charges $30 per day plus $0.25 per mile driven.
Second car company charges $40 per day plus $0.10 per mile driven.
To find: how many miles must you drive for a one-day rental at the second company to be less expensive than the same rental at the first company?
Solution: Let the distance driven on a day be x miles.
As per question,
The first rental company will charge [tex]=30+0.25x[/tex]
The second rental company will charge [tex]=40+0.10x[/tex]
Now, we want the rental charges of second company to be less expensive then the first.
So we get the inequality,
[tex]30+0.25x>40+0.10x[/tex]
[tex]0.25x-0.10x>40-30[/tex]
[tex]0.15x>10[/tex]
[tex]x>\frac{1000}{15}[/tex]
[tex]x>66.667[/tex] miles
Hence, at least 66.667 miles should be driven on a day.
1. Factor the expression 3x^3 + 4x^2 - 15x - 20 Please show work!
Answers
Factor 3x^3 + 4x^2 and -15x - 20 seperately
x^2 (3x + 4) - 5(3x + 4)
(x^2 - 5)(3x + 4) is your answer
hope this helps
The expression 3x^3 + 4x^2 - 15x - 20 can be factored into the form (3x + 4)(x^2 - 5) by grouping terms, factoring out common components, and simplifying.
Explanation:The provided expression to be factored is [tex]3x^3 + 4x^2 - 15x - 20.[/tex]Factoring this involves finding common factors and breaking the terms down until we cannot do so any further.
Group terms that look like they might have common factors: [tex](3x^3 + 4x^2) - (15x + 20).[/tex]Factor out the common factors: [tex]x^2(3x + 4) - 5(3x + 4).[/tex]Notice that we have the binomial of (3x + 4) common between both terms. We can now factor that out: [tex](3x + 4)(x^2 - 5).[/tex]
So, the factored form of the expression is [tex](3x + 4)(x^2 - 5).[/tex]
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BRAINLIESTTTTTTTT!!!!!!!!!!!!!!!!!!
Answers
For x = 21, f(x) = 105.
To find the average rate of change, subtract 105 - 95.
Then subtract 21 - 11.
Then divide the first difference by the second difference.
Which function represents the graph of f(s)=-4[x] after it is translated 3 units down?
Answers
Miguel is going for a walk. he takes 3 hours to walk 7.5 miles. what is his speed?
Answers
We want to know how many miles he can walk in 1 hour so, divide both sides by 3 -> 1 hour / 2.5 miles
He is walking at 2.5 mph
divide total distance by time
7.5 miles / 3 hours = 2.5 miles per hour is his speed