Answers
Answer:
a) The equation is (y - 1)² = -8 (x - 4)
b) The equation is (x - 1)²/25 + (y - 4)²/16 = 1
c) The equation of the ellipse is (x - 3)²/16 + y²/4 = 1
Step-by-step explanation:
a) Lets revise the standard form of the equation of the parabola with a
horizontal axis
# (y - k)² = 4p (x - h), (h , k) are the coordinates of its vertex and p ≠ 0
- The focus of it is (h + p , k)
* Lets solve the problem
∵ The focus is (2 , 1)
∵ focus is (h + p , k)
∴ h + p = 2 ⇒ subtract p from both sides
∴ h = 2 - p ⇒ (1)
∴ k = 1
∵ It opens left, then the axis is horizontal and p is negative
∴ Its equation is (y - k)² = 4p (x - h)
∵ k = 1
∴ Its equation is (y - 1)² = 4p (x - h)
- The parabola contains point (2 , 5), substitute the coordinates of the
point in the equation of the parabola
∴ (5 - 1)² = 4p (2 - h)
∴ (4)² = 4p (2 - h)
∴ 16 = 4p (2 - h) ⇒ divide both sides by 4
∴ 4 = p (2 - h) ⇒ (2)
- Use equation (1) to substitute h in equation (2)
∴ 4 = p (2 - [2 - p]) ⇒ open the inside bracket
∴ 4 = p (2 - 2 + p) ⇒ simplify
∴ 4 = p (p)
∴ 4 = p² ⇒ take √ for both sides
∴ p = ± 2, we will chose p = -2 because the parabola opens left
- Substitute the value of p in (1) to find h
∵ h = 2 - p
∵ p = -2
∴ h = 2 - (-2) = 2 + 2 = 4
∴ The equation of the parabola in standard form is
(y - 1)² = 4(-2) (x - 4)
∴ The equation is (y - 1)² = -8 (x - 4)
b) Lets revise the equation of the ellipse
- The standard form of the equation of an ellipse with center (h , k)
and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1
- The coordinates of the vertices are (h ± a , k )
- The coordinates of the foci are (h ± c , k), where c² = a² - b²
* Now lets solve the problem
∵ Its vertices are (-4 , 4) and (6 , 4)
∵ The coordinates of the vertices are (h + a , k ) and (h - a , k)
∴ k = 4
∴ h + a = 6 ⇒ (1)
∴ h - a = -4 ⇒ (2)
- Add (1) and (2) to find h
∴ 2h = 2 ⇒ divide both sides by 2
∴ h = 1
- Substitute the value of h in (1) or (2) to find a
∴ 1 + a = 6 ⇒subtract 1 from both sides
∴ a = 5
∵ The foci at (-2 , 4) and (4 , 4)
∵ The coordinates of the foci are (h + c , k) , (h - c , k)
∴ h + c = 4
∵ h = 1
∴ 1 + c = 4 ⇒ subtract 1 from both sides
∴ c = 3
∵ c² = a² - b²
∴ 3² = 5² - b²
∴ 9 = 25 - b² ⇒ subtract 25 from both sides
∴ -16 = -b² ⇒ multiply both sides by -1
∴ 16 = b²
∵ a² = 25
∵ The equation of the ellipse is (x - h)²/a² + (y - k)²/b² = 1
∴ The equation is (x - 1)²/25 + (y - 4)²/16 = 1
c) How to identify the type of the conic
- Rewrite the equation in the general form,
Ax² + Bxy + Cy² + Dx + Ey + F = 0
- Identify the values of A and C from the general form.
- If A and C are nonzero, have the same sign, and are not equal
to each other, then the graph is an ellipse.
- If A and C are equal and nonzero and have the same sign, then
the graph is a circle
- If A and C are nonzero and have opposite signs, and are not equal
then the graph is a hyperbola.
- If either A or C is zero, then the graph is a parabola
* Now lets solve the problem
∵ x² + 4y² - 6x - 7 = 0
∵ The general form of the conic equation is
Ax² + Bxy + Cy² + Dx + Ey + F = 0
∴ A = 1 and C = 4
∵ If A and C are nonzero, have the same sign, and are not equal to
each other, then the graph is an ellipse.
∵ x² + 4y² - 6x - 7 = 0 ⇒ re-arrange the terms
∴ (x² - 6x ) + 4y² - 7 = 0
- Lets make x² - 6x completing square
∵ 6x ÷ 2 = 3x
∵ 3x = x × 3
- Lets add and subtract 9 to x² - 6x to make the completing square
x² - 6x + 9 = (x - 3)²
∴ (x² - 6x + 9) - 9 + 4y² - 7 = 0 ⇒ simplify
∴ (x - 3)² + 4y² - 16 = 0 ⇒ add 16 to both sides
∴ (x - 3)² + 4y² = 16 ⇒ divide all terms by 16
∴ (x - 3)²/16 + 4y²/16 = 1 ⇒ simplify
∴ (x - 3)²/16 + y²/4 = 1
∴ The equation of the ellipse is (x - 3)²/16 + y²/4 = 1
Related Questions
Divide. Write the quotient in lowest terms.
Answers
Answer:
[tex] \frac{11}{12} [/tex]
The quotient in lowest terms is 2.
The quotient step by step for the given expression:
1. Given Expression:
[tex]\[ \frac{3}{\frac{2}{4}} : 3 \][/tex]
2. Step 1: Simplify the Complex Fraction:
- The complex fraction is [tex]\( \frac{3}{\frac{2}{4}} \).[/tex]
- To simplify, multiply the numerator by the reciprocal of the denominator:
[tex]\[ \frac{3}{\frac{2}{4}} = 3 \times \frac{4}{2} = 6 \][/tex]
3. Step 2: Divide by 3:
- Now divide the simplified fraction (6) by 3:
[tex]\[ 6 : 3 = 2 \][/tex]
Therefore, the quotient in lowest terms is 2.
Simplify the expression 3/2 (5/3) -1 1/4 + 1/2
Answers
Answer:
7/4, 1.25 or 1 3/4
Step-by-step explanation:
Answer:
Exact form 7/4
Decimal form 1.75
Mixed Number 1 3/4
Step-by-step explanation:
The roots of the equation 2×^2 + 3x -4=0 are a and b.
find the values of
a^2ß^2
Answers
Answer:
hello : a²b² =4
Step-by-step explanation:
2ײ + 3x - 4=0
The roots of this equation exist because (2)(-4)<0
note : a'x²+b'x +c' =0.......The roots of this equation : a and b
a×b = c'/a' a' =2 and b'=3 and c' = - 4
in this exercice ; a²b² = (ab)² = (c'/a')² = (-4/2)² = (-2)² =4
Answer:
4
Step-by-step explanation:
given a quadratic equation in standard form
y = ax² + bx + c = 0 : a ≠ 0
with roots α and β, then
the sum of the roots α + β = - [tex]\frac{b}{a}[/tex] and
the product of the roots αβ = [tex]\frac{c}{a}[/tex]
2x² + 3x - 4 = 0 ← is in standard form
with a = 2, b = 3 and c = - 4
αβ = [tex]\frac{-4}{2}[/tex] = - 2, hence
α²β² = (αβ)² = (- 2)² = 4
What does it mean for data to be continuous?
Answers
Answer:
For data to be continuous, it can take on any value.
Step-by-step explanation:
For example, a line on a coordinate graph never stops at a certain point, if it does, it would be discrete.
how much is 2/3 × 5
Answers
Answer:
Answer:3.33
Answer:3.33 Step-by-step explanation:
The answer is 3.33
2/3 × 5 = 3.33
Answer:
Step-by-step explanation:
2/3 × 5 = 10/3
Given: -x > 4. Choose the solution set.
Answers
Final answer:
The solution to the inequality -x > 4 is all real numbers less than -4, which can be expressed as the interval (-∞, -4). This is found by dividing both sides by -1 and reversing the inequality to x < -4.
Explanation:
When considering the inequality -x > 4, we are trying to find the set of all values for the variable x that make the inequality true. The solution to such an inequality requires inverse operations and understanding the rules for inequalities, especially the rule that multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol.
Step by step, let's solve the given inequality:
Divide both sides of the inequality by -1 to isolate x. It is important to remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality, so our inequality becomes x < -4 after this step.Now that we have x isolated, we can interpret the solution set. The values of x that satisfy this inequality are all real numbers less than -4. Therefore, the solution set can be written in interval notation as (-∞, -4).This means that any number lower than -4 will be a valid solution for the inequality -x > 4. It's also valuable to visualize this set on a number line, where everything to the left of -4 (but not including -4 itself) is part of the solution set.
Which expression is equivalent to (x^4/3 x^2/3)^1/3?
Answers
Answer: [tex]x^{\frac{2}{3} }[/tex]
Step-by-step explanation:
We have several properties of exponents in use here. The two that are used are:
[tex](x^{a})(x^{b}) = x^{a + b}[/tex] (Exponents with the same base that are being multiplied together can have the exponents added)
[tex](x^{a})^{b} = x^{(a)(b)}[/tex] (A base raised to a power, and then raised to another power means that you can multiply the exponents to get the same result as doing inside operations and then outside operations)
Let's apply it!
First, let's simplify what's inside the parenthesis.
[tex]x^{\frac{4}{3} } x^{\frac{2}{3} }[/tex] (Remember, they have the same base of "x", so we can add the exponents)
[tex]x^{\frac{4}{3} + \frac{2}{3} }[/tex] = [tex]x^{\frac{6}{3} }[/tex] = [tex]x^{2}[/tex]
Now we have [tex](x^{2})^{\frac{1}{3} }[/tex]. Let's use the second rule.
[tex](x^{2})^{\frac{1}{3} }[/tex] = [tex]x^{\frac{2}{3} }[/tex]
Hope this helps! :^)
Answer:
B
Step-by-step explanation:
Just took the test
What is the value of cos A?
Answers
Answer:
3/5
Step-by-step explanation:
cos A = [tex]\frac{AC}{AB}[/tex]=[tex]\frac{9}{15}[/tex]=[tex]\frac{3}{5}[/tex]
Answer:
Cos A = 3/5
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ = Opposite side/Adjacent side
From the figure we can see a right angled triangle, ABC
AC = 9, CB = 12 and AB = 15
To find the value of Cos A
Cos A = Adjacent side/Hypotenuse
= AC/AB
= 9/15 = 3/5
Therefore the value of Cos A = 3/5
What is the value of x?
50°
100
А. 50°
Ов. 150°
Ос. 100°
Op. 30°
Answers
Answer:
The answer is 30
Step-by-step explanation:
BC the inside of a triangle equals 180
it takes 41 minutes for 9 people to paint 9 walls. How long doe sit take for 14 people to paint 14 walls
Answers
41 minutes
Explanation:When 9 people are painting 9 walls, there are the same amounts of people and walls. This means all of the walls are being painted at the same time, with one person painting each wall.
The same applies to 14 people painting 14 walls. All of the walls are being painted at the same time, with one person painting each wall.
Even if there was only one person painting one wall, it would take 41 minutes.
Answer:
41 minutes
Step-by-step explanation:
It takes 41 minutes for 9 people to paint 9 walls.
9 walls/ 9 people = 1 wall / person
So it takes 41 minutes for 1 person to paint 1 wall
14 walls/ 14 people = 1 wall / person
It will take the same amount of time
41 minutes
-52 - x = 9(x+9) + 9x
Answers
Step-by-step explanation:
-52-1x= 9(x+9)+9x
-52-1x= 9x+81+9x (now combine like terms)
-52-1x= 18x+81
-1x= 18x+81
-52
-1x=18x+29
-1x=29
+18x
17x= 29
÷17
x=1.705
Hope this helps, I'm not good at explaining it with words, so I just showed the work...
Hamid ha gained weight, he now weighs 88kg which is 10% higher than the normal, what i Hamid normal weight?
Answers
Answer:
80 kg is Hamid's normal weight
Step-by-step explanation:
The following equation will help you to find the answer:
(1.10)x = 88
Answer:79.2kg
Step-by-step explanation:
10%of 88kg is 8.8. Subtract 8.8 from 88 and the answer is 79.2.
If an airplane flies at an average speed of 7.5 miles per minute, in 1 1/2 hours it will have flown?
Answers
Answer:
675 miles
Step-by-step explanation:
7.5*90 (for the 1 1/2 hour)
Answer:
1 1/2= 90 minutes
90 minutes/7.5 miles per minute
Multiply
90/7.5
= 675 miles in 1 1/2
Hope this helped :)
Isaac wants the equation below to have no solution when the missing number is placed in the box.
Which number should he place in the box?
Answers
Answer: 4
Step-by-step explanation: To have an equation with no solution you have to get something like 0=1 meaning you have to remove all the variables. In this equation you would distribute to get xy+2y+2x=2x+12+4x where y is the missing number. then combining like terms you get xy+2x+2y=6x+12. Subtracting 2x from both sides you get xy+2y=4x+12. Now to get the variables gone y has to be 4 so that the variables to cancel out. By plugging in 4 you can see this works; 4x+8=4x+12 and by subtracting 4x from both sides you get 8=12 which is not true meaning there is no solution.
ANSWER
[tex]^{\boxed {}} = 4.[/tex]
EXPLANATION.
The given equation is
[tex] \boxed {}(x + 2) + 2x = 2(x + 6) + 4x[/tex]
Let us expand the right hand side to obtain:
[tex]\boxed {}(x + 2) + 2x = 2x + 12+ 4x[/tex]
We group similar terms and keep the expression with the box on the left.
[tex]\boxed {}(x + 2) = 2x - 2x+ 12+ 4x[/tex]
Simplify
[tex]\boxed {}(x + 2) = 4x + 12[/tex]
We can see that the value of box the will be the equation to have no solution is 4.
Let us substitute 4 for box.
[tex]4(x + 2) = 4x + 12[/tex]
[tex]4x + 8 = 4x + 12[/tex]
[tex]4x - 4x = 12 - 8[/tex]
[tex]0 = 4[/tex]
This is not true. Hence the equation has no solution when
[tex]\boxed {} = 4[/tex]
Consider the following equation
Select the equation that has the same solution as the given equation.
Answers
Answer:
Option C [tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]
Step-by-step explanation:
we have that
The given equation is
[tex]-16p+37=49-21p[/tex]
Solve for p
Group terms that contain the same variable
[tex]-16p+21p=49-37[/tex]
Combine like terms
[tex]5p=12[/tex]
[tex]p=12/5[/tex]
[tex]p=2.4[/tex]
we know that
If a equation has the same solution as the given equation, then the solution of the given equation must satisfy the equation
Verify each case
case A) we have
[tex]2+1.25p=-3.75p+10[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]2+1.25(2.4)=-3.75(2.4)+10[/tex]
[tex]5=1[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
case B) we have
[tex]-55+12p=5p+16[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]-55+12(2.4)=5(2.4)+16[/tex]
[tex]-26.2=28[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
case C) we have
[tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex](3/2)(2.4)-5+(9/4)(2.4)=7-(5/4)(2.4)[/tex]
[tex]4=4[/tex] ----> is true
therefore
The equation has the same solution as the given equation
case D) we have
[tex]-14+6p=-9-6p[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]-14+6(2.4)=-9-6(2.4)[/tex]
[tex]0.4=-5.4[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
Suppose an elevator is 400 feet above the ground. It descends at a steady rate.
After 15 seconds, it is 250 feet above the ground.
Write a linear function for the height of the elevator as a function of time.
Answers
Answer:
The answer is....
Step-by-step explanation:
y= -10x+400
Follow below steps:
The student's question involves writing a linear function for the height of an elevator as a function of time, given that the elevator descends from 400 feet to 250 feet in 15 seconds.
First, let's find the rate of descent by calculating the change in height over the change in time. This gives us (250 feet - 400 feet) / (15 seconds) = -10 feet per second. The negative sign indicates a downward movement.
Now, we can construct the linear function for height h(t), where t is the time in seconds. The initial height is 400 feet, so the y-intercept of our linear equation is 400. With a slope of -10, the function takes the form:
h(t) = -10t + 400
This function represents the height of the elevator after t seconds.
In parallelogram ABCD, AB=7cm and the perimeter of ABCD is 30cm. What is the length of AD?
Answers
Answer:
8cm
Step-by-step explanation:
Ab=7cm
Since opposite sides are equal
Cd=7cm
7cm + 7cm = 14cm
Perimeter equals 30cm
:.30cm - 14cm =16cm (bc+ad)
Since both bc and ad are equal,
16cm/2=8cm
:.ad=8cm
Final answer:
In a parallelogram, opposite sides are equal, so by using the given perimeter of 30 cm and one side of 7 cm, we find the length of the adjacent side AD to be 8 cm.
Explanation:
In the given problem with parallelogram ABCD, we know AB = 7 cm and the perimeter is 30 cm. In a parallelogram, opposite sides are equal in length, so if AB = 7 cm, then CD also equals 7 cm. The perimeter P of a parallelogram is the sum of all its sides:
P = AB + BC + CD + DA
Given P = 30 cm and AB = CD = 7 cm, we can find the length of AD (which is also equal to BC) using the formula:
P = 2(AB + AD)
30 = 2(7 + AD)
30 = 14 + 2(AD)
30 - 14 = 2(AD)
16 = 2(AD)
AD = 16 / 2 = 8 cm
Therefore, the length of AD is 8 cm.
A triangle in the coordinate plane has coordinates of (2,3), (-4,-5), and (-2, 4). It is translated 3 units down. What are its new coordinates?
A) (5,3), (-1,-5), (1,4)
B) (2,6), (-4,-2), (-2, 7)
C) (2,0), (-4,-8), (-2, 1)
D) (-1,3), (-7,-5), (-5,4)
Answers
Answer: C) (2,0), (-4,-8), (-2, 1)
Step-by-step explanation:
The translation rule for translating a point (x,y) by k units down :-
[tex](x,y)\rightarrow(x,y-h)[/tex]
Given : A triangle in the coordinate plane has coordinates of (2,3), (-4,-5), and (-2, 4). It is translated 3 units down.
Then, its new coordinates will be :
[tex](2,3)\rightarrow(2,3-3)=(2,0)[/tex]
[tex](-4,-5)\rightarrow(-4,-5-3)=(-4,-8)[/tex]
[tex](-2, 4)\rightarrow(-2,4-3)=(-2,1)[/tex]
Hence, the new coordinates = (2,0), (-4,-8), (-2, 1)
Which is the definition of a line sediment
Answers
Answer:
If it is sediment: A sediment trap is a T-shaped pipe configuration designed to catch any debris in a gas line before it goes into the appliance.
Or if it was a typo and its supposed to say segment:line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
Step-by-step explanation:
I know this because of the help of google.
What is the volume of the pyramid?
A solid right pyramid has a square base. The length of the
base edge is 4 cm and the height of the pyramid is 3 cm.
Answers
Answer: 16 cm^2.
Step-by-step explanation: The volume of a pyramid is equal to one-third the product of the area of the base and the height:
[tex]V=\frac{1}{3}A*h[/tex]
In this case, the base is a square, so its area is:
A=L^2 where "L" is the lenght of the base edge
So the volume would be:
[tex]V=\frac{1}{3}L^{2} *h[/tex]
[tex]V=\frac{1}{3}4^{2} *3[/tex]
V=16*3/3
[tex]V=16cm^{2}[/tex]
Select the correct answer and then click Done
What is the median of the set of values?
307 309 323 304 390 398
Answers
Answer : The median of the given set of data of values is, 323
Step-by-step explanation :
Median : It is the middle term that is sorted by the list of numbers. It is determine by placing the numbers in increasing order.
For odd observations the formula will be: [tex]\frac{n+1}{2}[/tex]
For even observations the formula will be: [tex]\frac{n}{2}+1^{th}\text{ term}[/tex]
As we are given that the set of data:
307, 309, 323, 304, 390, 398
First we have to placing the numbers in increasing order.
304, 307, 309, 323, 390, 398
Now we have to determine the median.
For even data:
[tex]\frac{n}{2}+1^{th}\text{ term}[/tex]
n = 6
[tex]\frac{6}{2}+1^{th}\text{ term}[/tex]
[tex]4^{th}\text{ term}[/tex]
The number at 4th position is, 323
Thus, the median of the given set of data of values is, 323
At a point on the ground 60 Ft
from the base of a tree, the distance
to the top of the tree is 4 ft more
than 2 times the height of the tree.
Find the height of the tree in ft.
Answers
The height of the tree is 32 feet.
Step-by-step explanation:
Let the height of the tree be x.
Connect the top of the tree, the point on the ground, and the bottom of the tree to form a right triangle.
Use Pythagorean theorem to solve for x.
(4+2x)^2 = x^2 + 60^2
x = 32
The height of the tree is 4 feet.
Explanation:To find the height of the tree, we can set up a right triangle with the tree height as one leg, the distance from the base of the tree as the other leg, and the distance to the top of the tree as the hypotenuse. Let's call the tree height x. From the given information, we can write the equation:
x = 2x + 4
Simplifying this equation, we get:
x = 4
Therefore, the height of the tree is 4 feet.
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Is 23/48 less than 1/2
Answers
Answer:
yes.
Step-by-step explanation:
24/48 is half. Anything less than 24 would be less than half.
Answer:
Yes.
Step-by-step explanation:
Half of 2 is 1, so 1/2 means half.
Half of 48 is 24, so 24/48 is also half.
23/48 is less than 24/48, so 23/48 is less than 1/2.
PLEASE HELP
solve for R
what is R equal to
Answers
Steps:
First, move r to the left side of the equation and change its sign.
-r + p = - c
Then, move p to the right side and change its sign.
-r = -c - p
Multiply both sides of the equation by -1. This will change the variables back to positives, because any expression multiplied by -1 equals its opposite.
-1(-r) = -1(-c) -1(-p) =
r = c + p (don’t forget to change the sign)
So, your final solution is: r = c + p or r = p + c
he simultaneous equations
5x + y = 21
x - 3y = 9
With working out
Answers
Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
5x + y = 21 → (1)
x - 3y = 9 → (2)
Multiply (1) by 3 and add the result to (2) to eliminate y term
15x + 3y = 63 → (3)
Add (2) and (3) term by term
(x + 15x) + )- 3y + 3y) = (9 + 63)
16x = 72 ( divide both sides by 16 )
x = 4.5
Substitute x = 4.5 into (1) for corresponding value of y
22.5 + y = 21 ( subtract 22.5 from both sides )
y = - 1.5
Solution is (4.5, - 1.5 )
Northlake High School has two lunch periods. Students can eat their lunch in
the cafeteria or on an outside patio. About 42% of students who have first
lunch eat outside. Compare this with the percentage of second-lunch
students who eat outside.
First lunch
Second lunch
Total
Eat outside
0.19
0.21
0.40
Eat inside
0.26
0.34
0.60
Total
0.45
0.55
10
|
Select the true statement.
O
A. A greater percentage of second-lunch students (45%) eat outside.
O
B. A smaller percentage of second-lunch students (21%) eat outside.
O
C. A greater percentage of second-lunch students (55%) eat outside.
O
D. A smaller percentage of second-lunch students (38%) eat outside.
Answers
Answer: d
Step-by-step explanation:
The true statement is a smaller percentage of second-lunch students (38%) eat outside.
What is the true statement?Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentages is %.
Percentage of the second lunch students that eat outside = (0.21/0.55) x 100 = 38%
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(4x^2y^3+2xy^2-2y)-(-7x^2y^3+6xy^2-2y)
Answers
Answer:
x y^2 (11 x y - 4)
Step-by-step explanation:
Simplify the following:
4 x^2 y^3 + 2 x y^2 - 2 y - (-7 x^2 y^3 + 6 x y^2 - 2 y)
Factor y out of -7 x^2 y^3 + 6 x y^2 - 2 y:
4 x^2 y^3 + 2 x y^2 - 2 y - y (-7 x^2 y^2 + 6 x y - 2)
-y (-2 + 6 x y - 7 x^2 y^2) = 2 y - 6 x y^2 + 7 x^2 y^3:
4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3
Grouping like terms, 4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3 = (4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y):
(4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x^2 y^3 4 + x^2 y^3 7 = 11 x^2 y^3:
11 x^2 y^3 + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x y^2 2 + x y^2 (-6) = -4 x y^2:
11 x^2 y^3 + -4 x y^2 + (2 y - 2 y)
2 y - 2 y = 0:
11 x^2 y^3 - 4 x y^2
Factor x y^2 out of 11 x^2 y^3 - 4 x y^2:
Answer: x y^2 (11 x y - 4)
Answer: xy2 • (11xy - 4)
Step-by-step explanation:
4 x^2 y^3 + 2 x y^2 - 2 y - (-7 x^2 y^3 + 6 x y^2 - 2 y)
Factor y out of -7 x^2 y^3 + 6 x y^2 - 2 y:
4 x^2 y^3 + 2 x y^2 - 2 y - y (-7 x^2 y^2 + 6 x y - 2)
-y (-2 + 6 x y - 7 x^2 y^2) = 2 y - 6 x y^2 + 7 x^2 y^3:
4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3
Grouping like terms, 4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3 = (4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y):
(4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x^2 y^3 4 + x^2 y^3 7 = 11 x^2 y^3:
11 x^2 y^3 + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x y^2 2 + x y^2 (-6) = -4 x y^2:
11 x^2 y^3 + -4 x y^2 + (2 y - 2 y)
2 y - 2 y = 0:
11 x^2 y^3 - 4 x y^2
Factor x y^2 out of 11 x^2 y^3 - 4 x y^2:
Answer: x y^2 (11 x y - 4)
Translate into an equation: 5 times the sum of V and 48 is 290.
Answers
Answer:
5(V + 48) = 290
Step-by-step explanation:
5 times the sum of V and 48 is 290: V + 48
5 times the sum of V and 48 is 290: 5(V + 48)
5 times the sum of V and 48 is 290: 5(V + 48) = 290
a pair of shoes is on sale for 30% off . the original price is p. which expression can be used to find the price of shoes after the dicount?
Answers
Answer:
.30p
Step-by-step explanation:
I NEED HELP NOW!!!! I'LL MARK YOU BRAINLIEST IF YOU ANSWER!!!!!
Answers
Answer:
0, 5, 7, 11, ...
Step-by-step explanation:
1^2 = 1; 1 - 1 = 0; 0 is divisible by 6
5^2 = 25; 25 - 1 = 24; 24 is divisible by 6
7^2 = 49; 49 - 1 = 48; 48 is divisible by 6
11^2 = 121; 121 - 1 = 120; 120 is divisible by 6