[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ y=a(x- h)^2+ k \qquad\qquad vertex~~(\stackrel{2}{ h},\stackrel{-7}{ k}) \\\\\\ y=a(x-2)^2-7~\hspace{4em}\stackrel{\textit{y-intercept}}{(0, -3)}~~ \begin{cases} x=0\\ y=-3 \end{cases}\implies -3=a(0-2)^2-7 \\\\\\ 4=a(-2)^2\implies 4=4a\implies \cfrac{4}{4}=a\implies 1=a~\hfill y=1(x-2)^2-7 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y(x-2)^2-7~\hfill[/tex]
The quadratic function with the vertex (2,-7) and y-intercept -3 is f(x) = x² - 4x - 3.
To find the quadratic function given the vertex (2,-7) and the y-intercept -3, we can use the vertex form of a quadratic equation, which is f(x) = a(x - h)² + k, where (h, k) is the vertex.
Substituting the vertex into the equation, we get f(x) = a(x - 2)² - 7. To find 'a', we can use the fact that the y-intercept is -3, which occurs when x = 0. Thus, we substitute x = 0 into the equation to get -3 = a(0 - 2)² - 7.
Simplifying further,
-3 = 4a - 7
4a = 4
a = 1
With this value of 'a', the quadratic function is f(x) = (x - 2)² - 7, or in expanded form f(x) = x² - 4x + 4 - 7, which simplifies to f(x) = x² - 4x - 3.
This function has a vertex at (2, -7) and passes through the y-axis at y = -3, confirming that we calculated the correct equation for the parabola.
Can soneone help me with these basic vector math problems?!
Given an initial point (5,3) and a terminal point (10,-8), find the component form for vector v.
A. (2, 18)
B. (15, -5) <-- My choice
C. (5, -11)
D. (13, 13)
2. Is vector v with an initial point of (0,0) and a terminal point of (50, 120), equal to vector u with an initial point of (50, 120) and a terminal point of (0,0)?
A. No, the two vectors have different directions.
B. No, the two vectors have different initial points. <-- I think it's this one
C. Yes, the two vectors have the same magnitude.
D. Yes, the two vectors have the same slope.
The solution to the basic vector problems are given as,
1) (5, -11), option C is correct.
2) . No, the two vectors have different initial points, option B is correct.
Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.
Here,
1)
initial point (5,3) and a terminal point (10,-8),
Vector = 10i -8j - 5i - 3j
Vector = 5i - 11j or [5, -11]
2)
Vector v with an initial point of (0,0) and a terminal point of (50, 120), is not equal to vector u with an initial point of (50, 120) and a terminal point of (0,0).
Thus, the solution to the basic vector problems are given as,
1) (5, -11), option C is correct.
2) . No, the two vectors have different initial points, option B is correct.
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Final answer:
To find the component form for vector v, subtract the initial point from the terminal point. The answer is option C. The vectors in the second question have different initial points, so they are not equal.
Explanation:
To find the component form for vector v, we need to subtract the initial point from the terminal point. Subtracting the x-coordinates and y-coordinates separately, we get (10 - 5, -8 - 3), which simplifies to (5, -11). Therefore, the component form for vector v is option C, (5, -11).
For the second question, the vectors have the same initial points but different terminal points, so they cannot be equal. Therefore, the correct choice is option B, No, the two vectors have different initial points.
Marta received $5 for helping her dad in the back yard. She spent $2.40 on drinks and $1.33 on snacks.
(a) Write an equation to show how much money she has left. Remember to define your unknown.
(b) Solve the equation from part (a). Show your work.
If 3 pairs of pants cost $63 what is the cost of 16 pairs of pants?
Answer:
336 dollars
Step-by-step explanation:
Set up a proportion. Because you know that three pairs of pants costs sixteen dollars, you can put three over sixteen because they are both the same part of the equation, the same part being that they are pairs of pants. Then you set up another proportion, sixty three over x, because you do not know how much sixteen pairs of pants costs. It should look like this. Then you cross multiply and divide.
3 63
--- = ----
16 x
16 times 63 = 1008
1008/3 = 336
Answer: $336
Given m(x)=3x-2 and p(x)=-4+2, what is (m-p)(x)?
Final answer:
(m-p)(x) represents the subtraction of function p(x) from m(x). Assuming p(x) is -4x + 2, (m-p)(x) simplifies to 7x - 4.
Explanation:
To calculate (m-p)(x), we need to subtract the function p(x) from the function m(x).
Given m(x) = 3x - 2 and noting there seems to be an error in p(x), as it should likely be a function of x, let's assume the student meant p(x) = -4x + 2 based on the pattern of the provided information.
The subtraction of these two functions is performed as follows:
m(x) - p(x) = (3x - 2) - (-4x + 2)
Simplify by distributing the negative sign through the second polynomial:
(3x - 2) + 4x - 2 = 3x + 4x - 2 - 2
Combine like terms:
7x - 4
So, (m-p)(x) = 7x - 4.
Write the ratio of the area of a circle with radius r to the circumference of the same circle
Answer:
[tex]\frac{r}{2\pi r} =\frac{1}{2\pi }[/tex]
Step-by-step explanation:
A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.
To write a ratio, we count the number of each quantity we are comparing or use the variable for that quantity. We write radius:circumference. Recall, the circumference of a circle can be found using [tex]\pi d[/tex] or [tex]2\pi r[/tex].
We write r: [tex]\pi d[/tex] or r:[tex]2\pi r[/tex].
We can also write in fraction form:
[tex]\frac{r}{\pi d}[/tex] or [tex]\frac{r}{2\pi r} =\frac{1}{2\pi }[/tex]
You can use the fact that ratio of one quantity to other is fraction involving one quantity over another quantity.
The specified ratio is given as
[tex]r:2\\\\or\\\\\dfrac{r}{2}[/tex]
What is the ratio of a to b ?The ratio of a to b is [tex]\dfrac{a}{b}[/tex]
It is sometimes written as [tex]a:b[/tex]
We can remove common factors of a and b to simplify them.
Thus, if
[tex]a = c \times x\\b = d \times x\\[/tex]
then
[tex]\dfrac{a}{b} = \dfrac{c \times x}{d \times x} = \dfrac{c}{d}[/tex]
What is the area of a circle and circumference of a circle with radius r units?The area of a circle with radius r units is
[tex]Area = \pi r^2[/tex]
The circumference of a circle with radius r units is
[tex]Circumference = 2 \pi r[/tex]
( Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times x = 2x[/tex] )
Their ratio is
[tex]\dfrac{Area_r}{Circumference_r} = \dfrac{\pi r^2}{2\pi r} = \dfrac{r}{2}[/tex]
Thus,
The specified ratio is given as
[tex]r:2\\\\or\\\\\dfrac{r}{2}[/tex]
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At an apple orchard Margaret picked 19 1/2 Pounds of apples the cashier put the apples in the three bags with the same weight How many pounds of apples are in each bag
Use photo math
Hope this helps
Answer:
the answer would be 6.5 pounds
Step-by-step explanation: 19 1/2 divided by three
[tex]50 + (40 - 15) \div 6[/tex]
Answer:
12.5
Step-by-step explanation:
first you do the one in the 40-15 then you add 50 the you divide by 6
Answer: [tex]54\frac{1}{6}[/tex]
Step-by-step explanation:
Order of Operations (PEMDAS) states that we need to do the parenthesis first then division and then addition.
50 + (40 - 15) ÷ 6
parenthesis: 50 + 25 ÷ 6
division: 50 + [tex]4\frac{1}{6}[/tex]
addition: [tex]54\frac{1}{6}[/tex]
Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k. k = ______ Graph of two lines. f of x equals 1 over 3 x plus 2 and g of x equals 1 over 3 x plus 5
Solution:
As given , g(x)= f(x) + k --------(1)
As also given : f(x) = [tex]\frac{1}{3}[/tex](x+2)
g(x) = [tex]\frac{1}{3}[/tex](x+5)
Putting the value of f(x) and g(x) in equation (1).
→ [tex]\frac{1}{3}[/tex](x+5) = [tex]\frac{1}{3}[/tex](x+2) + k
→ [tex]\frac{1}{3}[x+5-x-2][/tex]= k
→ k = [tex]\frac{1}{3} \times 3=1[/tex]
So , the value of k is 1.
Answer:
K=5
Step-by-step explanation:
there you go
graphing polynomial functions?
NOTES:
Degree: the largest exponent in the polynomial
End Behavior:
Coefficient is POSITIVE, then right side goes to POSITIVE infinityCoefficient is NEGATIVE, then right side goes to NEGATIVE infinityDegree is EVEN, then left side is SAME direction as right sideDegree is ODD, then left side is OPPOSITE direction as right sideMultiplicity (M): the exponent of the zero. e.g. (x - 3)² has a multiplicity of 2
Relative max/min: the y-value of the vertices.
Find the axis of symmetry (the midpoint of two neighboring zeros)Plug the x-value from 1 (above) into the given equation to find the y-value. (which is the max/min)Repeat 1 and 2 (above) for each pair of neighboring zeros.Rate of Change: slope between the two given points.
********************************************************************************************
1. f(x) = (x-1)²(x + 6)
a) Degree = 3
b) end behavior:
Coefficient is positive so right side goes to positive infinityDegree is odd so left side goes to negative infinityc) (x - 1)²(x + 6) = 0
x - 1 = 0 x + 6 = 0
x = 1 (M=2) x = -6 (M=1)
d) The midpoint between 1 and -6 is -3.5, so axis of symmetry is at x = -3.5
y = (-3.5 - 1)²(-3.5 + 6)
= (-4.5)²(2.5)
= 50.625
50.625 is the relative max
e) see attachment #1
f) The interval at which the graph increases is: (-∞, -3.5)U(1, ∞)
g) The interval at which the graph decreases is: (-3.5, 1)
h) f(-1) = (-1 - 1)²(-1 + 6)
= (-2)²(5)
= 20
f(0) = (0 - 1)²(0 + 6)
= (-1)²(6)
= 6
Find the slope between (-1, 20) and (0, 6)
m = [tex]\frac{20-6}{-1-0}[/tex]
= [tex]\frac{14}{-1}[/tex]
= -14
********************************************************************************************
2. y = x³+3x²-10x
= x(x² + 3x - 10)
= x(x + 5)(x - 2)
a) Degree = 3
b) end behavior:
Coefficient is positive so right side goes to positive infinity
Degree is odd so left side goes to negative infinity
c) x(x + 5)(x - 2) = 0
x = 0 x + 5 = 0 x - 2 = 0
x = 0 (M=1) x = -5 (M=1) x = 2 (M=1)
d) The midpoint between -5 and 0 is -2.5, so axis of symmetry is at x = -2.5
y = -2.5(-2.5 + 5)(-2.5 - 2)
= -2.5(2.5)(-4.5)
= 28.125
28.125 is the relative max
The midpoint between 0 and 2 is 1, so axis of symmetry is at x = 1
y = 1(1 + 5)(1 - 2)
= 1(6)(-1)
= -6
-6 is the relative min
e) see attachment #2
f) The interval at which the graph increases is: (-∞, -2.5)U(1, ∞)
g) The interval at which the graph decreases is: (-2.5, 1)
h) f(-1) = -1(-1 + 5)(-1 - 2)
********************************************************************************************
3. y = -x(x + 2)(x - 7)(x - 3)
a) Degree = 4
b) end behavior:
Coefficient is negative so right side goes to negative infinity
Degree is even so left side goes to negative infinity
c) -x(x + 2)(x - 7)(x - 3) = 0
-x = 0 x + 2 = 0 x - 7 = 0 x - 3 = 0
x = 0 (M=1) x = -2 (M=1) x = 7 (M=1) x = 3 (M=1)
d) The midpoint between -2 and 0 is -1, so axis of symmetry is at x = -1
y = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)
= 1(1)(-8)(-4)
= 32
32 is a relative max
The midpoint between 0 and 3 is 1.5, so axis of symmetry is at x = 1.5
y = -(1.5)(1.5 + 2)(1.5 - 7)(1.5 - 3)
= -1.5(3.5)(-5.5)(-1.5)
= -43.3125
-43.3125 is the relative min
The midpoint between 3 and 7 is 5, so axis of symmetry is at x = 5
y = -(5)(5 + 2)(5 - 7)(5 - 3)
= -5(7)(-2)(2)
= 140
140 is the relative max
e) see attachment #3
f) The interval at which the graph increases is: (-∞, -1)U(1.5, 5)
g) The interval at which the graph decreases is: (-1, 1.5)U(5, ∞)
h) f(-1) = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)
= 1(1)(-8)(-4)
= 32
f(0) = -(0)(0 + 2)(0 - 7)(0 - 3)
= 0
Find the slope between (-1, 32) and (0, 0)
m = [tex]\frac{32-0}{-1-0}[/tex]
= [tex]\frac{32}{-1}[/tex]
= -32
Y=
Pls help solve for
Answer:
[tex]y=39\degree[/tex]
Step-by-step explanation:
The given triangle is a right angle triangle .
The known sides of the triangle that is opposite to angle y is 8 units while the side adjacent is 10 units.
The value of y can be calculated using the tangent ratio.
[tex] \tan(y)=\frac{8}{10}[/tex]
We solve for y to get,
[tex]y=arctan(\frac{4}{5})[/tex]
We evaluate to obtain,
[tex]y=38.66[/tex]
[tex]y=39\degree[/tex] to the nearest degree
Solve the equation for the letter L: V = LWH
Answer:
L = V / WH
Step-by-step explanation:
Solve for L: V = LWH
To solve, all you have to do is get L on its own on one side.
Because the only operation used in this equation is multiplication, only one operation is needed to solve it: division. Just divide both sides by WH to isolate L.
V / WH = LWH / WH
V / WH = L
[tex]LWH=V\qquad\text{divide both sides by}\ WH\neq0\\\\\boxed{L=\dfrac{V}{WH}}[/tex]
in one hour a seamstress can sew 52 yards of material. How many yards can she sew in 45 minutes?
Answer:
39 yards
hope it helps
Step-by-step explanation:
52 ÷ 4 = 13 per quarter of an hour
we are gonna divide by four because there are 4 quarters in a hour and in 3 quarters there is 45 minutes
13 x 3 = 39
The seamstress can sew 39 yards of material in 45 minutes.
Explanation:To find out how many yards the seamstress can sew in 45 minutes, we need to convert 45 minutes into hours. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours.
Next, we can use the given information that the seamstress can sew 52 yards of material in one hour. Multiply the yards per hour by the fraction of an hour to find out how many yards can be sewn in 45 minutes:
Yards in 45 minutes = 52 yards/hour × 0.75 hours = 39 yards.
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Write the following equation in the general form Ax + By + C = 0. 2x + y = 6
Given two random points, A and B, let's find the locus of point P, such that PA=PB.
If PA = PB ,then P is located on perpendicular bisector of AB.
Look at the picture.
What is the probability of choosing a vegetable
Wrongs guys ok don’t pick it
Answer: It's A. 2/5
Step-by-step explanation:
1. It's asking for the probability of picking a vegetable
We can see in the model that 2 carrots and 2 broccoli are vegetables so 4
2. Add up the values
2+2+2+1+2+1= 10
3. 4/10---> 2/5
To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 6x + 5y = 2 4x + 2y = 8
Answer:
Multiply each equation by the coefficient of y in the other one.
Step-by-step explanation:
(1) 6x + 5y = 2
(2) 4x + 2y = 8
Multiply each equation by the coefficient of y in the other one.
Multiply (1) by 2 and (2) by 5.
(3) 12x + 10y = 4
(4) 20 x + 10y = 40 Subtract (3) from (2)
8x = 36 Solve for x
x = 9/2
Answer:
Subtract 5 times the first equation from 2 times the second equation
Step-by-step explanation:
2(6x + 5y = 2)
5(4x + 2y = 8)
12x + 10y = 4
20x + 10y = 40
Subtracting the second equation from first gives:
−8x = −36
x =
−36
−8
x =
9
2
There are 16 dolphins in a pod. Each pod has the same number of males and females. The female dolphins are swimming in pairs. How many pairs of female dolphins are there?
Final answer:
To determine the number of pairs of female dolphins, the total number of dolphins is divided equally between males and females, resulting in 8 female dolphins. Then, dividing by 2 as they swim in pairs, we find there are 4 pairs of female dolphins.
Explanation:
The question involves dividing the total number of dolphins in the pod by two to find out how many male and female dolphins there are since the pod has an equal number of each gender. Since the females are swimming in pairs, we then divide the number of female dolphins by two to find out how many pairs there are.
There are 16 dolphins in total. Half of them are females, so there are 8 female dolphins. The females swim in pairs, so to find the number of pairs we divide the number of female dolphins by two:
8 females ÷ 2 = 4 pairs of female dolphins.
height of an object t seconds after it is launched is modeled by the function h(t) = -5t^2 + 30t + 200. the object will hit the ground in how many seconds.
Answer:
10 seconds
Step-by-step explanation:
AS it is given in the question that
h(t) = -5t² + 30t + 200 ...........................(i)
We have to find the time when it will touch the ground
so it will be touching the ground when its height from ground will be zero
i.e. h(t)=0
so equation (i) becomes
0 = -5t² + 30t + 200
Now we will solve this to get the value of t
Dividing whole equation with (-5) it will give us
t² - 6t - 40 = 0
Using the mid term breaking rule which will break the mid term and we will get the factors from the mid term
t² - 10t + 4t - 40 = 0
Now we will do the factorization of it
t(t-10)+4(t-10)=0
(t-10)(t+4)=0
so either
t-10 = 0 or t+4=0
t=10 or t= - 4
as t is time so it can not be negative
so
t=10 seconds will be the time in which it will touch the earth
Answer: 10 seconds
Step-by-step explanation:
When the object hits the ground, the height (y-value) is 0.
h(t) = -5t² + 30t + 200
0 = -5t² + 30t + 200 set height equal to zero
0 = -5(t² - 6t - 40) factored out -5
0 = -5(t - 10)(t + 4) factored the quadratic
0 = t - 10 0 = t + 4 applied the Zero Product Property
t = 10 t = -4 solved for t
↓
t = -4 is not valid (since time cannot be negative)
So, t = 10
If f(x)=(-x) cubed, then f(-3)?
Answer:
f(-3) = 27
Step-by-step explanation:
f(x) = (-x)^3
We want the value when x =-3
Substitute this in
f(-3) = (--3)^3
f(-3) = 3^3
f(-3) = 27
If ABCD is a parallelogram which of the following statements is not true
Answer: A+C = 180 (first answer choice)
This statement is only true if and only if we are dealing with a rectangle (where all four angles are 90 degrees). Otherwise, the statement is false.
---------------
side notes:
The second statement that AN = NC and DN = NB is true because a parallelogram has its diagonals bisect each other. In other words, the diagonals cut in each other in half.
The third statement that AD = BC and DC = AB is true because opposite sides of a parallelogram are parallel and congruent.
The fourth statement is true because opposite angles of a parallelogram are congruent. If A = C = 90, then A+C = 90+90 = 180 backing up the claim I made earlier, but it's possible that A and C are non-right angles making this parallelogram non-rectangular.
Answer:
m∠A + m∠C = 180
Step-by-step explanation:
WILL GIVE BRAINLY!!!
.
.
Convert a repeating decimal two an improper fraction or mixed number. Upload all of your work as part of your final answer.
___
3.152
Answer:
3149/999 = 3 152/999
Step-by-step explanation:
I'll assume the bar is over 152 and there is a typo.
Use a step-by-step calculator (I recommend Symbolab) OR:
Let x equal 3.152...
1000x = 3152.152...
1000x-x = 3152.152... - 3.152...
999x =
3152.152...
- 3.152...
3149
Cancel out the .152...
999x = 3149
Divide by 999 on each side
x=3149/999 = 3 152/999
Answer:
The given number is 3.152.
Notice that this is a rational number without a repetition pattern, that means we just need to divide all digist without the decimal point by 1000, because the number of zeros always depends on the number of decimals, which are three in this case.
[tex]\frac{3152}{1000}[/tex]
Then, we simplfy
[tex]\frac{3152}{1000}=\frac{1576}{500}=\frac{788}{250}=\frac{394}{125}[/tex]
So, the improper fraction equal to 3.152 is 394/125.
The mixed number is [tex]\frac{394}{125}=3\frac{19}{125}[/tex]
The difference between two numbers is 15. The greater number is two less than twice the lesser number.
Find the numbers.
Answer:
x=32, y=17
Step-by-step explanation:
Difference between two numbers is 15:
x-y=15
Greater number (x) is two less than twice the lesser number:
x=2y-2
-----
x-y=15,
x=2y-2.
x-y-x=15-2y+2
-y=15-2y+2
y=15+2
y=17
-----
x-y=15
x-17=15
x=17+15
x=32
To solve the word problem, we transcribe the information into algebraic equations. We then isolate one variable to solve for it first, and then substitute that variable's value into the second equation. The solution we find is that the two numbers are 17 and 32.
Explanation:To solve the problem, we must translate the word problem into algebraic equations. We're trying to find two numbers based on the information that's given to us: their difference is 15, and the larger number is two less than twice the smaller number.
First, let's define the numbers as follows: x = smaller number and y = larger number. Now we can set up our two equations based on the problem:
y - x = 15 (because the difference between two numbers is 15) y = 2x - 2 (because the larger number is two less than twice the smaller number)
Now we can substitute equation (2) into equation (1) which gives us: 2x -2 - x = 15. Simplify the equation, we get x = 17 and substitute x = 17 into equation (2), we get y = 32.
So, the two numbers are 17 and 32.
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to make 1 1/2 dozen muffins, a recipe uses 3 1/2 cups of flour.
How many cups of flour are needed for every dozen muffins made?
Final answer:
To find how many cups of flour are needed for every dozen muffins made, set up a ratio using the given information, and solve for x.
Explanation:
To find how many cups of flour are needed for every dozen muffins made, we can set up a ratio using the information given in the question. We know that to make 1 1/2 dozen muffins, 3 1/2 cups of flour are needed. So we can set up the ratio:
1 1/2 dozen muffins : 3 1/2 cups of flour = 1 dozen muffins : x cups of flour
To solve for x, we can cross multiply, and divide:
(1 1/2) * x = (1) * (3 1/2)
x = (1 * 3 1/2) / (1 1/2) = 7/2 cups of flour
Therefore, for every dozen muffins made, 7/2 cups of flour are needed.
if y=6x+8 and y=-4x-2,what is the value of x+y when the two equations are equal?
Answer:
x + y = 1
Step-by-step explanation:
If the two equations are the same, then it can be shown by this:
6x + 8 = -4x - 2
We need to isolate the x values, so we need to move the -4x over to the other side making it a +4x:
6x + 4x + 8 = -2
Next, move the +8 over to the other side making it a -8:
6x + 4x = -2 - 8
10x = -10
x = -1
So now we can plug this value into the first equation:
6(-1) + 8 = y
-6 + 8 = y
y = 2
x + y = -1 + 2 = 1
So x + y = 1
find the maximum value of c=4x+2y
2x+2y less than or equal to 10
3x+y less than or equal to 9
Answer: 14
Step-by-step explanation:
Step 1: Graph both equations to find the vertices (see attached):
The graph shows vertices at: (0, 0), (3, 0), (0, 5) and (2, 3)Step 2: Input the coordinates of the vertices into the given function (c = 4x + 2y):
(0, 0): 4(0) + 2(0) = 0(3, 0): 4(3) + 2(0) = 12(0, 5): 4(0) + 2(5) = 10(2, 3): 4(2) + 2(3) = 14Step 3: Evaluate the value from Step 2 to find the maximum (largest).
the largest value between {0, 12, 10, 14} is 14Marcus finds that (3x2-2y2+5x)+(4x2+12y2-7x)=7x2-10y2-2x. What error did Marcus make?
He combined the terms 5x and –7x incorrectly.
He combined the terms 3x2 and 4x2 incorrectly.
He combined the terms –2y2 and 12y2 incorrectly.
He subtracted the polynomials instead of adding.
Given : (3x² - 2y² + 5x) + (4x² + 12y² - 7x)
Rearranging like terms, we get :
⇒ (3x² + 4x²) + (12y² - 2y²) - 7x + 5x
⇒ 7x² + 10y² - 2x
But, Marcus got the Answer as : 7x² - 10y² - 2x
Marcus combined the terms -2y² and 12y² Incorrectly
Following are the solution to the given expression:
Given:
[tex]\bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2x}[/tex]
To find:
Solve equation=?
Solution:
[tex]\to \bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2x}[/tex]
Solving the L.H.S part:
[tex]\to \bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)}\\\\\to \bold{(3x^2-2y^2+5x+4x^2+12y^2-7x)}\\\\\to \bold{(7x^2+10y^2-2x)}\\\\[/tex]
Solving the R.H.S part:
[tex]\bold{=7x^2-10y^2-2x}[/tex]
Since in this question the [tex]L.H.S \neq R.H.S[/tex] , and when we solve the equation so, except the third choice all were correct.
Therefore, the final answer is " He combined the terms [tex]\bold{-2y^2\ and\ 12y^2}[/tex]incorrectly."
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brainly.com/question/2402445
in a group of 20 students 25% wear glasses how many do not wear glasses?
Answer:
15
Step-by-step explanation:
25 percent of 20 is 5, and 20-5 equals 15.
In a group of 20 students, 15 do not wear glasses.
if you borrow $421 for nine years at an interest rate of 4% how much interest will you pay
Answer:
the answer is $151.56
Step-by-step explanation:
our formula of interest is I = PxRxT
P (principal) = 421
R (rate) = 4% (we have to turn it into a decimal which is 0.04)
T (time) = 9 years
so :
I = 421 x 0.04 x 9
I = 151.56
The total interest paid will be $151.56.
To find out how much interest you will pay on a loan of $421 over nine years at an annual interest rate of 4%, we can use the formula for simple interest:
Simple Interest = Principal × Rate × Time
Where the Principal amount is $421, the Rate is 4% (or 0.04 when converted to a decimal), and the Time is 9 years.
Let's plug the values into the formula:is 9.36 less. than. 9.359
Answer:
Its more because 9.36 has a bigger beginning then 9.359.
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Answer:
No
Step-by-step explanation:
9.36= 9.360
9.360> 9.359
The hundredeth's place of 9.360 is greater than the hundredth's place of 9.359.
solve this equation 11/20 +x= 9/10
11/20 + x = 9/10
x = 9/10 - 11/20
x = 18/20 - 11/20
x = 7/20
Answer:
x = 7/20
Step-by-step explanation:
11/20 +x= 9/10
Subtract 11/20 from each side
11/20-11/20 +x= 9/10-11/20
x = 9/10-11/20
We need a common denominator of 20
x = 9/10 *2/2 - 11/20
x =18/20 -11/20
x = 7/20