Answers
Answer:
D. -1/7
Step-by-step explanation:
Substitute and solve
Answer:
[tex]-\frac{1}{7}[/tex]
Step-by-step explanation:
When given the following expression,
[tex]\frac{a+c}{a^2-c^2}[/tex]
With the information that the values (a = -2) and (c = 5), one is asked to evaluate the expression. One's first instinct is probably to substitute the values into the expression and solve, however, a faster approach is to simplify the expression. The denominator is the difference of squares, thus one can rewrite it as the product of two linear expressions. Then one can simplify it by canceling out like terms in the denominator and the numerator. Finally, one can then substitute the values of the (a) and (c) into the simplified expression and solve.
[tex]\frac{a+c}{a^2-c^2}[/tex]
[tex]=\frac{a+c}{(a+c)(a-c)}[/tex]
Cross out like terms in the numerator and denominator,
[tex]=\frac{a+c}{(a+c)(a-c)}[/tex]
[tex]=\frac{1}{a-c}[/tex]
Now substitute the values of (a) and (c) into the expression and simplify to evaluate,
[tex]=\frac{1}{a-c}[/tex]
[tex]=\frac{1}{(-2)-(5)}\\\\=\frac{1}{-2-5}\\\\=-\frac{1}{7}[/tex]
Related Questions
The price of a laptop was first increased by 10% and then the new price was decreased by 20%. The final price was what percent of the initial price.
Answers
Answer:
88%
Step-by-step explanation:
to initial price (100%) was increased by 10% (resulting in 110% of the initial price).
then these 110% were decreased by 20%.
so, the final price is actually 80% of 110% of the initial price
20/100 = 1/5
80/100 = 4/5
so, the customer pays only 4/5 of the 110% price.
110 × 4/5 = 22 × 4 = 88%
so, the final price was 88% of the initial price
What is the scale of the y-axis in this coordinate graph?
A. 1 tick mark represents 1 unit
B. 1 tick mark represents 8 units
C. 1 tick mark represents 12 units
D. 1 tick mark represents 16 units
Answers
Answer:
Obviously B
Step-by-step explanation:
Lines L and M are parallel.
Help I’ll make u brainliest if it’s right!!
Answers
Answer:
∠3 = 142°
Step-by-step explanation:
L // M
∠2 = 38° {Corresponding angles are congruent}
∠2 + ∠3 = 180 {Linear pair}
38 + ∠3 = 180
∠3 = 180 - 38
∠3 = 142°
the answer is 142 degrees, get 180 degrees from a straight lines and subtract the acute angle from 180 to get the answer, 180-38
There are 11900 films on Netflix. 13% of the films are action. How many films are action?
Answers
13% of 11900 films are action films =1547 films.
Answer:
[tex]{ \tt{ = \frac{13}{100} \times 11900 }} \\ = 1547 \: action \: films[/tex]
find m to cos²x-(m²-3)sinx+2m²-3=0 have root
Answers
Answer:
[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex] would ensure that at least one real root exists for this equation when solving for [tex]x[/tex].
Step-by-step explanation:
Apply the Pythagorean identity [tex]1 - \sin^{2}(x) = \cos^{2}(x)[/tex] to replace the cosine this equation with sine:
[tex](1 - \sin^{2}(x)) - (m^2 - 3)\, \sin(x) + 2\, m^2 - 3 = 0[/tex].
Multiply both sides by [tex](-1)[/tex] to obtain:
[tex]-1 + \sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 3 = 0[/tex].
[tex]\sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 2 = 0[/tex].
If [tex]y = \sin(x)[/tex], then this equation would become a quadratic equation about [tex]y[/tex]:
[tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex].
[tex]a = 1[/tex].[tex]b = m^{2} - 3[/tex].[tex]c = -2\, m^{2} + 2[/tex].However, [tex]-1 \le \sin(x) \le 1[/tex] for all real [tex]x[/tex].
Hence, the value of [tex]y[/tex] must be between [tex](-1)[/tex] and [tex]1[/tex] (inclusive) for the original equation to have a real root when solving for [tex]x[/tex].
Determinant of this quadratic equation about [tex]y[/tex]:
[tex]\begin{aligned} & b^{2} - 4\, a\, c \\ =\; & (m^{2} - 3)^{2} - 4 \cdot (-2\, m^{2} + 2) \\ =\; & m^{4} - 6\, m^{2} + 9 - (-8\, m^{2} + 8) \\ =\; & m^{4} - 6\, m^{2} + 9 + 8\, m^{2} - 8 \\ =\; & m^{4} + 2\, m^{2} + 1 \\ =\; &(m^2 + 1)^{2} \end{aligned}[/tex].
Hence, when solving for [tex]y[/tex], the roots of [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] in terms of [tex]m[/tex] would be:
[tex]\begin{aligned}y_1 &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) + \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) + (m^{2} + 1)}{2} = 2\end{aligned}[/tex].
[tex]\begin{aligned}y_2 &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) - \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) - (m^{2} + 1)}{2} \\ &= \frac{-2\, m^{2} + 2}{2} = -m^{2} + 1\end{aligned}[/tex].
Since [tex]y = \sin(x)[/tex], it is necessary that [tex]-1 \le y \le 1[/tex] for the original solution to have a real root when solved for [tex]x[/tex].
The first solution, [tex]y_1[/tex], does not meet the requirements. On the other hand, simplifying [tex]-1 \le y_2 \le 1[/tex], [tex]-1 \le -m^{2} + 1 \le 1[/tex] gives:
[tex]-2 \le -m^{2} \le 0[/tex].
[tex]0 \le m^{2} \le 2[/tex].
[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].
In other words, solving [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] for [tex]y[/tex] would give a real root between [tex]-1 \le y \le 1[/tex] if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].
On the other hand, given that [tex]y = \sin(x)[/tex] for the [tex]x[/tex] in the original equation, solving that equation for [tex]x\![/tex] would give a real root if and only if [tex]-1 \le y \le 1[/tex].
Therefore, the original equation with [tex]x[/tex] as the unknown has a real root if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].
The x- intercepts of a parabola are (0,-6) and (0,4). The parabola crosses the y- axis at -120. Lucas said that an equation for the parabola is y=5x^2+10x-120 and that the coordinates of the vertex are (-1, -125). Do you agree or disagree? List why?
Answers
Given:
The x- intercepts of a parabola are (0,-6) and (0,4).
The parabola crosses the y- axis at -120.
Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).
To find:
Whether Lucas is correct or not.
Solution:
The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.
[tex]y=a(x+6)(x-4)[/tex] ...(i)
The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).
[tex]-120=a(0+6)(0-4)[/tex]
[tex]-120=a(6)(-4)[/tex]
[tex]-120=-24a[/tex]
Divide both sides by -24.
[tex]\dfrac{-120}{-24}=a[/tex]
[tex]5=a[/tex]
Substituting [tex]a=5[/tex] in (i), we get
[tex]y=5(x+6)(x-4)[/tex]
[tex]y=5(x^2+6x-4x-24)[/tex]
[tex]y=5(x^2+2x-24)[/tex]
[tex]y=5x^2+10x-120[/tex]
So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].
The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:
[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].
[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]
[tex]-\dfrac{b}{2a}=-1[/tex]
Putting [tex]x=-1[/tex] in the equation of the parabola, we get
[tex]y=5(-1)^2+10(-1)-120[/tex]
[tex]y=5-10-120[/tex]
[tex]y=-125[/tex]
So, the vertex of the parabola is at point (-1,-125).
Therefore, Lucas is correct.
Finish solving the system of equations.
x – 5y = 6
–x + 2y = –3
–3y = 3
What is the value of y?
Substitute the value of y back into one of the original equations to find the value of x. What is the value of x?
Answers
Answers: x = 1 and y = -1
Explanation:
Start where your teacher left off, which is -3y = 3.
We solve for y by dividing both sides by -3
That turns -3y = 3 into y = -1
Then we use this y value to find x
x - 5y = 6
x - 5(-1) = 6
x + 5 = 6
x = 6-5
x = 1
The solution is (x,y) = (1, -1)
Answer:
-1,1
Step-by-step explanation:
Express each of the following negative angles as its equivalent positive angle between 0°and360°
+120°
Answers
Answer:
Dilated pupils
Long periods of wakefulness
Loss of appetite
Overconfidence
Over-excitement
Paranoia
Runny nose or frequent sniffles
White powder around nostrils
Legal issues
Missing or being late to work
Financial problems
Mood swings
Irritability
Depression
A oil company has a large tank that holds the oil before it is distributed. If it costs $3.20 per cubic meter for oil, how much money would it cost to fill the entire tank?
A. $65,280
B. $68,000
C. $5,440
D. $67,200
Answers
Answer:
Option A, $65,280
Step-by-step explanation:
The volume of the tank is,
12×20×15+40×(50-15)×12
= 3600+16800
=20400 cubic meters
For each cubic meter, it costs $3.20, so for 20400 cubic meters it'll cost,
20400×$3.20
= $65,280
Answered by GAUTHMATH
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Passing through (-3, -6) and (2,9)
What is the equation of the line in point-slope form?
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
What is the equation of the line in slope-intercept form?
Answers
Answer:
slope-inercept form: y = 3x + 3 point-slope form: y - 9 = 3(x - 2)
Step-by-step explanation:
slope-intercept form:
y2 - y1 / x2 - x1
9 - (-6)/ 2 - (-3)
= 3
y = 3x + b
9 = 3(2) + b
9 = 6 + b
3 = b
y = 3x + 3
point-slope form:
y - 9 = 3(x - 2)
how do you get sin theta
Answers
And 1/csc
And root 1-cos^2
solve (algebra 1)− 0.32 + 0.18 = 0.25 − 1.95
Answers
Answer:
0.50=1.7. They do not equal each other
Step-by-step explanation:
Thats what I got from this question
How many fives makes 6 tens
Answers
Answer:
12.
Step-by-step explanation:
6x10 = 60.
60 divided by 12 =5.
Answer:
12
Step-by-step explanation:
5x = 60
x = 12
Factor completely x2 + 16
Answers
Answer:
not a factorable number i think
Step-by-step explanation:
Tìm x €N: a) 24:(2x-4)+14=26
Answers
B a 135899933
Can someone help me with this math homework please!
Answers
Answer:
1 = Input G
2 = Input F
3 = Input H
Step-by-step explanation:
divide x3-3x2+x-2 by 10x4-14x3-10x2+6x-10 the quotient is and the remainder is
Answers
Answer:
The quotient is 10x+16
The remainder is 28x²+10x+22
Step-by-step explanation:
Solution,
___________________________
x^3 - 3x^2 + x - 2 ] 10x^4 - 14x^3 - 10x^2 + 6x - 10 [ 10x + 16
10x^4 - 30x^3 + 10x^2 - 20x
16x^3 - 20x^2 + 26x - 10
16x^3 - 48x^2 + 16 x - 32
28x^2 + 10x + 22
Answer:
The quotient is 10x+16
The remainder is 28x²+10x+22
Step-by-step explanation:
What is the soution of (Image below)
Answers
Answer:
A
Step-by-step explanation:
Starting with the original equation:
[tex]\sqrt{1-3x} =x+3[/tex]
Squaring both sides to remove the root, and expanding the right side:
[tex]1-3x=(x+3)(x+3)[/tex]
Multiplying the right side:
[tex]1-3x=x^{2} +6x+9[/tex]
Combine like terms:
[tex]x^{2} +9x+8[/tex]
Factor:
(x+8)(x+1)
If x+8=0, then x= -8
If x+1=0, then x=-1
Last year, sales at a book store increased from $5,000 to $10,000. This year, sales decreased to $5,000 from $10,000. What percentage did sales
increase last year? What percentage did sales decrease this year?
Sales increased
last year, from $5,000 to $10,000. When sales dropped from $10.000 to $5,000 this year, sales decreased
Answers
Answer:
Last year sales increased by 200%. This year sales decreased by 50%.
Step-by-step explanation:
received good return from m center of rs 5000 (journal entry)
Answers
Answer:
Date Account Title Debit Credit
XX-XX-XXX Sales returns and Allowances Rs. 5,000
Accounts receivable - M Center Rs. 5,000
Inventory Rs. 5,000
Cost of Goods sold Rs. 5,000
In which figure is DE BC
Answers
Answer:
Given: DB = 7.2 cm, AE = 1.8 cm and EC = 5.4 cm and DE || BC.
DB
AD
=
AC
AE
[by basic proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same.
7.2
AD
=
5.4
1.8
AD=
5.4
7.2×1.8
AD=
10
24
⟹AD=2.4cm
on a coordinate gride what is the distance between (1,3) and (6,15)
Answers
Answer:
13
Step-by-step explanation:
Distance between points (1, 3) and (6, 15) is 13
if x-y=9 and xy=2,find the value of (x square + y square)
Answers
Answer:
x² + y² = 85
Step-by-step explanation:
Using the expansion
(x - y)² = x² + y² - 2xy , then
x² + y² - 2xy = (x - y)² ( add 2xy to both sides )
x² + y² = (x - y)² + 2xy ← substitute given values
= 9² + 2(2)
= 81 + 4
= 85
Evaluate function from their graph
Answers
Answer:
f(-5) = 7
Step-by-step explanation:
f(-5) means find the y value when x = -5
y = 7 when x = -5
The area of a wall in a house is 10.37 square metres. If a can of paint covers 3.1 square metres, how many cans of paint are needed to paint the wall?
Answers
Answer:
4 cans of paint
Step-by-step explanation:
Take the area of the wall and divide by the area that the can of pain will cover
10.37 / 3.1
3.34516129 cans
We need to round up to make sure we buy enough cans of paint
4 cans of paint
We can take area as,
Area = A
The required formula is,
→ A of wall ÷ A that paint's can will cover
Then find the no. of cans of paint that are needed to paint the wall.
Now use the formula,
→ A of wall ÷ A that paint's can will cover
→ 10.37 ÷ 3.1
→ 3.34516129032
→ 4 cans (by nearest value)
Hence, we need 4 cans to paint the wall.
Evaluate each of the following. help plz
Answers
Answer:
5!= 120
13!= 6227020800
12!/6!= 665280
10!/7! 3!= 120
5(4!)= 120
Step-by-step explanation:
the area of the rectangle is 48cm^2
show that x satisfies the equation x^2 + 7x -78 = 0
Answers
Answer:
No its doesn't satisfy the equation.
[tex]{ \bf{area = 2(l + w)}} \\ { \tt{48 = 2((x + 10) + (x - 3))}} \\ { \tt{24 = 2x + 7}} \\ 2x = 17 \\ x = 8.5 \\ \\ { \bf{in : \: {x}^{2} + 7x - 78 = 0 }} \\ x = 6 \: \: and \: \: - 13[/tex]
Isabell drove 819 miles in 13 hours. at the same rate how many miles would she drive in 7 hours
Answers
Answer:
441 miles
Step-by-step explanation:
Rate of the Car: 819/13 = 63mph
Miles Driven in 7 Hours: 63*7 = 441 miles
Answer:
441 miles
Step-by-step explanation:
* means multiply
819/13 = x/7
13 * x = 819 * 7
13x = 5733
x = 5733 ÷ 13
x = 441
I WILL GIVE BRAINLIEST I NEED HELP NOW!!! I PROMISEThe table shows the relationship “Kevin read 35 pages per hour.”
Hours (h)
Pages (p)
1
35
2
70
3
105
4
140
5
175
Which statements are correct? Check all that apply.
The variable h is the independent variable.
The variable p is the independent variable.
The number of pages read increases as the amount of time decreases.
The number of hours spent reading causes a change in the number of pages read.
The variable p is the dependent variable.
The variable h is the dependent variable.
The more pages that are read, the less time it takes.
Answers
Answer:
The correct answers are:
The variable p is the independent variable.
The number of hours spent reading causes a change in the number of pages read.
The variable p is the dependent variable.
Step-by-step explanation: Hope this helps :)))
These two statements are correct and applicable
(1) The number of hours spent reading causes a change in the number of pages read.
(2) The variable p is the dependent variable.
What is a variable?"A Variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables."
What is a dependent variable?"A dependent variable is the variable that changes as a result of the independent variable manipulation."
What is a linear graph?"A Line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. A Line graph has two axes(X- axis and Y-axis)"
We have,
Kelvin read 35 pages per hour
According to the question,
Number of hours increasing, number of pages also increasing
∵ The table data shows linear graph
We can clearly say that from a line graph definition,
These two are correct and applicable to Kelvin's situation
(1) The number of hours spent reading causes a change in the number of pages read.
(2) The variable p is the dependent variable.
Learn more about Line graph and variable here
https://brainly.com/question/20106471
https://brainly.com/question/20291071
#SPJ2
Find the coordinates of the other endpoint when given midpoint (point M) and one of the endpoints (point P). P=(3,5) and M=(-2,0)
Answers
Answer:
About Points
S = (x,y) searched point (it will be in the third quadrant )
M = (-2,0) Midpoint | SP |
P = (3,5) one end of the segment | SP |
You have to draw Cartesian.
we set in a point M and P. We both points by a simple and we extend it for the third quarter of the system. Compass measure the distance from the point M to the point P. From the point M we set a compass point S. Figure attached. Received point S = ( -7 , -5 ) . It sought a point that calculate .
We use the information that | SM | = | MP |
Answer : S = (-7,-5)
Step-by-step explanation:
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad \underline{Q}(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+3}{2}~~,~~\cfrac{y+3}{2} \right)=\stackrel{M}{(-2,0)}\implies \begin{cases} \cfrac{x+3}{2}=-2\\[1em] x+3=-4\\ \boxed{x = -7}\\[-0.5em] \hrulefill\\ \cfrac{y+3}{2}=0\\[1em] y+3=0\\ \boxed{y=-3} \end{cases}[/tex]