The equivalent expression of a + 5 is -(-a - 5)
How to rewrite the expression?The expression is given as:
a + 5
Multiply by 1
1 * (a + 5)
Express 1 as -1 * -1
-1 * -1 * (a + 5)
Open the bracket
-1 * (-a - 5)
This gives
-(-a - 5)
Hence, the equivalent expression of a + 5 is -(-a - 5)
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Part 2 - Find the error(s) and solve the problem correctly.
The error is present in second step when cancelling numerator and denominator and the solution of the expression [tex](1+1/x)/(1-1/x^{2} )[/tex] is [tex]x/x-1[/tex].
Given Expression [tex](1+1/x)/(1-1/x^{2} )[/tex] and incorrect solution. and we need to identify the error and solve the expression correctly.
The expression is [tex](1+1/x)/(1-1/x^{2} )[/tex]
In the solution given the second step of cancelling 1's in numerator and denominator is wrong.
The solution which is correct is as under:
[tex](1+1/x)/(1-1/x^{2} )[/tex]
firstly take LCM in numerator and denominator
=[tex](x+1)/x/(x^{2} -1)/x^{2}[/tex]
Now we can write the expression properly.
=[tex](x+1)*x^{2} /(x^{2} -1)*x[/tex]
Power of [tex]x^{2}[/tex] to be deducted from x
=[tex](x+1)*x/(x^{2} -1)[/tex]
Now [tex]x^{2} -1[/tex] can be written as (x+1)(x-1)
=[tex](x+1)*x/(x+1)(x-1)[/tex]
(x+1) will be deducted now from numerator and denominator.
=x/(x-1)
Hence the solution of the given expression is x/(x-1).
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The answer to this question is x/x₋1
Given the expression is 1₊1/x /1₋1/x²
Take the LCM of the denominators
we get, x₊1/x / x²₋1/x²
Now multiply the expression
=x₊1/x × x²/x²₋1
=(x₊1) x²/ x(x²₋1)
(x²₋1) is in the form of (a²₋b²)=(a₊b)(a₋b)
Therefore, (x₊1)x²/x(x₋1)(x₊1)
After cancelling like terms we get the answer as:
x/(x₋1)
Hence we get the simplification answer as x/(x₋1).
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Graph the system below and write its solution.
y = -1/2x+2
3x+y=-3
Note that you can also answer "No solution" or "Infinite
The graph of the system can be seen below, there we can see that the solution is (-2, 3).
How to solve a system graphically?To do so, we just need to graph both equations on the same coordinate axis and see where the graphs intercept.
The interceptions will be the solutions of the system of equations.
Here we have the system:
y = (-1/2)*x + 2
3x + y = -3
The graph can be seen below, where the green line is the first equation, and the blue line is the second equation.
On the graph, you can see that the lines intersect at the point (-2, 3), so that is the solution of the system.
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Section 6.1 Add and Subtract Polynomials
Add and Subtract Monomials
In the following exercises, add or subtract the monomials.
594. 12q − (−6q)
Answer:
The simplified form of [tex]12 q-(-6 q) \text { is } 18 q[/tex].
Step-by-step explanation:
[tex]- Given: $12 q-(-6 q)$\\ - Simplify.\\ - The simplified form of $12 q-(-6 q)=(12+6) q$ i.e., $18 q$.[/tex]
In an Italian class, 65 percent of the students were women. At the end of the class, 52 percent of the men and 44 percent of the women received a certificate. What percentage of those who received a certificate were men
47% of those who received a certificate were men
It is given that in an Italian class, 65 percent of the students were women. At the end of the class, 52 percent of the men and 44 percent of the women received a certificate.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
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Let f(x)=1/x+x, where is a nonzero number.what is the product of all the values of a, such that f(a)=f(2a)?
The product of all the values of a, such that f(a)=f(2a) is -1/2
Functions and expressionsGiven the function below;
f(x)=1/x + x
f(a) = 1/a + a
f(2a) = 1/2a + 2a
If f(a) = f(2a), hence;
1/a + a = 1/2a + 2a
Collect the like terms
1/a - 1/2a = 2a - a
2-1/2a = a
1/2a = a
Cross multiply
2a² = 1
a² = 1/2
a = ±√1/2
The values of a are √1/2 and -√1/2
Product = -√1/2 * √1/2
Product = -1/2
Hence the product of all the values of a, such that f(a)=f(2a) is -1/2
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If (x+ 1) is a factor of the polynomial x³ + px² + x + 6 = 0. Find p.
Answer:
p=4
Step-by-step explanation:
plug x=-1 into the polynomial with the unknown
(-1)³+p(-1)+(-1)+6=0
-1-p-1+6=0
-p+4=0
p=4
Find x A. 212√2 B. 212–√ C. 213√2 D. 7
The value of x in the triangle is (d) 7
How to solve for x?The complete question is in the attached image.
From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function
[tex]\sin(45) = \frac{x}{7\sqrt 2}[/tex]
Evaluate sin(45)
[tex]\frac 1{\sqrt 2} = \frac{x}{7\sqrt 2}[/tex]
Solve for x
[tex]x = \frac{7\sqrt 2}{\sqrt 2}[/tex]
Divide
x = 7
Hence, the value of x in the triangle is (d) 7
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what is the area of a rectangle whose length is 3x and breadth is 2x
Answer:
Your answer is 6x
Step-by-step explanation:
Given,
length(l) = 3x
breadth(b) = 2x
area of a rectangle(A) = ?
Now,
A = l*b
A = 3x*2x
A = 6x ans.
Hope its helpful!
Please mark me as brainlist.
Answer:
6 x^2
Step-by-step explanation:
Area = Length * Breadth
= 3x * 2x = 6x^2
Write each square number as a product of its prime factors.
a)9
b)36
c)81
d)144
e)225
f)576
g)625
h)2401
Answer:
the answer is provided down below
Step-by-step explanation:
steps
9 - ( 1 3 x 3 x3)
36 - (3 x 2 x2x3)
81 -( 3 x 3 x 3 x 3)
144 - ( 2 x 3 x 3 x 2 x 2 x 2 x 2)
225 - ( 5 x 5 x 3 x 3)
576 -( 2 x 2 x 2 x 2 x 2 x 2 x 3 x3)
625 - ( 5 x 5 x 5 x5 )
2401 - ( 7 x 7 x 7 x 7)
A father is 38 years old. his sons are 13 and 5 years old, and his daughter is 8 years old. In how many years will the father be the same age as his children put together?
Answer:
6 years
Step-by-step explanation:
So each person's age can be represented as a linear equation, since each year our age increases by 1. It can be represented in the slope-intercept form: y=mx+b. The slope in this case is going to be 1, since the time is going to be years, and each year everyone's age goes up by 1 (of course if you're still alive...) and y-intercept in this case represents their current age.
So the father can be represented as: y=x+38
The sons can be represented as: y = x+13 and y=x+5
The daughter can be represented as: y=x+8
So adding up all his children you get:
(x+13)+(x+5)+(x+8)
This gives you the equation:
3x+26
Now set this equal to the father's age to solve for x (in this context it's years)
3x+26=x+38
Subtract from both sides
2x+26=38
Subtract 26 from both sides
2x=12
Divide both sides by 2
x=6
So in 6 years the father will be the same age as his children put together
Annoying me I’ve been at this for hours
At a farmers market, Samuel bought 3 pounds of apples for x dollars per pound and 2 bags of spinach for y dollars each. The next day he returned and bought 5 pounds of apples for x dollars per pound and 3 bags of spinach for y dollars each. Which expression represents the total amount he spent at the market on both days? 8x Plus 5y 8y Plus 5x 6y + 7x 6x + 7y
Answer:
A. 8x+5y
Step-by-step explanation:
First day: 3x+2y
Second day: 5x+3y
Add both expressions together.
(3x+2y)+(5x+3y) =
= 3x+2y+5x+3y=8x+5y
Hope this helps!
If not, I am sorry.
HELP HELP HELP
Quick algebra 1 question for 15 points!
Explain the difference between slope-intercept form and point-slope form.
Answer:
slope intercept is used when you are given a point (most likely a y intercept) on the graph and a slope. The point slope is a larger formula that is used when you are given a slope and the coordinates of a point.
Step-by-step explanation:
slope intercept : y=mx+b
point slope : y-y1= m(x-x1)
See photo, it’s got to do with Pythagoras theorem but I don’t understand. Please help
Answer:
x = 12.0 cm
Step-by-step explanation:
If we draw a line parallel to the 12 cm line right below the line x, a right-angled triangle is formed, with x as the hypotenuse and the shortest side equal to (8 - 7 = ) 1 cm.
∴ x² = 12² + 1²
⇒ x = [tex]\sqrt{12^2 + 1^2}[/tex]
⇒ x = [tex]\sqrt{144 + 1}[/tex]
⇒ x = [tex]\sqrt{145}[/tex]
⇒ x = 12.0 cm [3 s.f.]
Answer:
12.0 cm
Step-by-step explanation:
See attached image for steps. Take the figure and convert it into a rectangle and right triangle by drawing a single line. The Pythagorean Theorem can then be used.
The Eiffel Tower in Paris, France is 1063 feet tall. If you took an elevator 3/4 the way up the tower, how far from the ground would you be in feet?
Answer: 797 feet 3 inches
Step-by-step explanation:
[tex]\frac{3}{4} *1063=\frac{3189}{4} =797.25[/tex]
a cheerleading team plans to sell t-shirts as a fundraiser. the teams goal is to make profit of at least $1248. the profit on each t-shirt sold is $6.50. The teams goal is written as a inequality shown below.
6.5t>1 2 4 8 where t=number of t-shirts sold.
The minimum number of shirt they will sell to make the given profit is 192 shirts
Inequality expressionInequalities are equations not separated by an equal sign.
If a cheerleading team plans to sell t-shirts as a fundraiser and the teams goal is to make profit of at least $1248 with each t-shirt sold at $6.50, then the equation required is;
6.50t ≥ 1246
Divide both sides by 6.50
6.50t/6.50 ≥1246/6.5
t ≥ 192
Hence the minimum number of shirt they will sell to make the given profit is 192 shirts
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Reffect shape A in the line y=-x
th
6
2
A
--5-32-10 12345
2 6
M
The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)
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16) Find the lateral area of the regular pyramid. 5 cm www 24 cm
Answer:
LA = 624 cm²
Step-by-step explanation:
h² = 5² + 12²
h = 13
LA = 4 × bh/2
LA = 4 × (24 cm)(13 cm)/2
LA = (48 cm)(13 cm)
LA = 624 cm²
What is the solution to the system of equations?
5
5
5.
OA. (4,-1)
y=x+3
5
y=-x+5
Answer:
C
Step-by-step explanation:
the solution is at the point of intersection of the 2 lines.
the lines intersect at (1, 4 ) , then
solution to the system of equations is (1, 4 )
Please help pleasehelp
Answer:
≥ and ≤ will both be solid dots, as it includes the number
x ≥ -7 is everything greater than -7; x ≤ 4 is everything less than 4.
to include both, you'd click -7, drag right, and stop at 4
need rn!
If a point C is inside AVB, then mAVC + mCVB = ______.
Answer:
Hi sorry if the reply is late! The answer is
OPTION (B)m∠AVC+m∠CVB=m∠AVB
Step-by-step explanation:
Given: It is given that a point C is inside ∠AVB and ∠AVC=39° and ∠CVB=23°.
From the figure, we can see that C is inside ∠AVB, therefore ∠AVB is divided into two parts that is ∠AVC and ∠CVB, thus
m∠AVC+m∠CVB=c
⇒39°+23°=62°
A quadratic polynomial with real coefficients and leading coefficient is called if the equation is satisfied by exactly three real numbers. Among all the disrespectful quadratic polynomials, there is a unique such polynomial for which the sum of the roots is maximized. What is
p(1) = 1
Let p(x) = x2 + bx = c
then, p(p(x)) = (x2 + bx + c)² + b(x2 + bx + c) + c
Sum of roots of p(p(x)) is given by = - (coefficient of x3/constant term)
= -2b/c2+bc+c = f(a,b) (say)
For critical points,
∂f/∂c = 0 and ∂f/∂b = 0
= 2b(2c+b+1)/c2+bc+c = 0 and - {( c2+bc+c)²- 2b (c)/ ( c2+bc+c)²}= 0
= b(2c+b+1) =0
= b= 0 or b= - (1+2c) = -(2c(c+1))/c2+bc+c = 0
If c=0 , b= -1 => c= 0 or c=-1
If c = -1 ,b = 1
thus we have the following possibility for (b,c)
(0,0) , (0,-1) , (-1,0) ,(1,-1).
At (0,0) f(0,0) = not defined
(0,-1) f(0,-1) = 0
(1,-1) f(1,-1) = 2
(-1,0) is not possible.
p(x) = (x2 +x-1)² + (x2 +x-1) -1
= p(1) = (1+1-1)² + (1+1-1) -1
= 1
Hence, p(1) = 1
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The graph of g(x)=|x-h|+k is shown on the coordinate grid.what must be true about the signs of h and k?
The correct option is the last one. h is negative and k is positive.
What can we say about h and k?
For the absolute value function:
g(x) = |x - h| + k
We know that the vertex is on the point (h, k).
On the graph, we can see that the vertex is on the point (-2, 1), then we have:
h = -2
k = 1
So the sign of h is negative and the sign of k is positive. The correct option is the last one.
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Part B
Question
Use an online graphing tool to find the equation that best models the data in the table.
Enter the correct equation in standard form. Round parameters to the nearest tenth.
Answer:
y=17.2x²-226.3x+2184.5
What is the equation of the line parallel to 3x + 2y = -4 that goes through the point (4, -1)?
y =
2x+4
y =
2³x + 5
y =
¾x + 5
Oy = =
x +5
=
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + 2y = - 4 ( subtract 3x from both sides )
2y = - 3x - 4 ( divide terms by 2 )
y = - [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = - [tex]\frac{3}{2}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 6 + c ⇒ c = - 1 + 6 = 5
y = - [tex]\frac{3}{2}[/tex] x + 5 ← equation of parallel line
Solve a) with Substitution and b) with Elimination (check attached picture)
a) Solve the first equation for [tex]x[/tex].
[tex]x + 3y = 7 \impiles x = 7 - 3y[/tex]
Substitute this into the second equation and solve for [tex]y[/tex].
[tex]2x + 4y = 12 \implies 2(7 - 3y) + 4y = 12 \\\\ \implies 14 - 6y + 4y = 12 \\\\ \implies -2y = -2 \\\\ \implies \boxed{y=1}[/tex]
Solve for [tex]x[/tex].
[tex]x = 7 - 3y \implies x = 7-3\times1 \\\\ \implies \boxed{x = 4}[/tex]
b) Eliminate [tex]y[/tex] by combining the two equations in appropriate parts, namely
[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3)[/tex]
and solve for [tex]x[/tex].
[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3) \implies 4x - 2y + 3x + 2y = 6 - 3 \\\\ \implies 7x = 3 \\\\ \implies \boxed{x = \dfrac37}[/tex]
Solve for [tex]y[/tex].
[tex]2x - y = 3 \implies 2\times\dfrac37 - y = 3 \\\\ \implies \dfrac67 - y = 3 \\\\ \implies -y = \dfrac{15}7 \\\\ \implies \boxed{y = -\dfrac{15}7}[/tex]
Price of an article is 400 and sold with discount including 13% vat at 339 find discount rate
An amount of money 960gh was contributed by 80 students. If 714gh was contributed equally by 68 girls and the remaining amount was also contributed equally by boys. How much did each
i. Girl contribute
ii. Boy contribute
Each girl contributed 10.50gh
Each boy contributed 20.50gh
These are further explained and computed below:
The measure of central tendency being tested here is the mean, in other words, the resulting average when the total amount contributed by girls or boys is divided by the number of girls or boys.
The fact that 68 of the 80 students are girls means that the remaining 12 students are boys because 80 minus 68 gives 12.
each girl's contribution=total girls' contribution/number of girls
each girl's contribution=714/68
each girl's contribution=10.50gh
Total boys' contribution=total contribution-total girls' contribution
Total boys' contribution=960-714
Total boys' contribution=246
each boy's contribution=Total boys' contribution/number of boys
each boy's contribution=246/12
each boy's contribution=20.50gh
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Each girl contributed 10.5gh and each boy contributed 20.5gh
How to determine the amount contributed?The given parameters are:
Total amount = 960gh
Number of students = 80
Amount contributed by girls = 714gh
Number of girls = 68
The amount contributed by each girl is:
Girl = Amount contributed by girls/Number of girls
This gives
Girl = 714gh/68
Evaluate
Girl = 10.5gh
The amount contributed by each boy is:
Boy = (Total - Amount contributed by girls)/(Total students - Number of girls)
This gives
Boy = (960gh - 714gh)/(80 -68)
Boy = 246gh/12
Evaluate
Boy = 20.5gh
Hence, each girl contributed 10.5gh and each boy contributed 20.5gh
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What is the inverse of f(x)= 1/3x + 2?
Answer:
y^-1 = 3x - 6
Step-by-step explanation:
f(x) = 1/3x + 2
The inverse function is where we swap out y for x and x for y. f(x) represents y, so we will be replacing it with x. Then, we solve and get a new equation for the inverse of y.
x = 1/3y + 2 (subtract 2 from both sides)
x - 2 = 1/3y (multiply by 3 on both sides)
y^-1 = 3x - 6
Brainliest, please :)
Answer:
f(x) = 3x- 2
Step-by-step explanation:
The easiest way to find the inverse of a function is to replace y with x and rearrange the equation.
x = 1/3y + 2
-2 -2
______________
x-2 * 3 = 1/3y * 3
y = 3x-2
4. Write the linear equation whose graph contains the
points (-2,5) and (4,1).
Thee linear equation which contains the points (-2,5) and (4,1) is [tex]4x+6y-22=0[/tex]
Graph The points which is in the equation (-2,5) and (4,1).
Equation is basically a relationship between two or more variables and it is usually in equal to form. It is equated to find the value of variables. We can also make graphs of different equations. Linear equation is a equation whose graph looks like straight line means values comes from a relationship. It not necessarily means parallel to any axis.
The linear equation can be found by:
[tex](y-y_{1} )=(y_{2} -y_{1} )/(x_{2} -x_{1} )* (x-x_{1} )[/tex] where the coordinates are [tex](x_{1},y_{1}), (x_{2},y_{2})[/tex]
[tex](y-5)=(1-5)/(4+2)*(x+2)[/tex]
[tex](y-5)=-4/6 *(x+2)[/tex]
[tex]6y-30=-4x-8[/tex]
[tex]y=(22-4x)/6[/tex]
Hence the equation which has points (-2,5)(4,1) is [tex]4x+6y-22=0[/tex]
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