[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &\$75000\\ P=\textit{original amount deposited}\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &10 \end{cases} \\\\\\ 75000=Pe^{0.035\cdot 10}\implies 75000=Pe^{0.35}\implies \cfrac{75000}{e^{0.35}}=P \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 52851.61\approx P~\hfill[/tex]
z varies directly with x4 and inversely with y.
When x = 2 and y = 4, z = 3.
What is the value of z when x = 4 and y = 9?
Answer:
[tex]z=\frac{63}{4}[/tex]
Step-by-step explanation:
When two variables vary in a directly proportional way, it means that when one variable grows, the other also grows.
This is represented by the following equation
[tex]y = kx[/tex]
Where k is the constant of proportionality
When two variables vary in an inversely proportional way, it means that when one variable grows, the other decreases.
This is represented by the following equation
[tex]y = \frac{k}{x}[/tex]
In this case we know that:
z varies directly with [tex]x^4[/tex] and inversely with y.
We write this as:
[tex]z = k\frac{x ^ 4}{y}[/tex]
We know that When [tex]x = 2[/tex] and [tex]y = 4,\ z = 3[/tex].
So we use this information to find the constant k
[tex]3 = k\frac{2 ^ 4}{4}[/tex]
[tex]3 = k\frac{16}{4}[/tex]
[tex]3 = 4k[/tex]
[tex]k = \frac{3}{4}[/tex]
So the equation is:
[tex]z = \frac{3}{4}\frac{x ^ 4}{y}[/tex]
Finally when x = 4 and y = 9 then:
[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]
[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]
[tex]z=\frac{63}{4}[/tex]
A dog begins his stay at the kennel with 25 fleas. Each day, the number of fleas triples. Which of the following statements is true about the function that represents this situation?
The relationship is linear with an increase of 3 fleas per day.
The relationship is exponential, and the number of fleas increases by a factor of 3 per day.
The relationship is exponential, and the number of fleas increases by a factor of 25 per day.
The relationship is linear with an increase of 75 fleas per day.
Answer:
It is the second statement.
Step-by-step explanation:
y = 25(3)^(n - 1) where y = the number of fleas and n = the number of days.
On day 1, y = 25 3^0 = 25
On day 2, y = 25(3^1 = 75
On day 3, y = 25(3) ^2 = 225 and so on.
Exponential growth.
Answer: Second Option
Step-by-step explanation:
Initially there are 25 fleas, and each day triples the amount.
So:
Day 1: 25
Day 2: [tex]25 * 3 = 75[/tex]
Day 3: [tex]25 * (3) ^ 2 = 225[/tex]
Day 4: [tex]25 * (3) ^ 3 = 675[/tex]
Day n: [tex]25 * (3) ^ {n-1}[/tex]
Note that the function that models the number of fleas for day n is an exponential growth function with an increase factor of 3 and an initial quantity of 25. Therefore, the answer is the second option.
P^-4q^3r^-7 over p^-2q^3p^-2 simplify
[tex]\bf \cfrac{p^{-4}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ r^{-7}}{p^{-2}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ p^{-2}}\implies \cfrac{1}{p^{4}p^{-2}p^{-2}r^7}\implies \cfrac{1}{p^{4-2-2}r^7}\implies \cfrac{1}{p^0r^7}\implies \cfrac{1}{r^7}[/tex]
Answer:
[tex]\large\boxed{r^{-7}=\dfrac{1}{r^7}}[/tex]
Step-by-step explanation:
[tex]\dfrac{p^{-4}q^3r^{-7}}{p^{-2}q^3p^{-2}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=p^{-4-(-2)-(-2)}q^{3-3}r^{-7}\\\\=p^{-4+2+2}q^0r^{-7}\\\\=p^0q^0r^{-7}\\\\=r^{-7}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{r^7}[/tex]
a^-4+b^2 when a=2 and b=3/4 answer as a reduced fraction
[tex]\bf a^{-4}+b^2\implies \cfrac{1}{a^4}+b^2\qquad \begin{cases} a=2\\ b=\frac{3}{4} \end{cases}\implies \cfrac{1}{2^4}+\left( \cfrac{3}{4} \right)^2\implies \cfrac{1}{16}+\cfrac{3^2}{4^2} \\\\\\ \cfrac{1}{16}+\cfrac{9}{16}\implies \cfrac{1+9}{16}\implies \cfrac{10}{16}\implies \cfrac{5}{8}[/tex]
Identify an equation in point-slope form for the line parallel to y=-2/3x+8 that
passes through (4,-5).
O A. y+5 = (x-4)
O B. y 4= {(x+5)
O C. y-5--}(x+4)
O D. 4+5--xx-4)
Answer:
[tex]\large\boxed{y+5=\dfrac{2}{3}(x-4)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
Parallel lines have the same slope.
We have the equation in the slope-intercept form (y = mx + b)
[tex]y=-\dfrac{2}{3}x+8\to m=\dfrac{2}{3}[/tex]
Put to the point-slope equation value of the slope and the coordinates of the point (4, -5):
[tex]y-(-5)=\dfrac{2}{3}(x-4)\\\\y+5=\dfrac{2}{3}(x-4)[/tex]
The equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y - (-5) = (-2/3)(x - 4), which is option C.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
The equation of a line in point-slope form is given by:
y - y₁ = m(x - x₁)
where m is the slope of the line, and (x₁, y₁) is a point on the line.
We are given that the line we want to find is parallel to y = (-2/3)x + 8, which means it has the same slope of -2/3.
We are also given that the line passes through the point (4, -5).
Substituting the values into the point-slope form equation, we get:
y - (-5) = (-2/3)(x - 4)
Therefore, the equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y - (-5) = (-2/3)(x - 4), which is option C.
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Alice is selling lemonade and fresh squeezed orange juice at a booth. she sells cups of lemonade for $1 each and cups of orange juice for $3 each. write an expression that represents the amount of money that Alice selling drinks
Answer:
$1x + $3y = c
Step-by-step explanation:
To write an expression you need to pick a variable to represent the cups of orange juice and lemonade.
x = cups of lemonade sold
y = cups of orange juice sold
Now you have the variables to represent the amount of cups sold, so now you need a variable to represent the total cost.
c = amount of money earned from selling drinks
Now you have all the variables, so you need to write how much is cost for that drink.
$1 for one cup of lemonade so $1x
$3 for one cup of orange juice so $3x
Now put the expression together:
$1x + $3y = c
The expression that represents the amount of money that Alice selling drinks is $ (a+ 3b)
What are Algebraic expressions?An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
How to find the expression that represents the amount of money that Alice selling drinks ?According to the problem,
Alice sells cups of lemonade for $1 each.She also sells cups of orange juice for $3 each.Let the number of cups of lemonade sold are a and the cups of orange juice sold are b.
Cost of 1 cup of lemonade is $ 1
∴Cost of a cups of lemonade = $ a
Similarly we can say,
Cost of 1 cup of orange juice is $ 3
∴ Cost of b cups of orange juice is $ 3b
So the total cost is represented by the expression : $(a + 3b)
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Find the center of a circle with the equation:
x2+y2+10x−16y+75=0
Answer: (-5,8)
Step-by-step explanation: since the radius of a circle square root of 14 so
x² + y² + 10x − 16y + 75 = 0
x² +10x + y² − 16y = -75
x² +10x + 25 + y² − 16y + 64 = -75 + 25 + 64
(x + 5)² + (y − 8)² = 14
ANSWER
The center is
[tex](-5,8)[/tex]
EXPLANATION
The given circle has equation
[tex] {x}^{2} + {y}^{2} + 10x - 16y + 75= 0[/tex]
An easy way to find the center is by comparing to the general equation of the circle
[tex] {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0[/tex]
where (-g,-f) is the center.
By comparing, we have
[tex]2gx = 10x[/tex]
[tex] \implies \: 2g = 10[/tex]
Divide both sides by 2.
[tex]g = 5[/tex]
Also,
[tex]2fy = - 16y[/tex]
[tex]2f = - 16[/tex]
Divide both sides by 2
[tex]f = - 8[/tex]
Therefore the center is
[tex](-5,- - 8) = (-5,8)[/tex]
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A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x
and the number of seats in each row by the function g(x) = 5x-2
Which function represents the total number of seats?
65x + 26
65x – 26
65x2 + 26x
65x2 – 26x
Answer:
65x^2 – 26x
Step-by-step explanation:
To determine the total number of seats, take the number of rows and multiply by the number of seats per row
f(x) * g(x)
13x * (5x-2)
65x^2 -26x
Answer:d
Step-by-step explanation:A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x and the number of seats in each row by the function g(x) = 5x – 2.Which function represents the total number of seats?65x + 2665x – 2665x2 + 26x65x2 – 26x
evaluate expression for given value 7x=8 WHEN X=2
Final answer:
The expression 7x = 8 evaluated with x = 2 results in 14, not 8. There was a misunderstanding in the question as it was not asking for a solution to the equation but rather an evaluation of the expression with a given value of x.
Explanation:
The question asks us to evaluate the expression 7x = 8 when x = 2. However, there seems to be a misunderstanding in the way the question is framed. Normally, an expression such as 7x = 8 would be an equation we solve to find the value of x. But since we are given that x = 2, it appears the task is to substitute this value into the expression 7x and see if it equals 8. Let's clarify and solve accordingly.
First, substitute x = 2 into the expression 7x:
7 * 2 = 14
Therefore, when we substitute x = 2 into the expression 7x, we get 14, not 8. It seems there was confusion in the question regarding what was being asked. If the task was to solve 7x = 8, then x would not equal 2 since 7*2 = 14. However, the original instruction was misunderstood, and the correct task was to substitute x = 2 into the expression and evaluate it, which we did correctly.
Match each equation to its factorized version and solution.
Answer:
[tex]24x -{6x}^{2} = 0 \: matches \: with \: 6x(4 - x) \: and \: the \: solution \: x = 0 \ \: or \: \: x = 4[/tex]
[tex]2 {x}^{2} + 6x = 0 \: matches \: with \: 2x(x + 3) = 0 \: and \: the \: solution \: x = 0 \: or \: x = - 3[/tex]
[tex]4x - {x}^{2} = 0 \: matches \: with \: x(4 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 4[/tex]
[tex]14x - {7x}^{2} = 0 \: matches \: with \: 7x(2 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 2
[/tex]
Points A and B are on opposite sides of a lake. A point C is 105.6 meters from A. The measure of ∠BAC is 70.5°, and the measure of ∠ACB is determined to be 38.833°. Find the distance between points A and B (to the nearest meter).
Answer:
= 70 Meters
Step-by-step explanation:
We can use the sine rule as follows:
Angle ABC=180-(70.5+38.833)
=70.667°
Using the sine rule and sides AB, AC and angles ABC and ACB:
b/Sin B=c/Sin C
Replacing with the values above we get:
AC/Sin ABC= AB/Sin ACB
105.6/Sin 70.667=AB/Sin 38.833
AB=(105.6 Sin 38.833)/Sin 70.667
=70.17 meters
The distance between the two points to the nearest meter is 70 meters
Answer:
70 m
Step-by-step explanation:
I got it correct on founders edtell
Kate used 555 grams of wool to knit a sweater, a hat, and a scarf. She used 5 times fewer grams for the hat than for the sweater. She used 5 grams more for the hat than for the scarf. How many grams of wool did she use to knit each item?
Answer:
Sweater =400 grams
Hat =80 grams
Scarf =75 grams
Step-by-step explanation:
The amount of wool used to make a sweater, a hat and a scarf=555 grams
Let the amount of wool used to make a sweater be = x
The amount of wool for the sweater =x/5
The amount of wool used for the scarf=x/5 -5
Total amount of wool used = x+(x/5)+(x/5-5)
x+x/5 +x/5-5=555
Multiply all through by the LCM 5
5x+x+x-25=2775
7x=2800
x=400
Sweater =400 grams
Hat=400/5=80 grams
Scarf =400/5 -5=75 grams
What is the equation of the line, in general form, that passes through the point (1,1) and has a y-intercept of 2.
(
x - y + 2 = 0
@dry-2=0
Ox-y-2=0
Answer:
x + y - 2 = 0Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept.
Put the given y-intercept b = 2 and the coordinates of the point (1, 1) to the equation:
[tex]1=1m+2[/tex] subtract 2 from both sides
[tex]-1=m\to m=-1[/tex]
The equation of a line:
[tex]y=-1x+2\to y=-x+2[/tex]
The general form of an equation of a line:
[tex]Ax+By+C=0[/tex]
Convert:
[tex]y=-x+2[/tex] add x to both sides
[tex]x+y=2[/tex] subtract 2 from both sides
[tex]x+y-2=0[/tex]
Not sure how to do this
Answer:
Answer in picture.
Step-by-step explanation:
First step: You must plot the point (-3,5).
To graph this point, start at the origin.
The point says move left 3 and up 5 and put your dot (your point).
Second step: Use your slope to find a second point to plot. The slope is [tex]\frac{-1}{2}[/tex].
Slope is rise/run. So it says down 1 and right 2.
So starting at the first point you plotted and you count down 1 and then go right 2 and put your second point.
Third step: Connect the two points with a straight-edge. Extend in both directions.
The two points I used to graph my line is (-3,5) and (-1,4).
Step-by-step explanation:
[tex]slope=\dfrac{rise}{run}=\dfrac{\Delta y}{\Delta x}\\\\\Delta y-\text{run up (+) or down (-)}\\\\\Delta x-\text{run to the right (+) or to the left (-) }\\\\\text{We have}\ slope=-\dfrac{1}{2}=\dfrac{1}{-2}\to\Delta y=1\ (\text{1 unit up}),\ \Delta x=-2\ (\text{2 units to the left})\\\\\text{Mark the point (-3, 5) in the coordinates system. Go 1 unit up}\\\text{and 2 units to the left. Mark next point.}\\\text{Draw a line passing through the given points.}\\\\\bold{Look\ at\ the\ picture.}[/tex]
Assume that 4.5% is an annual interest rate. Find the interest rate for an account that is compounded
quarterly and monthly.
Answer:
B.
Step-by-step explanation:
Quarterly interest rate is 4.5 / 4 = 1.125%.
Monthly rate is 4.5 / 12 = 0.375%.
Answer:
B 1.25%-0.375%
Step-by-step explanation:
Compounded quarterly means there are 4 interest periods in 1 year, so divide the annual interest rate by 4.
4.5% ÷ 4 = 1.125%
Compounded monthly means there are 12 interest periods in 1 year, so divide the annual interest rate by 12.
4.5% ÷ 12 = 0.375%
Which answer choice correctly describes the inequality?
Answer:
the Answer is: D
Step-by-step explanation:
so that means he makes 11 dollars an hour so at most he can make that because he can work really work however long which means he can't really have less than 11 dollars an hour therefore its D
The function that represents a geometric sequence.
Answer:
C
Step-by-step explanation:
c is the answer to your question
Answer:
C
Step-by-step explanation:
What is the surface area of the cone? (radius 10in height 26in)
A) 425pi in2
B) 460pi in2
C) 360pi in2
D) 390pi in2
Answer:
C) 360pi in2
Step-by-step explanation:
Given:
radius, r= 10in
height, h=26in
surface area of the cone, T.S.A= ?
T.S.A=πrl +πr^2
=π(10)(26) +π(10)^2
=260π+100π
=360π^2 !
what is 362 equal to 126 substracted from r?
Answer:
488 = r
Step-by-step explanation:
362 = -126 + r
126 +126
----------------
488 = r
I am joyous to assist you anytime.
5/-7x (-9y/8)
multiply and simplify
Answer:
[tex]\large\boxed{\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{45y}{56x}}[/tex]
Step-by-step explanation:
[tex]\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{(5)(-9y)}{(-7x)(8)}=\dfrac{-45y}{-56x}=\dfrac{45y}{56x}[/tex]
Alexis has a stamp collection of 3 cent stamps and 8 cent stamps. She has 1 less 8 cent stamps as 3 cent stamps. If the collection has a face value of 69 cents, how many of each does she have?
She has ____ 3 cent stamps and _____ 8 cent stamps.
Answer:
She has seven 3 cents stamps and six 8 cents stamps.
Step-by-step explanation:
7*3 = 21
6*8 = 48
48 + 21 = 69
Answer: She has SEVEN 3 cent stamps and SIX 8 cent stamps.
Step-by-step explanation:
Let be "x" the number of 8 cent stamps and "y" the number of 3 cent stamps.
Set up the following system of equations:
[tex]\left \{ {{x=y-1} \atop {8x+3y=69}} \right.[/tex]
Substitute the first equation into the second one and the solve for "y":
[tex]8(y-1)+3y=69\\\\8y-8+3y=69\\\\11y=77\\\\y=7[/tex]
Substitute the value of "y" into the first equation:
[tex]x=7-1\\\\x=6[/tex]
The volume of a cone is 3.x cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
Answer:
Radius of the cone's base is 3x ....
Step-by-step explanation:
We have given that the volume of a cone is 3πx³
Height = x units.
The volume of a cone of radius r and height h units is given by:
V= 1/3 π r² *h
Simply plug the values given in the question into the above mentioned equation:
1/3πr²*x = 3*π*x³
1/3r²*x= 3x³
r² = 3*3*x³/x
r²=9x²
Taking square root at both sides we get:
√r² =√9x²
r = 3x
Thus the radius of the cone's base is 3x.
Answer: The volume given is 3Pi(x^3) and the radius is x. The formula for the volume of a cone is V= [1/3]Pi(r^2)*height => [1/3]Pi (r^2) x = 3Pi(x^3) => (r^2)x = 3*3(x^3) => (r^2)x = 9(x^3) => (r^2) = 9x^2 => r = sqrt[9x^2] = 3x. So THE CORRECT Answer is: A) r = 3x
Step-by-step explanation: I just paid for this answer
how do i do these using the following functions
Step-by-step explanation:
(f+g)(x) means f(x) + g(x).
(f−g)(x) means f(x) − g(x).
So all you have to do is add them and subtract them.
1. (f+g)(x) = f(x) + g(x)
(f+g)(x) = (3x − 7) + (2x − 4)
(f+g)(x) = 5x − 11
2. (f−g)(x) = f(x) − g(x)
(f−g)(x) = (3x − 7) − (2x − 4)
(f−g)(x) = 3x − 7 − 2x + 4
(f−g)(x) = x − 3
3. (f+g)(x) = f(x) + g(x)
(f+g)(x) = (2x + 3) + (x² + ½ x − 7)
(f+g)(x) = x² + 2½ x − 4
4. (f−g)(x) = f(x) − g(x)
(f−g)(x) = (2x + 3) − (x² + ½ x − 7)
(f−g)(x) = 2x + 3 − x² − ½ x + 7
(f−g)(x) = -x² + 1½ x + 10
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Based on the figure below, what is the value of x? A right angle is shown divided in two parts. The measure of the angle of one part is 30 degrees and the measure of the other part is 5x plus 15 degrees. 3 9 12 15
Answer:
x=9
Step-by-step explanation:
90-30= 60
now set 60 = 5x + 15
solve for x
45= 5x
divide by 5
x = 5
Which of the following data represents an actual probability?
A computer randomly generates 6 out of 100 numbers.
An observer notes the number of pepperoni, cheese, vegetarian pizzas are ordered out of 100 orders.
None of the above.
Answer:
(A.)A computer randomly generates 6 put of 100 numbers.
Step-by-step explanation:
This is an actual probability.
14. Find the average of the 1000 whole numbers
from 1 to 1000 inclusive.
(A)499.5
(B) 500.0
(C) 500.5
(D) 501.0
Answer:
500.5
Step-by-step explanation:
The average of a set of numbers is the sum of the numbers divided by the number of numbers.
The sum of all whole number form 1 to n is n(n + 1)/2.
The sum of all whole numbers from 1 to 1000 is
1000(1000 + 1)/2 = 1000(1001)/2 = 500,500
The average is the sum of the numbers divided by the number of numbers.
average = 500,500/1000 = 500.5
what is the slope of the line graphed below (1,1) (2,-2)
Answer:
slope is
Step-by-step explanation:
slope of line is -3
Answer:
The answer is -3.
Step-by-step explanation:
I just got it correct.
What is the sum of the geometric series?
–122
–2
40
54
The sum of the first six terms of the geometric series will be -364. Hence, option (B) will be correct.
What is geometric series?A geometric series is a series in which the division of any consecutive two terms will be the same.
For example 3, 6, 12, 24 here if you divide 6 by 3 then it gives you 2, and if you divide 12 by 6 then also it gives you 2, and so on.
here, we have,
Given up series is 2, – 6, 18, – 54
The common ratio of this GP is -3 by that
The remaining elements of this gp will be 162, -486
So the sum will be 2 - 6 + 18 - 54 + 162 - 486 = -364 so it will the summation of the given gp.
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Some polyhedrons are both prisms and pyramids.
True or False?
Answer:
Some polyhedrons are both prisms and pyramids.- False
The provided statement "Some polyhedrons are both prisms and pyramids" is false.
What is geometry?It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional and three-dimensional figures.
We have a statement:
Some polyhedrons are both prisms and pyramids.
As we know,
A polygon-based solid figure is known as a polyhedron, for instance, a soccer ball, a cuboid, etc.
A strong figure with two equal bases is a prism for instance: Cube. Cylinder, Cuboid, etc.
A polyhedron with a base and an top at the top is called a pyramid, cone, a pyramid with triangles as its base, etc.
Thus, the provided statement "Some polyhedrons are both prisms and pyramids" is false.
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if 2x - 3 + 3x equals -28 what is the value of x
Chapter : Linear equations
Lesson : Math of Junior High School
2x - 3 + 3x = -28
= 5x - 3 = -28
= 5x = -28 + 3
= 5x = -25
= x = -25 / 5
= x = 5
For this case we must find the value of "x" of the following expression:
[tex]2x-3 + 3x = -28[/tex]
We add similar terms:
[tex]5x-3 = -28[/tex]
We add 3 to both sides of the equation:
[tex]5x = -28 + 3[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]5x = -25[/tex]
We divide between 5 on both sides of the equation:
[tex]x = \frac {-25} {5}\\x = -5[/tex]
ANswer:
[tex]x = -5[/tex]