Isolate x:
2x + 7y = -1
2x = -1 -7y
x = -1/2 - 7/2y
Substitute the equation of x:
4x - 3y = -19
4(-1/2 - 7/2y) - 3y = -19
-2 - 14 - 3y = -19
-3y = -19 + 14 + 2
-3y = -3
y = 1
Substitute to find x:
2x + 7y = -1
2x + 7(1) = -1
2x = -1 - 7
2x = -8
x = -4
(-4, 1)
What are the rules of the system of equations?
Multiply one or both equations through an integer in order that one time period has the same and contrary coefficients within the equations. Add the equations to provide a single equation with one variable. clear up for the variable. alternative the variable back into one of the equations and resolve for the other variable.
Conclusion: A system of equations is fixed of 1 or greater equations related to some of the variables. The solutions to systems of equations are the variable mappings such that every one component equations are satisfied—in other phrases, the locations at which all of these equations intersect.
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HELPPP MEEE PLSSSS meee outttt
Answer: x = 32
Step-by-step explanation:
If m∠ORS = m∠SRQ = 3x - 6 and since the two angles are a linear pair they total 180°. This means half or only one section = 90°
solve for x
3x - 6 = 90
add 6 to both sides
3x = 96
divide each side by 3
x = 32
Petrol costs $1.65 per litre. Calculate how much, correct to the nearest cent, the
petrol will cost Anne for a journey of 120km.
The petrol cost for Anne's journey of 120km is $16.236
How to find the cost for 120 km?Her car has a fuel consumption of 8.2 litres per 100 km .
Therefore,
100 km = 8.2 litres
120 km = ?
cross multiply
volume(litres) = 8.2 × 120 / 100 = 984 / 100 = 9.84 litres
Therefore,
1 litres = 1.65 dollars
9.84 litres = ?
cross multiply
cost of fuel used = 1.65 × 9.84 / 1
cost of fuel used = $16.236
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Use the digits 1-20, at most one time each, to create a true statement for polynomial below.
(the _ are blanks that need to be filled in)
_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2
The complete equation of the polynomial is 2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2
How to complete the blanks?The equation is given as:
_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2
Complete the blanks using alphabets
ax(x^2 - bx) + cx^3 = dx(ex^2 + fx) - x^2
Open the brackets
ax^3 - abx^2 + cx^3 = dex^3 + dfx^2- x^2
Factorize the expression
(a + c)x^3 - abx^2 = dex^3 + (df - 1)x^2
By comparison, we have:
a + c = de
-ab = df - 1
Rewrite the second equation as:
ab + df = 1
So, we have:
a + c = de
ab + df = 1
Set a = 2 and c = 10.
So, we have:
a + c = de ⇒ de = 2 + 10 ⇒ de = 12
ab + df = 1 ⇒2b + df = 1
Express 12 as 3 * 4 in de = 12
de = 3 * 4
By comparison, we have:
d = 3 and e = 4
So, we have:
2b + df = 1
This gives
2b + 3f = 1
Set b = 11.
So, we have:
2 * 11 + 3f = 1
This gives
22 + 3f = 1
Subtract 22 from both sides
3f = -21
Divide by 3
f = -7
Hence, the complete equation is:
2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2
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Solve each triangle. Round answers to the nearest tenth.
Step-by-step explanation:
1.) ˆ B = 7∘ , ˆ A = 28 ∘ , a = 27
-----------------------------------------------------------------------------------------
2.) c ≈ 28.0
-----------------------------------------------------------------------------------------
3.) The triangle has the following measures.
A = 36 ˚
a = 14 units
B = 105 ˚
b = 23 units
C = 39 ˚
c = 15 units
------------------------------------------------------------------------------------------
4.) a ≅ 15.0 units
B = 145 ˚
b ≅ 22.9 units
prove that the value of each expression is divisible by the given number 8^10-2^27 is divisible by 14
Answer:
Proof below
Step-by-step explanation:
General Strategy:Find factors of divisorUse algebraic properties to reveal those factors in the given expression.Divisibility
A number, p, is divisible by another number, d, if and only if there is some non-negative integer, n, such that n*d=p.
To prove that, 300 is divisible by 10 because, 30 is a non-negative integer, and 10*30=300.
Strategies for Divisibility by a composite number
Note that in the previous example, 10 is a composite number. This means that both one 2 and one 5 (the full list of 10s factors) had to be factored out of the 300.
In the given problem, we are to prove that the number is divisible by 14. Observe 14 is composite with factors of 2 and 7.
Properties of exponentsSince the expression is given with exponents, it will be helpful to recall a few exponent properties to algebraically manipulate the expression.
Recall the following property of exponents:
[tex]x^{a}*x^{b}=x^{(a+b)}[/tex] [tex](x^{a})^{b}=x^{ab}[/tex]Finding a factor of 14 in the given expressionOriginal expression...
[tex]8^{10}-2^{27}[/tex]
Recognizing 8 as a power of 2...
[tex](2^3)^{10}-2^{27}[/tex]
Simplifying and rewriting so that both terms are powers of 2...
[tex]2^{30}-2^{27}[/tex]
Observing that both terms have 27 twos as factors...
[tex]2^{27}*2^{3}-2^{27}[/tex]
Factoring out 27 twos...
[tex]2^{27}*(2^{3}-1)[/tex]
Simplifying the expression in the parenthesis:
[tex]2^{27}*(8-1)[/tex]
[tex]2^{27}*(7)[/tex]
Knowing that we also need a factor of 2, use properties of exponents, and associative property of multiplication...
[tex](2^{26}*2^1)*7[/tex]
[tex]2^{26}*(2^1*7)[/tex]
[tex]2^{26}*(2*7)[/tex]
[tex]2^{26}*14[/tex]
Since 2^26 is a non-negative integer, the original expression is divisible by 14.
what should be added to 51 to get the answer -1 ?
Please answer Urgent!
Answer:
Let the no. be x
51 + x = -1
x = -1-51
x = 1 + 51
x = -52Answer:
-52
Step-by-step explanation:
51 + (-52) = -1
A new computer loses 1/3 of its value every year. Which graph- a, b, c, or d – could represent the relationship between the year and the computers value? Justify your choice.
The graph which represents the relationship between the year and the computers value is; Choice A.
Which graph represents the relationship?According to the task content, it follows that the computer loses 1/3 of its value every year. Hence, it follows that the value of the computer each year is 2/3 of its previous value.
Hence, the relationship can best be modelled by an exponential function, a decay function to be more specific and can best be represented by Choice A.
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i need answer
because this is hella hard and i m trying to cheat but apps trying to make your boy pay and i aint doing it lol
Answer:
C) 12 m
Step-by-step explanation:
Express the radical using the imaginary unit i
Answer:
[tex]\huge\boxed{\sf \pm 10i}[/tex]
Step-by-step explanation:
Given radical:[tex]\pm \sqrt{-100}[/tex]
We can write it as:
[tex]\pm \sqrt{-1 \times 100} \\\\\pm \sqrt{-1} \times \sqrt{100} \\\\\underline{We \ know \ that:}\ i =\sqrt{-1} \\\\\pm i \times 10\\\\\boxed{\pm 10i}\\\\\rule[225]{225}{2}[/tex]
Select the correct answer.
The graph of function f is shown.
Which statement about function f is true?
answers:
The function f has an inverse because it passes the vertical line test.
The function f does not have an inverse because it is not one-to-one.
The function f has an inverse because it is one-to-one.
The function f does not have an inverse because its domain is not .
Answer:
The function f has an inverse because it is one-to-one.
Step-by-step explanation:
The condition for a function to have an inverse is that every x coordinate maps to a single y - coordinate. As illustrated by the diagram attached in the second picture, every x value maps to one y value therefore satisfying the condition making the function have an inverse.
In the race Math , drivers must complete laps of miles each. Dave drove the first laps at mph and the last laps at mph. What was Dave's average speed for the race, in miles per hour
The average speed in approximately 184.62 miles per hour.
We have been given that in the race Math 600, drivers must complete 200 laps of 3 miles each. Dave drove the first 150 laps at 180 mph and the last 50 laps at 200 mph.
First of all, we will find the number of miles in 150 laps and 50 laps as:
150 X 3 miles = 450 miles
50 X 3 miles = 150 miles.
Now, we will find time taken to complete each distance as:
Time = 450/180 =2.5 hr
Time = 150/200 = 0.75 hr
Average speed = 184.62
The average speed in approximately 184.62 miles per hour.
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b=(1-1/3).(1-1/3).(1-1/4).................(1-1/2004)
When the above complex expression has been simplified the solution to the above expression is = 2003/8016.
What is the formula for solving the above?The formula is given as:
1 - [tex]\frac{1}{n}[/tex] = [tex]\frac{n-1}{n}[/tex]
From the stated express, we have:
(1 - (1/2)) * (1 - (1/3)) * (1 - (1/4)) *( 1 - (1/2004))
→ ((2-1)/2) ((3-1)/3) ((4-1)/4) ((2004 -1)/2004)
→ (1/2) * (2/3) * (3/4) * (2003/2004)
→ [tex]\frac{ 1* 2003}{4*2004}[/tex]
= 2003/8016
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Answer:
When the above complex expression has been simplified the solution to the above expression is = 2003/8016.
What is the formula for solving the above?
The formula is given as:
1 - =
From the stated express, we have:
(1 - (1/2)) * (1 - (1/3)) * (1 - (1/4)) *( 1 - (1/2004))
→ ((2-1)/2) ((3-1)/3) ((4-1)/4) ((2004 -1)/2004)
→ (1/2) * (2/3) * (3/4) * (2003/2004)
→
= 2003/8016
Step-by-step explanation:
PLEASE HELP ASAP!!!!!!!!
Find the equation of this line.
y
--2
Simplify the fractions.
Enter
k
Answer:
y = - 6/7 x - 10/7
Step-by-step explanation:
Slope = (y2-y1) / (x2-x1)
= 6/-7 = -6/7
y = -6/7 x - a
passes by (-4,2)
2 = 24/7 - a, a = -10/7
y = -6/7 x - 10/7
Choose the expression that is equivalent to the expression: 2³
a.2x2x2
b.2x3
c.3x3
d.2x2x3
Hello,
2³ = 2 × 2 × 2 → answer A
After using a compass and a straightedge to generate this figure, Jeremy claims AABC is an equilateral triangle inscribed in circle O.
How can Jeremy prove his claim?
A.He can show that the measures of arcs AB, AC, and BC are all equal to 60°.
B. He can show that the lengths of segments AB, AC, and BC are all equal to the length of the circle's radius.
C. He can show that the measures of arcs AB, AC, and BC are all equal to 120°.
D.He can show that the lengths of segments AB, AC, and BC are all equal to the length of the circle's diameter.
Answer: C. He can show that the measures of arcs AB, AC, and BC are all equal to 120°.
Step-by-step explanation:
Each angle of an equilateral triangle measures 60°, so by the inscribed angle theorem, each arc created by a pair of adjacent vertices will measure 120°.
what is the slope for (3, 8) and (2, 6). ?
Answer:
m = 2
Step-by-step explanation:
[tex]m = \frac{rise}{run} =\frac{y_{2}-y_1}{x_2-x_1}[/tex]
[tex]=\frac{6 - 8}{2 - 3} \\= \frac{-2}{-1}\\ = 2[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{The formula for finding the slope:}[/tex]
[tex]\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}[/tex]
[tex]\huge\textbf{Some people understand formula like:}[/tex]
[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]
[tex]\huge\textbf{Breaking down the question:}[/tex]
[tex]\mathbf{y_2 \rightarrow \boxed{\textbf{6}}}[/tex]
[tex]\mathbf{y_1 \rightarrow \boxed{\textbf{8}}}[/tex]
[tex]\mathbf{x_2 \rightarrow \boxed{\textbf{2}}}[/tex]
[tex]\mathbf{x_1 \rightarrow \boxed{\textbf{3}}}[/tex]
[tex]\huge\textbf{What your equation should look like:}[/tex]
[tex]\mathbf{\dfrac{6 - 8}{2 - 3} = slope}[/tex]
[tex]\huge\textbf{Simplify the equation we came up with:}[/tex]
[tex]\mathbf{\dfrac{6 - 8}{2 - 3} = slope}[/tex]
[tex]\mathbf{\rightarrow \dfrac{-2}{-1} = slope}[/tex]
[tex]\mathbf{\rightarrow -2 \div -1 = slope}[/tex]
[tex]\mathbf{\rightarrow 2 = slope}[/tex]
[tex]\huge\textbf{Thus, the answer should most likely be:}[/tex]
[tex]\huge\boxed{\mathsf{Slope \rightarrow \boxed{\textsf{2}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphite1040:)}[/tex]NEED HELP
pls & thank you
We have proven that BC = DE using the Segment addition postulate
Segment addition postulateThe segment addition postulate states that given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC
The reasons for the proof are given below:
Statement Reason
BD = BC + CD Segment addition postulate
CE = CD + DE Segment addition postulate
BD = CE Given
BC + CD = CD + DE Substitution property
BC = DE Subtraction property
Hence, we have proven that BC = DE using the Segment addition postulate
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Triangle QRS is to be dilated using the rule D Subscript P, three-fourths.
Point P is the center of dilation. Triangle Q R S is shown. The length of P S is 8.
What will be the distance from the center of dilation, P, to the image S'?
2 units
4 units
6 units
8 units
The distance from the center of dilation, P, to.the image vertice S' is; 6 units.
What is the distance from the center of dilation, P, to the image S'?It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.
Hence, since the dilation factor as given in the task content is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6units.
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For the following exercises, solve each inequality and write the solution in interval notation.
32. | x − 4 | ≥ 8
Answer:
The solution of the given set in interval form is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].
Step-by-step explanation:
It is given in the question an inequality as [tex]$|x-4| \geq 8$[/tex].
It is required to determine the solution of the inequality.
To determine the solution of the inequality, solve the inequality [tex]$x-4 \geq 8$[/tex] and, [tex]$x-4 \leq-8$[/tex]
Step 1 of 2
Solve the inequality [tex]$x-4 \geq 8$[/tex]
[tex]$$\begin{aligned}&x-4 \geq 8 \\&x-4+4 \geq 8+4 \\&x \geq 12\end{aligned}$$[/tex]
Solve the inequality [tex]$x-4 \leq-8$[/tex].
[tex]$$\begin{aligned}&x-4 \leq-8 \\&x-4+4 \leq-8+4 \\&x \leq-4\end{aligned}$$[/tex]
Step 2 of 2
The common solution from the above two solutions is x less than -4 and [tex]$x \geq 12$[/tex].
The solution set in terms of interval is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].
please help me out with this
Answer:
25
Step-by-step explanation:
sin © =36/(35+x)=21/35
36/(35+x)=21/35
x=(36*35/21)-35
x=25
Step-by-step explanation:
SOLUTION::
please watch the image for explanation
Given a sphere with a radius of 2 cm, find its volume to the nearest whole
number.
A. 8 cm³
B. 17 cm³
о C. 33 cm³
O D. 3 cm³
Answer: 34
Step-by-step explanation:
[tex]V=\frac{4}{3}(\pi)(2^{3}) \approx \boxed{34}[/tex]
The eleventh term of an AP is four times the second term. If the sum of the first seven terms of the AP is 175, find the first term and the common difference.
Step-by-step explanation:
a11 = 4 × a2
a + 10d = 4 × (a + d)
a + 10d - 4d = 4a
a + 6d = 4a
6d = 4a - a
6d = 3a
(6/3)d = a
2d = a ----- eq. 1
now, sum of 7 terms = s7 = 175
7/2 {2a+6d} = 175
7/2 { (2 × 2d ) + 6d} = 175
7 ( 4d + 6d ) = 175 × 2
7 ( 10d ) = 350
70d = 350
d = 350/70
d = 5
Now from eq. 1,
2d = a
2(5) = a
a = 10, d = 5
THANK YOU........
What is the Value of the expression? 2 (1/4)^2
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
2 ( [tex]\frac{1}{4}[/tex] )²
= 2 × [tex]\frac{1}{16}[/tex] ← cancel 2 and 16 by 2
= 1 × [tex]\frac{1}{8}[/tex]
= [tex]\frac{1}{8}[/tex]
Pls answer ASAP it is almost due TYSMMM
There are 357 people attending a school play.
Assuming that all but one row of seats in the
theatre is completely full and that each row fits
24 people, how many rows of seats are there in
the theatre?
There are 15 rows of seats in the theater
How to determine the number of rows?The given parameters are:
Total number of people = 357People per row = 24The number of rows is calculated as:
Rows = Total number of people/People per row
This gives
Rows = 357/24
Evaluate the quotient
Rows = 14.875
Round up the number
Rows = 15
Hence, there are 15 rows of seats in the theater
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9. Evaluate 14(-6x +10) - 16x - 100x + 140 for x = -2.
Answer:
680
Step-by-step explanation:
14(-6x +10) - 16x - 100x + 140 for x = -2.
14(-6(-2) + 10) - 16(-2) - 100(-2) + 140
14(12 + 10) + 32 + 200 + 140
14(22) + 372
308 + 372
680
Simplify the following:
A.
(-x)^4/4x * 8(-x)^-3/x^-3/4
Answer:
Answer for (a) -2x^4/3
Answer for (b) 2^5x/4^3x
Answer:
a. [tex]-2x\sqrt[3]{x}[/tex]
b. [tex]\frac{1}{2^x}[/tex]
Step-by-step explanation:
a.
Original equation:
[tex]\frac{(-x)^4}{4x}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]
So (-x)^4 can be seen as (-x * -x) * (-x * -x), which becomes x^2 * x^2 = x^4, the negatives cancel out of the degree is even. So it becomes:
[tex]\frac{x^4}{4x}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]
Cancel out one of the x's on the left fraction:
[tex]\frac{x^3}{4}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]
Rewrite the exponent in the numerator: [tex]a^{-x} = \frac{1}{a^x}[/tex]
[tex]\frac{x^3}{4}*\frac{8*\frac{1}{-x^3}}{x^{-\frac{4}{3}}}[/tex]
Simplify the numerator:
[tex]\frac{x^3}{4}*\frac{\frac{8}{-x^3}}{x^{-\frac{4}{3}}}[/tex]
Keep numerator, change division to multiplication, flip the denominator:
[tex]\frac{x^3}{4}*\frac{8}{-x^3} * \frac{1}{x^{-\frac{4}{3}}}[/tex]
multiply the denominator using the exponent identity: [tex]x^a*x^b=x^{a+b}[/tex]
[tex]\frac{x^3}{4}*\frac{8}{-x^{\frac{5}{3}}}[/tex]
Multiply the numerators and denominators:
[tex]\frac{8x^3}{-4x^{\frac{5}{3}}}[/tex]
Use the fact that: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] to divide the x^3 and x^(5/3) and divide the 4 by the -8
[tex]-2x^{\frac{4}{3}}[/tex]
Rewrite the exponent using the exponent identity: [tex]x^{\frac{a}{b}} = \sqrt[b]{x^a}=\sqrt[b]{x}^a[/tex]
[tex]-2\sqrt[3]{x^4}[/tex]
Rewrite as two radicals: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]
[tex]-2\sqrt[3]{x^3} * \sqrt[3]{x}[/tex]
Simplify:
[tex]-2x\sqrt[3]{x}[/tex]
b.
[tex]2^{2x}\div4^{3x}*64^{\frac{x}{2}}[/tex]
Rewrite the 4 as 2^2
[tex]2^{2x}\div(2^2)^{3x}*64^{\frac{x}{2}}[/tex]
Use the exponent identity: [tex](x^a)^b=x^{ab}[/tex]
[tex]2^{2x}\div2^{6x}}*64^{\frac{x}{2}}[/tex]
Use the exponent identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]2^{2x-6x} = 2^{-4x}[/tex]
Rewrite this part using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = \frac{b}{a^x}[/tex].
[tex]\frac{1}{2^{4x}} * 64^{\frac{x}{2}}[/tex]
Multiply:
[tex]\frac{64^{\frac{x}{2}}}{2^{4x}}[/tex]
rewrite 64 as 2^6
[tex]\frac{(2^6)^{\frac{x}{2}}}{2^{4x}}[/tex]
Use the identity: [tex](x^a)^b=x^{ab}[/tex]
[tex]\frac{2^{3x}}{2^{4x}}[/tex]
Use the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]2^{-x}[/tex]
rewrite using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = \frac{b}{a^x}[/tex]
[tex]\frac{1}{2^x}[/tex]
Deepika has drawn a rhombus and a square, each with side length 5 cm. Which of these will be different for both the shapes?
1. lengths of the two diagonals
2. angles between the two diagonals
3. lengths of the adjacent sides
4. angles between the adjacent side
The difference for both the rhombus and square are as follows;
Lengths of the two diagonalsAngles between the two diagonalsAngles between the adjacent sideProperties of a square?All the sides are equal.Opposite sides are parallel.All the angles are 90 degrees each.The diagonal bisect each otherProperties of a rhombusAll the sides are equal.Opposite sides are parallel.All the angles are not 90 degrees.The length of the diagonals are not the same.Therefore, the difference for both the shapes(square and rhombus)are as follows:
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The circle above has an area of 36π and is divided into 8 congruent regions. What is the perimeter of one of these regions?
A) 6+1.5π
B) 6+2π
C) 12+ 1.5π
D) 12+2π
The perimeter of each region is 12 + 1.5π if a circle with an area of 36π is divided into 8 congruent regions
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let r represent the area of the circle, hence:
Area = πr²
36π = πr²
r = 6 units
Perimeter = 2πr = 2π(6) = 12π
The circle has 8 congruent regions, hence:
Perimeter of each region = 6 + 6 + 12π/8 = 12 + 1.5π
The perimeter of each region is 12 + 1.5π if a circle with an area of 36π is divided into 8 congruent regions
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Please answer with everything needed i appreciate everyones help:00
Answer:
y = 5
Step-by-step explanation:
Step-by-step explanation:
the slope of a line is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.
when the slope is 0, it means the y coordinate change is 0 for all points. that means y is a constant. and the line is a horizontal line.
to go through (-2, 5) this constant y has to be the y value of the point.
so,
y = 5
that's it. that is the whole equation for that line, because the slope m is 0. what remains is the y-axis intercept (y = 5).
Every year, the value of a surveying machine depreciates by 25 % of its value in the previous year.
If the value of the machine was $ 11 250 in 2012, find its value in 2010.
Answer:
$17578.13
Step-by-step explanation:
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