The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex] and for line 2x + 3y = 6 will be,[tex]\rm y = \frac{-2}{3}x+2[/tex]
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
a) 2x + 3y = -6
The line in which the standard form is found as;
Ax + By + C = 0
The typical form of a slope intercept is
y = mx+c
where m denotes the slope and b the line's y-intercept.
[tex]3y= -6-2x\\\\ y=\frac{-6-2x}{3}\\\\ y= -\frac{2}{3}x -2[/tex]
To obtain the slope standard form, we rewrite. The obtained equation is in the form of the slope-intercept.
b) 2x + 3y = 6
The line in which the standard form is found as;
Ax + By + C = 0
The typical form of a slope intercept is
y = mx+c
where m denotes the slope and b the line's y-intercept.
[tex]\rm 3y= 6-2x \\\\ y= \frac{6-2x}{3} \\\\ y = \frac{-2}{3}x+2[/tex]
Hence, The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex]
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What is the equation of the graphed line written in standard form?
2x + 3y = -6, 2x + 3y = 6
Summary:
a. The equation of the graphed line 2x + 3y = -6 written in standard form is y= -2/3 x -2.
b. The equation of the graphed line 2x + 3y = 6 written in standard form is y= -2/3 x +2.
Name the polygon shape in the picture below.
Answer:
There are eight sides so it's an octagon
Step-by-step explanation:
if a pen and a pencil cost 1.10$ but the pen cost is 1$ more than pencil
Answer:
The pencil cost $0.05 and the pen cost $1.05.
Step-by-step explanation:
Let, the price of the pencil is $ .
Given that the pen costs a dollar more than the pencil,
So, the price of the pen=$+1.
Therefore, ++1=1.10
, 2+1=1.10
, 2=1.10–1
, 2=0.10
, =0.10/2
, =0.05
The pencil cost $0.05 and the pen cost $1.05.
x+2y+3z = 12
x-3y + 4z=27
-x+y+2z=7
Show work
Answer:
x=1
y=−2
z=5
(heres how i got the answer)
Step-by-step explanation:
x+2y+3z=12
x−3y+4z=27
−x+y+2z=7
Solve x+2y+3z=12 for x.
x=−2y−3z+12
Substitute −2y−3z+12 for x in the second and third equation.
−2y−3z+12−3y+4z=27
−(−2y−3z+12)+y+2z=7
Solve equations for y and z respectively.
y=−3+
5
1
z
z=
5
19
−
5
3
y
Substitute −3+
5
1
z for y in the equation z=
5
19
−
5
3
y.
z=
5
19
−
5
3
(−3+
5
1
z)
Solve z=
5
19
−
5
3
(−3+
5
1
z) for z.
z=5
Substitute 5 for z in the equation y=−3+
5
1
z.
y=−3+
5
1
×5
Calculate y from y=−3+
5
1
×5.
y=−2
Substitute −2 for y and 5 for z in the equation x=−2y−3z+12.
x=−2(−2)−3×5+12
Calculate x from x=−2(−2)−3×5+12.
x=1
The system is now solved.
x=1
y=−2
z=5
Need help ASAP
A gives the area of the rectangle. Find the
11.
12.
A-35 m²
5 m
b
6 ft
Answer:
Area of a rectangle = l × b
11. 35 = 5 × b
b = 35/5
b = 7 m
12. 48 = 6 × h
h = 48/6
h = 8 ft
13. 24 = b × 3
b = 24/3
b = 8 in
Hope it helps!
Find the derivative of [tex]tan^{-1} x[/tex] by 1st principle of derivative.
Answer:
[tex]\dfrac{\text{d}}{\text{d}x} \tan^{-1}x=\dfrac{1}{1+x^2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Identity}\\\\$\tan^{-1}(A)-\tan^{-1}(B) \equiv \tan^{-1}\left(\dfrac{A-B}{1+AB}\right)$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{3 cm}$\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\end{minipage}}[/tex]
Given function:
[tex]\text{f}(x)=\tan^{-1}x[/tex]
[tex]\implies \text{f}(x+h)=\tan^{-1}(x+h)[/tex]
Differentiating from first principles:
[tex]\begin{aligned}\text{f}\:'(x) & =\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}(x+h)-\tan^{-1}x}{(x+h)-x}\right]\end{aligned}[/tex]
Using the trigonometric identity to rewrite the numerator:
[tex]\begin{aligned}& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{x+h-x}{1+x(x+h)}\right)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{h}\right]\end{aligned}[/tex]
[tex]\textsf{Multiply the denominator by }\dfrac{1+x^2+xh}{1+x^2+xh}:[/tex]
[tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h(1+x^2+xh)}{(1+x^2+xh)}}\right][/tex]
Separate:
[tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h}{(1+x^2+xh)}} \right] \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]
[tex]\textsf{Use }\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1:[/tex]
[tex]= 1 \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]
As h gets close to zero:
[tex]= 1 \cdot \left[\dfrac{1}{1+x^2}\right][/tex]
Simplify:
[tex]=\dfrac{1}{1+x^2}[/tex]
Answer:
To find the derivative of [tex]\tan^{-1} x[/tex] using the first principle of derivative, we need to use the definition of the derivative:
f'(x) = lim(h->0) [(f(x + h) - f(x)) / h]
where f(x) = [tex]\tan^{-1} x[/tex].
Substituting f(x) into the definition of the derivative, we get:
f'(x) = lim(h->0) [([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) / h]
To simplify this expression, we can use the formula for the inverse tangent of a sum:
[tex]\tan^{-1}[/tex](a + b) = [tex]\tan^{-1}[/tex]a + [tex]\tan^{-1}[/tex]b - [tex]\pi[/tex]/2
Using this formula, we can rewrite the numerator of the expression above as:
([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) = [tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))
Now, substituting this expression back into the definition of the derivative, we get:
f'(x) = lim(h->0) [[tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))] / h
We can simplify this expression using algebra and trigonometry, and we get:
f'(x) = lim(h->0) [h / (1 + x^2 + hx + h^2 + x^2h + xh^2)] / h
f'(x) = lim(h->0) 1 / (1 + x^2 + hx + h^2 + x^2h + xh^2)
Now we can simplify this expression by dropping the terms that contain h^2 or higher powers of h, since they will approach zero faster than h as h approaches zero. We also drop the term containing x^2h, since it is a second-order term and will also approach zero faster than h. This leaves us with:
f'(x) = lim(h->0) 1 / (1 + x^2 + hx)
Now we can evaluate the limit as h approaches zero:
f'(x) = 1 / (1 + x^2)
Therefore, the derivative of [tex]\tan^{-1} x[/tex] by first principle of derivative is:
[tex]\frac{d}{dx}[/tex][tex]\tan^{-1} x[/tex] = 1 / (1 + x^2)
Which equation has the same solution as x^2+8x+15 = -4x
2
+8x+15=−4?
The equation that has the same solution as x² + 8x + 15 = -4x is x = -6± √21.
Step 1 - Move terms to the left
x² + 8x + 15 = -4x
x² + 8x + 15-(-4x) = 0
Step 2 - Combine the terms
x² + 8x + 15 + 4x = 0
x² + 12x + 15 = 0
Step 3 - Apply the quadratic formula
x = (-b ± √(b² - 4ac) )/ 2a
Recall that form our equation:
a = 1
b = 12
c = 15
Thus, x = (-12 √(12² - 4 * 1 *15) )/2 *1
⇒x = -6 ± √21
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Carol buys a house for £234 900
She pays a 10% deposit.
Work out the amount of deposit paid by Carol.
Answer:
£23490
Step-by-step explanation:
10/100×£234900=23490
select all of the statements that are true for the given parabola?check all that apply(everything in picture)
The x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
Here the graph or equation is not given:
So we are assuming the equation for the parabola is:
y = x²—4
If we plot the graph of the parabola, we can say:
The x-intercepts are (-2, 0) and (2, 0) The minimum is at (0, -3)The line of symmetry is x = 0Thus, the x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4
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A 2100-square-foot home is for sale. The finished basement has an area of 455 square feet. The basement accounts for what percent of the total square footage?
Given the area of the house and the basement, the basement accounts for 21.67 percent of the total square footage.
What is Percentage?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given that;
Area of the house = 2100ft²Area of the basement = 455ft²Percentage of area occupied by the basement = ?Percentage = ( Part / Whole ) × 100%
Percentage = ( 455ft² / 2100ft² ) × 100%
Percentage = 0.21666 × 100%
Percentage = 21.67%
Given the area of the house and the basement, the basement accounts for 21.67 percent of the total square footage.
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When a retired police officer passes away, he leaves $45,000 to be divided among his three children and three grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?
The answer that I got is 7 500
Which two angles below are
complementary?
Select one:
O 20° and 160°
O 45° and 145°
O 1° and 89°
O 30° and 130°
When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The correct option is C.
What are Complementary Angle?When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
The two angles which are complementary angles are 1° and 89° because their sum is 90°.
Hence, the correct option is C.
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Jill, Ally, and Maria ran the 50-yard dash. Jill ran the race in 6.87 seconds. Ally ran the race in 6.82 seconds. Maria ran the race in 6.93. Who ran the race the fastest? Explain how you can use a place-value chart to find the answer.
Answer:
Ally
Step-by-step explanation:
The fastest time of the race will be the one lesser in value.
=============================================================
Comparing the tenths place :
⇒ Jill = 8 in the tenths place
⇒ Ally = 8 in the tenths place
⇒ Maria = 9 in the tenths place
Since Maria's time's tenth place value is greater than that of the other two, she had the slowest time.
===========================================================
Comparing the hundredths place (for Jill and Ally) :
⇒ Jill = 7 in the hundredths place
⇒ Ally = 2 in the hundredths place
Since Ally has the lower hundredths' place value, she has the fastest time.
6. Resuelve las ecuaciones. Anota la solución y tu procedimiento.
a) 2x - 6=4
Procedimiento:
Solución: x =
b) 3x-3 = 3
Procedimiento:
Solución: x =
Procedimiento:
Solución: x =
c) x + 3 = 4
Answer:
Step-by-step explanation:
a)
Planteamiento:
2x - 6 = 4
Procedimiento:
2x - 6 + 6 = 4 + 6
2x + 0 = 10
2x = 10
2x/2 = 10/2
1x = 5
x = 5
Comprobación:
2*5 - 6 = 4
10 - 6 = 4
Solución:
x = 5
b)
Planteamiento:
3x - 3 = 3
Procedimiento:
3x - 3 + 3 = 3 + 3
3x - 0 = 6
3x = 6
3x/3 = 6/3
1x = 2
x = 2
Comprobación:
3*2 - 3 = 3
6 -3 = 3
Solución:
x = 2
c
Planteamiento:
x + 3 = 4
x + 3 - 3 = 4 -3
x + 0 = 1
x = 1
Comprobación:
1 + 3 = 4
Solución:
x = 1
the distance on a ruler between 8cm and 26cm =
Answer:
18 cm
Step-by-step explanation:
To find the distance, take the larger number and subtract the smaller number
26 cm - 8 cm
18 cm
The milligrams of aspirin in a person's body is given by the equation a = 500*(3/4^t), where t is the number of hours since the patient took the medicine.
In the equation, what does 500 tell us about the situation?
SOMEONE ANSWER PLS!!
500 represents the initial amount of medication, since when t=0, a=500.
Find the area of the triangle with the given vertices.
(2, 4), (-1,0), (5,9)
Answer: 1.5
Step-by-step explanation:
If we translate the triangle right one unit, we get it has vertices (3,4), (0[tex]\frac{1}{2}|(9)(3)-(4)(6)|=\boxed{1.5}[/tex],0), and (6,9).
So, the area is
Which expression is the simplest form of 4(3x + y) + 2(x - 5y) + x²?
A. x² +14x-9y
B. x² +14x-6y
C. x² + 13x-9y
D. x² + 14x-y
Answer: [tex]x^{2}+14x-6y[/tex]
Step-by-step explanation:
[tex]4(3x+y)+2(x-5y)+x^{2} \\ \\ 12x+4y+2x-10y+x^{2} \\ \\ \boxed{x^{2}+14x-6y}[/tex]
How much of an 80% orange juice drink must be mixed with 12 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice
Answer:
12 gallons
Step-by-step explanation:
The amount of juice in the mix is the sum of the amounts of juice contributed by each of the constituents of the mix. Those amounts will be the product of the quantity of constituent and the fraction that is juice.
__
setupLet x represent the amount of 80% juice drink that must be added to the mix. The total amount of orange juice in the mix is ...
20% × 12 gallons + 80% × x gallons = 50% × (12 +x) gallons
__
solutionDividing by gallons, eliminating parentheses, and using decimals for percentages, we have ...
2.4 +0.80x = 6.0 +0.50x
0.30x = 3.6 . . . . . . . . subtract 0.50x+2.4
x = 12 . . . . . . . . . . . divide by 0.30
12 gallons of 80% juice drink must be added to obtain the desired mix.
_____
Additional comment
We notice that 50% is the average of 20% and 80%, so each must be half of the mix. If there are 12 gallons of 20%, then there must be 12 gallons of 80%.
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Solve Y/-6 + 5 = 9
It’s Algebra 1
Answer:
Y = - 24
Step-by-step explanation:
Y/-6 +5=9 /*6 (Multiply the whole equation by the number 6 to eliminate the fraction. That is, you multiply each member of the equation by 6 because 6 is in the denominator of the fraction.
[tex]\frac{Y}{-6} *6=-Y[/tex], [tex]5*6=30[/tex], [tex]9*6=54[/tex]
-Y + 30 = 54
-Y = 54-30
-Y=24 /*(-1)
Y= -24
Solve for the variable: 4+3(x+22)=5x-10
When we solve the equation, we will get the real answer x=40 as a variable.
First Degree EquationFirst degree equation is a mathematical sentence, which has values represented by letters.
These letters can indicate a variable or an unknown - which at the end of the equation will be the final value.
— To solve this equation, just: apply the distributive property (multiply the terms that are outside the parentheses, for the terms that are inside the symbol).
— Next, let's add the real numbers together. Next, we'll subtract the like terms before the equality, thus moving the common term after the equality by adding.
— Finally, let's divide the equation, thus obtaining the final result.
4 + 3(x + 22) = 5x - 10
4 + 3x + 66 = 5x - 10
70 + 3x = 5x - 10
3x - 5x = -10 - 70
-2x = -80
x = 80 ÷ 2
x = 40
Therefore, the correct value of X in this equation, will be x = 40.
You have decided to purchase a new computer with the Amtel processor. The new processor is the latest release of the hyperduoraging core threading processors. You local computer store has a computer with this processor and is offering a 36 month installment plan to finance the computer. The store requires no down payment. The salesperson tells you that you can finance the computer with 36 monthly payments of $98.20. Determine the total amount paid.
a.
$3,535.20
c.
$3,256.01
b.
$3,426.31
d.
$3,089.57
Answer:
A. $3,535.20.
To find the total amount paid, you can simply multiply the monthly payment by the number of payments:
$98.20 x 36 = $3,535.20
Find the value of x.
X
4
[?]
X =
Enter the number that belongs in
the green box.
Answer:
√33
Step-by-step explanation:
it is a right triangle and we use Pythagoras
x² = 7² - 4²
x² = 49 - 16
x² = 33
x = √33
Felix chose 3 integers between -10 and 10 at random. He chose the three integers listed below.
-1, 8, 4
Which integer does Felix need to choose next so that the product of all
four numbers chosen is 64?
[A] 2
[B] -2
[C] -1
[D] 4
Answer: -2
Step-by-step explanation: The answer is -2 because -1 x 8 = -8, and -8 x 4 = -32. Because multiplying two negatives cancels out and becomes positive, we can apply this same principle and figure out that -32 x -2 would give us positive 64. Hope this helps!
Select three deductions someone would see on their paystubs.
Marital Status Tax
Excise Tax
Medicare Tax
Federal Income Tax
Social Security Tax
The three deductions someone would see on their paystubs are:
A. Social Security Tax
C. Federal Income Tax
D. Medicare Tax
What is paystubs?Paystubs is a paycheck and can be defined as a check that an employer issued out to the employee for the service the employee rendered to the employer.
The three deductions someone would see on their paystubs are:
Social Security Tax
Federal Income Tax
Medicare Tax
Therefore the correct options are A, C, D.
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hosting a dinner party for 38 people, you plan to serve peach pie for dessert. Each pie has 8 slices. how many pies must your buy to ensure each guest gets 1 slice
Answer:
4.75 or round up to 5.
Step-by-step explanation:
if each pie has 8 slices, then you must do 8+8+8... and so on until u reach 38. However you wont get exactly 38 because 8 doesn't add up evenly into 38. You can find the exact number by divding the amount of people, 38, by the number of slices per pie, 8. The answer will be 4.75 but you can not buy a fraction of a pie so you must round up to 5 whole pies. There will be extra left over in the end, but you cant round down because 4 pies would not be enough, so you must buy 5.
Given: ABC is a right triangle with right angle C. AB = 18 centimeters and mZA = 22°.
What is BC?
Enter your answer, rounded to the nearest tenth, in the box.
cm
Heart of algebra
If 5=a^x, then 5/a=?
Step-by-step explanation:
[tex]5 = {a}^{x} [/tex]
[tex] \frac{5}{a} = \frac{a {}^{x} }{a} [/tex]
[tex] \frac{5}{a} = {a}^{x - 1} [/tex]
What is the missing coefficient of the x-term of the product (-x-5)² after it has been simplified?
O-25
O-10
O10
25
The missing coefficient of the x-term after finding the product of (-x - 5)², is: C. 10.
What is the Coefficient of a Variable?The coefficient of a variable is the numerical value that comes before the variable and multiplies it.
Find the product of (-x - 5)²:
(-x - 5)(-x - 5)
-x(-x - 5) -5(-x - 5)
x² + 5x + 5x + 25
x² + 10x + 25
The x-term is "10x". The coefficient is: 10.
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The product of a quarter of 3 more than a number a and two times a number b as an algebraic expression?
Algebraic expression of the product of a quarter of 3 more than a number a and two times a number b is equals to [tex](\frac{3}{4} +a)[/tex]×[tex](2b)[/tex]
What is an algebraic expression?" An algebraic expression is defined as the expression which is represents using variables, number and mathematical operation."
According to the question,
'a' represents a number
'b' represents another number
Algebraic expression as per the given condition we get,
The product of
Quarter of 3 more than a number a = [tex]\frac{3}{4} +a[/tex]
Two times a number b = 2b
Algebraic expression = [tex](\frac{3}{4} +a)[/tex]× [tex](2b)[/tex]
Hence, algebraic expression of the product of a quarter of 3 more than a number a and two times a number b is equals to [tex](\frac{3}{4} +a)[/tex]×[tex](2b)[/tex].
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Write the equation of the graph of y = cos(x) was shifted downwards by 3 units, shrink horizontally by a fourth of a unit, inverted horizontally and shifted 60° to the left. if it has an amplitude of 5 units.
The equation of the transformed function is y = 5cos(x/4 + 60) - 3
How to determine the equation?The equation of the graph is given as:
y = cos(x)
The rule of downward shift is:
(x, y) ⇒ (x, y - h)
So, the function when shifted downwards by 3 units is
y = cos(x) - 3
The rule of horizontal shrink is:
(x, y) ⇒ (x/k, y)
So, the function when shrink horizontally by a fourth unit is:
y = cos(x/4) - 3
The rule of left shift is:
(x, y) ⇒ (x +h, y)
So, the function when shifted left by 60 units is
y = cos(x/4 + 60) - 3
The amplitude is given as:
A= 5
So, we have:
y = 5cos(x/4 + 60) - 3
Hence, the equation of the transformed function is y = 5cos(x/4 + 60) - 3
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