A graph of 2 functions is shown below.



Which of the following is a solution for f(x) = g(x)?



Your answer:


x = −2


x = 1


x = 0


x = −1

Answer:

Part a)  In order to solve the equation, we will simplify both of them.  Once we do that, if we notice, they are the same equation, so therefore, if x=10, then we will be able to match the equation.

Part b) The reason the expressions are not equal when x=-1/2 is because if we see, that in the second expression, 2x^2, if x=-1/2, then the answer becomes -1, and we eventually end up with 1.

Part c)  As we can see, the expressions are the same, so if x is any number other than -1/2, then we will be able to show that the expressions are equal.

Step-by-step explanation:

You can simplify the explanation, also if you play ROBLOX, follow me at my username: BAMUNJI, or 24KBlingYT

By the way, this question is from the Art of Problem Solving, and you should not just copy answers or copy of them.

Part (a)  We shall simplify both of them in order to find the solution to the equation.

Part (b)  When x=-1/2, the answers to the second expression, 2x2, change to -1, and we eventually arrive in 1.

Part (c)  As we can see, the expressions are identical, thus we can demonstrate that they are equal if x is any number other than -1/2.

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Answer:7x12= 84

Step-by-step explanation:

7x10=70

7x2=14

70+14=84

have a good day

There are 84 inches in 7 feet.

Given that we need to determine that how many feet in 84 inches.

To convert inches to feet, you need to divide the number of inches by the number of inches in a foot.

There are 12 inches in a foot.

Given that you have 84 inches, you can divide this value by 12 to find the equivalent in feet:

84 inches ÷ 12 inches/foot = 7 feet

So, 84 inches is equal to 7 feet.

Hence there are 84 inches in 7 feet.

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Answer:(4,0) and (-9,0)

Step-by-step explanation:

Answer:

[tex]-y^{2}-4yi+4[/tex]

Step-by-step explanation:

we know that

[tex](a-b)^{2}=a^{2}-2ab+b^{2}[/tex]

we have

[tex](2-yi)^{2}[/tex]

substitute

[tex](2-yi)^{2}=(2)^{2}-2(2)(yi)+(yi)^{2}[/tex]

[tex](2-yi)^{2}=4-4yi+(y^{2})(i^{2})[/tex]

Remember that

[tex]i^{2}=-1[/tex]

substitute

[tex](2-yi)^{2}=4-4yi+(y^{2})(-1)[/tex]

[tex](2-yi)^{2}=4-4yi-y^{2}[/tex]

[tex](2-yi)^{2}=-y^{2}-4yi+4[/tex]

Answer:

y = 6x + 1

Step-by-step explanation:

linear equations (straight line) are expressed in the following general form:

y = mx + b, where m is the gradient and b is the y-ordinate of the point where the line crosses the y-axis (called the y-intercept)

Given : m = 6

we realize that point (0,1) is actually on the y-axis (i.e x=0), therefore this is coincidentally the y-intercept. Hence b = 1

Therefore the whole equation is

y = 6x + 1

The equation for a line is:

y = mx + c

Note:

y  is the y coordinate

m is the slope

x is the x coordinate

c is the y -intercept (where the line crosses the y-axis.

The question tells us that the slope is 6 (so m is 6)

It also tells that the coordinates are: (0 , 1)    (so x is 0    and y is 1)

Lets plug in these values into the equation and solve to get the missing value ( which is c) :

y = mx + c

1 = 6(0) + c

1 = c.

Now to get the equation of the line, we plug in the values for m and c into y= mx + c:

Equation of line: y = 6x + 1

-----------------------------------------------------------

Answer:

Equation of line with slop m = 6 and including point (0, 1) is:

y = 6x + 1

Answer:

D

Step-by-step explanation:

Use exponents property:

[tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]

1. Note that

[tex]\dfrac{x^9}{x^6}=x^{9-6}=x^3[/tex]

and

[tex]\dfrac{y^3}{y^{11}}=y^{3-11}=y^{-8}=\dfrac{1}{y^8}[/tex]

2. Now

[tex]\sqrt{25}=5\\ \\\sqrt{64}=8\\ \\\sqrt{x^3}=x\sqrt{x}\\ \\\sqrt{\dfrac{1}{y^8}}=\dfrac{1}{y^4}[/tex]

So

[tex]\sqrt{\dfrac{25x^9y^3}{64x^6y^{11}}}=\dfrac{\sqrt{25}\sqrt{x^3}}{\sqrt{64}\sqrt{y^8}}=\dfrac{5x\sqrt{x}}{8y^4}[/tex]

because [tex]x>0,\ y>0[/tex]

Answer: Last option.

Step-by-step explanation:

You need to remember the Quotient of powers property:

[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]

 Applying this property, we know that:

[tex]\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }=\sqrt{\frac{25x^3}{64y^8}}[/tex]

Descompose 25 and 64 into their prime factors:

[tex]25=5*5=5^2\\64=8*8=8^2[/tex]

Since:

[tex]\sqrt[n]{a^n}=a[/tex]

And according to the Product of powers property:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

You can simplify. So, the equivalent expression is:

[tex]\sqrt{\frac{5^2x^2*x}{8^2y^8}}=\frac{5x\sqrt{x} }{8y^4}[/tex]

Answer:

x = -80

Explanation

-40 divided by 1/2 is -80

Answer:

x = 9/7

Step-by-step explanation:

-5/4x-5 =-35

-5 = -35 * (4x-5)  

-5 = -35*4x - 5*(-35)

-5 = - 140x + 175

- 140x + 175 = -5

-140x = -5 - 175 = -180

x = -180 / -140 =18 / 14 = 9 /7

To solve the given equation, -5/4x = -35, for x, you multiply both sides by the reciprocal of -5/4 which is -4/5. This gives you x = 28 as the solution.

The given equation in your question is -5/4x = -35. In order to solve this equation for x, you would first want to isolate x on one side of the equation. Thus, we'll need to divide both sides of the equation by -5/4.

However, dividing by a fraction is the same as multiplying by its reciprocal. So, in this case, we'll multiply both sides by -4/5, which is the reciprocal of -5/4. This gives us:

x = (-35) * (-4/5)

Doing the multiplication results in x = 28.

Therefore, the solution for x in the equation is 28.

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Answer: A

Step-by-step explanation:

2,400 divided by 60 will give you 40. 40 multiplied by 0.50 give you $20.00.

2,400 divide by 80 will give you 30 but 30 multiplied but 0.75 gives you $22.50.

$22.50 minus $20.00 gives you $2.50

Let’s solve to answer the question.

Divide the amount of pencils the company needs by the amount of pencils the box holds.

2,400/60=40.

Now multiply it by the price.

40*.5=$20.

Repeat.

2400/80=30

30*.75=22.5

The cylindrical containers cost less.

Hope this helps!

Answer:

Point D, Segment CD, Ray CD

Step-by-step explanation:

Answer:

It's choice D.

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

= 3x - 2 + x^2 + 1

= x^2 + 3x - 1.

Answer:

D. x^2+3x-1

Step-by-step explanation:

You have:

f(x) = 3x-2

g(x)= x^2 +1

Then:

(f+g)(x)=f(x)+g(x)

(f+g)(x)=(3x-2)+(x^2+1)

(f+g)(x)=3x-1+x^2 (-2+1=-1)

(f+g)(x)=x^2+3x-1 (ordering terms)

Answer: b

Step-by-step explanation:

trust!!!

Yes! A radical Equation does use a radical in a Equation.

False

Step-by-step explanation:

Don’t listen to the AI answers

Answer:

4000 units

Step-by-step explanation:

In 2001 the total number of marketed units= 730,000

If this number represents 50% of what was marketed in 2004, then the total number of units marketed in 2004 was:

(100/50)× 730,000=1460000

To get the number for each of the 365 days in 2004 we divide the total for 2004 by 365

1460000/365= 4000 units

Answer: 4,000 units per day.

Step-by-step explanation:

You know that in 2001 its yearly volume was 50% of its volume for 2004.

Therefore, if in 2001 the company marketed 730,000 units of its product, in 2004 the volume is:

[tex]Yearly\ volume_{(2004)}=(730,000\ units)(2)=1,460,000\ units[/tex]

Let be "x" the number of units for each of the 365 days of 2004, you can find its value by dividing  the 2004 volume by 365.

The result is:

[tex]units=\frac{1,460,000\ units}{365}=4,000\ units.[/tex]

Hello There!

The volume of a cylinder is pi * r^2 * h. It's a circle times the height.

The volume of a cone is (1/3) * pi * r^2 * h. So it is one third of the volume of a cylinder with the same dimensions.

Answer:

The volume of a cone is one-third the volume of a cylinder.

Step-by-step explanation:

Answer:

[tex]x_{2} =24[/tex]

Step-by-step explanation:

Your welcome :)

Answer:

C

Step-by-step explanation:

4y-2y=10

y=5

Answer:

33.7 degrees

Step-by-step explanation:

As we go from (3,7) to (6,9), x increases by 3 and y increases by 2.  Thus, the gradient (slope) of the line connecting these two points is

m = rise / run = 2/3.  Using the slope-intercept formula y = mx + b, we obtain

7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5.  The y-intercept is (0, 5).

Next we find the x-intercept.  We set y = (2/3)x + 5 = to 0 and solve for x:

(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is

(-15/2, 0).  This line intersects the x-axis at (-15/2, 0).

Now look at the segment of this line connecting (-15/2, 0) and (0, 5).  Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is

tan Ф = 5 / (15/2) = 10 / 15 = 2/3.

Using the inverse tangent function, we get Ф = arctan 2/3, or approx.

33.7 degrees.

I believe you meant "the acute angle it makes with the positive x-axis."​

Final answer:

The gradient of the line is 2/3, and the acute angle it makes with the positive x-axis is found by taking the arctan of the gradient. which is approximately 33.69 degrees.

Explanation:

The gradient of the line joining two points, (x1, y1) and (x2, y2), is calculated using the formula:
Gradient = (y2 - y1) / (x2 - x1)

Substituting the given points (3,7) and (6,9) into the formula, we get:

Gradient = (9 - 7) / (6 - 3) = 2 / 3

The gradient is 2/3. To find the acute angle θ the line makes with the positive x-axis, we use the formula:
Tan(θ) = Gradient

So, θ = arctan(Gradient)

θ = arctan(2/3)

Calculating θ will give us the acute angle. which is approximately 33.69 degrees.

Answer:

x = 6 ± 3√10

Step-by-step explanation:

Since this is an unfactorable expression, apply the Quadratic Formula, -b ± √b² - 4ac\2a, according to the Quadratic Equation, y = Ax² + Bx + C. Applying the Quadratic Formula will give you the above answer.

NOTE: -b = OPPOSITE of b

I am joyous to assist you anytime.

Final answer:

To solve x² - 12x + 36 = 90 for x, we simplify the equation to x² - 12x - 54 = 0 and use the quadratic formula to find x = 6 + 3√10 and x = 6 - 3√10.

Explanation:

To solve the equation x² - 12x + 36 = 90, we can first simplify it by subtracting 90 from both sides to set it equal to zero:

Now we use the quadratic formula, which states that for any quadratic equation of the form ax² + bx + c = 0, the solutions for x can be found using:

Applying this to our equation with a = 1, b = -12, and c = -54, we get:

Thus, the solutions are x = 6 + 3√10 and x = 6 - 3√10.

Answer:  $24

Step-by-step explanation:

Let x represent the amount of Carrie's allowance.

[tex]\dfrac{1}{4}x+\dfrac{1}{3}x+8=22\\\\\\\dfrac{1}{4}x+\dfrac{1}{3}x=14\\\\\\(12)\dfrac{1}{4}x+(12)\dfrac{1}{3}x=(12)14\\\\\\3x + 4x = (12)14\\\\\\7x=(12)14\\\\\\x=(12)2\\\\\\x=24[/tex]

Answer:

x=lindas age

3 times lindas age (3 time x or 3x) is decreased by 36 (-36), the result (=) is twice lindas age (2 times x or 2x)

now we have

3x-36=2x

subtract 2x

x-36=0

add 36

x=36

age=36

Step-by-step explanation:

Using algebra to solve the problem, we create the equation L - 36 = 2L, representing Linda's age. Solving for 'L', we find that Linda is 36 years old.

This problem can be solved by using algebra, a branch of mathematics. Let's assume that Linda's age is denoted by the variable 'L'. According to the problem, if Linda's age is decreased by 36, the result is twice Linda's age. We can write this as an equation: L - 36 = 2L.

In order to solve for 'L', we'll need to get all terms involving 'L' on one side of the equation. We would then subtract 'L' from both sides, giving us -36 = L, or, re-arranged, L = 36. Therefore, Linda is 36 years old.

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The top right one, because for every argument there is only one corresponding value.

Answer:

Here is the answer.

x= 1/2(7+3i√3) and 1/2(7-3i√3)

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (8, -1) and (2, -5). Substitute:

[tex]m=\dfrac{-5-(-1)}{2-8}=\dfrac{-4}{-6}=\dfrac{2}{3}[/tex]

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

Substitute:

[tex]y-(-1)=\dfrac{2}{3}(x-8)[/tex]

[tex]y+1=\dfrac{2}{3}(x-8)[/tex] → the point-slope form

Convert to the standard form: [tex]Ax+By=C[/tex]

[tex]y+1=\dfrac{2}{3}(x-8)[/tex]        multiply both sides by 3

[tex]3y+3=2(x-8)[/tex]         use the distributive property a(b+c) = ab+ ac

[tex]3y+3=2x-16[/tex]      subtract 3 from both sides

[tex]3y=2x-19[/tex]       subreact 2x from both sides

[tex]-2x+3y=-19[/tex]       change the signs

[tex]2x-3y=19[/tex] → the standard form

Time= distance/speed (T = d/s)

Rate or speed are similar since they both represent some distance per unit time such miles per hour and kilometers per hour. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

distance = rate x time To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.

This is because, speed of the object refers distance travelled divided by time or it expressed as, Furthermore, 1 could also explain the relationship of the time with other two variables using this formula. Speed could be of 2 types, relative or average.

from the formula,

Distance = time * speed

Speed = distance/time

Time= distance/speed (T = d/s)

So basically distance divided both of them when it find speed distance divide time when fine time distance divide speed.

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Using Hooke's Law, the spring would stretch a total of 19.5 cm when 13 washers are placed on it.

To find out how much a spring would elongate when the number of washers is increased, we use Hooke's Law, which describes linear elasticity.

Since it is given that 3 washers cause the spring to stretch 4.5 cm, we can assume that each washer causes an equal amount of stretch under this elastic limit. Therefore, the amount of stretch per washer is 4.5 cm divided by 3, which is 1.5 cm per washer.

If you hang 13 washers on the spring, the total stretch can be calculated by multiplying the amount of stretch per washer with the total number of washers:

Stretch per washer × Number of washers = Total stretch

1.5 cm/washer × 13 washers = 19.5 cm.

So, with 13 washers, the spring would stretch a total of 19.5 cm.

[tex]\text{Hey there!}[/tex]

[tex]\text7x}^2\text{- 32x - 60}[/tex]

[tex]\text{The answer is: (7x + 10)(x - 6)}[/tex]

[tex]\text{Because if you follow the step to the answer (first you have to distribute}[/tex] [tex]\text{then combine the like terms after distributing) after all of that you SHOULD}[/tex] [tex]\text{get the equation back!}[/tex]

[tex]\text{Distribute}\downarrow\\\\\text{7x(x)=7x}^2\\ \text{7(-6x)= -42}\\\text{10(x)= 10x}\\\text{10(-6)= -60}[/tex]

[tex]\text{Combine your like terms (terms that has the almost the same thing)}\downarrow[/tex]

[tex]\text{-42x + 10x = -32x}[/tex]

[tex]\text{The other terms stays the same because they DON'T have like terms}[/tex]

[tex]\text{Original problem: 7x}^2\text{- 32x -60}[/tex]

[tex]\boxed{\boxed{\bf{Answer: (7x+10(x -6))}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

Step-by-step explanation:

Please, if you're indicating exponentiation, use the symbol " ^ " to indicate it.  Thanks.

The parent function here is f(x) = x^3.

                                              g(x) = (x + 6)^3 has the same graph as does

f(x) = x^3, except that the entire graph of x^3 is translated 6 units to the left.

                                              h(x) = -(x + 6)^3 has the same graph as

does g(x), except that the entire graph of g(x) is reflected in the x-axis.

The graph of h(x) = h(x) = –(x + 6)3 – 3 is the same as that of h(x) except that the entire graph is translated downward by 3 units.

Answer: B

Step-by-step explanation:

The polynomial (3x - 4x^2 + 8x^3) + (-6x + 2x^4 - 5x^2) simplifies to 2x^4 + 8x^3 - 9x^2 - 3x in standard form by combining like terms and ordering them by descending exponents.

To simplify the polynomial (3x - 4x2 + 8x3) + (-6x + 2x4 - 5x2) and write it in standard form, we combine like terms. Standard form for polynomials is to write the terms in descending order of their exponents. Here are the steps:

The simplified polynomial in standard form is:

2x4 + 8x3 - 9x2 - 3x

Answer: D

Step-by-step explanation:

W is the total number of oranges.

W/5 is the oranges being divided equally for 5 friends