solve the equation for a k=4a+9ab​

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=6[x-(-1)]\implies y+3=6(x+1) \\\\\\ y+3=6x+6\implies y=6x+3\implies -6x+y=3\implies 6x-y=-3[/tex]

let's notice the y-coordinate is the same for both points, thus is a horizontal line.

Check the picture below.

Answer:

The answer is C.250%

Step-by-step explanation:

Got it right on the quiz

Answer:

Step-by-step explanation:

[tex]f(x)=3x^2-2x+7\\\\f(-2)\to\text{put x = -2 to the equation of a function:}\\\\f(-2)=3(-2)^2-2(-2)+7=3(4)+4+7=12+4+7=23[/tex]

Answer:

The correct option is 4. The value of f(-2) is 23.

Step-by-step explanation:

The given function is

[tex]f(x)=3x^2-2x+7[/tex]

We have to find the value of f(-2). It means we need to find the value of function f(x) at x=-2.

Substitute x=-2 in the given function to find the value of f(-2).

[tex]f(-2)=3(-2)^2-2(-2)+7[/tex]

On simplification we get

[tex]f(-2)=3(4)-(-4)+7[/tex]

[tex]f(-2)=12+4+7[/tex]

[tex]f(-2)=23[/tex]

The value of f(-2) is 23. Therefore the correct option is 4.

Step-by-step explanation:

from the graph above, the intersect of both lines would give the answer...

C. 5 quarts, 25 gallons

You can substitute the values in both equations to verify the answer

Answer:

you would first have a straight, increasing line with a small slope. (walking slowly and consistently)

then you have a flat, straight line (not moving as you pet the kitten)

then you have a big, increasing slope (running fast)

then it's straight line again(distance doesnt change at friend's house)

and then a decreasing line with pretty big slope all the way to the x axis(running home)

Step-by-step explanation:

Volume of a cone is [tex]\pi r^{2} .height[/tex]/3 so [tex](3x)^{3}[/tex] is equal to

[tex]\pi r^{2} .x[/tex]/3 .  Also  [tex](3x)^{3}[/tex] = [tex]27x^{3}[/tex]

[tex]27x^{3}[/tex] = [tex]\pi r^{2} .x[/tex]/3. Pi equals to 3 so pi and the 3 in the denominator will simplfy each other. lets simplfy the "x" so [tex]r^{2}  = 27x^{2}[/tex] so the radius is 9x.

The expression that represents the radius of the cone's base is →

{r} = 3/√π.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write Volume as -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is that the volume of a cone is {3x} cubic units and its height is {x} units.

The volume of a cone is -

V = 1/3 πr²h

We can write the volume as -

3x = 1/3 πr²x

3 = 1/3 πr²

πr² = 9

r² = 9/π

r = 3/√π

Therefore, the expression that represents the radius of the cone's base is → {r} = 3/√π.

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Answer:

Step-by-step explanation:

The graph of g(x) is the same as that of f(x), EXCEPT that the graph of f(x) has been translated upward by 2 units.

The function is added and with a positive number so the function will shift towards the left , Option D is the correct answer.

A function can be defined as an algebraic expression which states relation between an independent and a dependent variable.

A function always comes with a defined range and domain.

It is given in the question that

There are two functions

g(x), f(x)

and they are related as

g(x)=f(x)+2.

and it has been asked that which statement given in the option describes it the best.

A. The graph of g(x) is the graph of f(x) shifted 2 units to the right.

B.The graph of g(x) is the graph of f(x) shifted 2 units down.

C.The graph of g(x) is the graph of f(x) shifted 2 units up.

D. The graph of g(x) is the graph of f(x) shifted 2 units to the left.

When a function is added , subtracted or multiplied it shifts or translates, and the new function is called the translated function

As the function is added and with a positive number so the function will shift towards the left.

Therefore , D is the answer the graph of G (x) is the graph of f(x) shifted 2 units to the left.

To know more about Function

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Answer:

5p-6 is your answer.

Step-by-step explanation:

p^2 + p - 6

-p^2 - 4p

leaves you with

p--4p-6, which equals p+4p-6,

so simplifying: 5p+6 is your answer.

Hope this helps!

For this case we must indicate an expression equivalent to:

[tex]\sqrt {\frac {2x ^ 5} {18}}[/tex]

We rewrite 18 as 2 * 9:

[tex]\sqrt {\frac {2x ^ 5} {2 * 9}} =[/tex]

We simplify common factors:

[tex]\sqrt {\frac {x ^ 5} {9}} =[/tex]

We rewrite:

[tex]x ^ 5 = x ^ 4 * x = (x ^ 2) ^ 2 * x\\9 = 3 ^ 2[/tex]

So, we have:

[tex]\sqrt {\frac {(x ^ 2) ^ 2 * x} {3 ^ 2}} =\\\sqrt {(\frac {x ^ 2} {3}) ^ 2 * x} =[/tex]

We get the terms of the radical "

[tex]\frac {x ^ 2} {3} \sqrt {x}[/tex]

Answer:

[tex]\frac {x ^ 2} {3} \sqrt {x}[/tex]

Answer:

The answer is A

Step-by-step explanation:

The other guy is correct I'm just making it easier to get the answer quickly.

Answer:

3rd choice

Step-by-step explanation:

In division for variables with same base, you do subtract top exponent minus bottom exponent. She did that correctly since -3-(-1)=-3+1=-2 and -2-1=-3.  

The problem said m=-2 and n=4 and she replace m with (-2) and n with (4). She did this correctly.

You can multiply base numbers unless the exponents are the same 4 doesn't have the exponent -2 on it so you can't do (4(-2))^(-2)

The error is the 3rd option.

We start with

[tex]\dfrac{4m^{-3}n^{-2}}{m^{-1}n}[/tex]

Simplifying the exponents, we have

[tex]\dfrac{4m^{-3}n^{-2}}{m^{-1}n} = 4m^{-3}n^{-2} (mn^{-1}) = 4m^{-3+1}n^{-2-1}=4m^{-2}n^{-3}[/tex]

So, the exponents are ok.

If we plug the values, we have

[tex]4m^{-2}n^{-3} \mapsto 4(-2)^{-2}(4)^{-3} = 4\cdot \dfrac{1}{(-2)^2}\cdot\dfrac{1}{4^3} = 4\cdot \dfrac{1}{4}\cdot \dfrac{1}{64} = \dfrac{1}{64}[/tex]

So, she didn't apply the exponent -2 correctly.

Answer:

Second option: One solution. Independent.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Since the equations of the system have this form, we know that they are lines.

We can identify that the y-intercept of the first equation [tex]y=-5x+1[/tex] is:

[tex]b=1[/tex]

Now we need to find the x-intercept. Substitute [tex]y=0[/tex] and solve for "x":

[tex]0=-5x+1\\\\5x=1\\\\x=\frac{1}{5}=0.2[/tex]

Then, we can graph the first line which passess through the points (0,1) and (0.2,0). Observe the graph attached.

The y-intercept of the second equation [tex]y=-2x-2[/tex] is:

[tex]b=-2[/tex]

Now we need to find the x-intercept. Substitute [tex]y=0[/tex] and solve for "x":

[tex]0=-2x-2\\\\2x=-2\\\\x=\frac{-2}{2}=-1[/tex]

Then, we can graph the second line, which passess through the points (0,-2) and (-1,0).

You can observe in the graph that the lines intersect at the point (1,-4). Therefore, that point is the solution of the system of equations.

Since the lines intersect, then there is one solution that is true for both equations. It is independent

Answer:

The best estimate for the solution of the system of equations is the ordered pair (7, 0.5)

Step-by-step explanation:

The way to solve this problem is to take a deep look into the picture, where we can see that the interception between the lines occurs right in x=7. thus, eliminating the first choice.

Next, we can see that the interception is somewhere far from the 'x' axis, hence 'y' variable can not be zero in this point.

Thus, we have our possible solution, without knowing anything else, the ordered pair (7, 0.5).

Remember, a system of equation has a solution when an interception occurs between its equations

dlqndpQAI:?s

Step-by-step explanation:

Konichiwa~! My name is Zalgo and I am here to help you out on this great day. Hmm, how do you define slope... Well, the slope or "gradient" of a line is a number that describes both the steepness and direction of the line itself. Now, slope is "a surface of which one end or side is at a higher level than another; a rising or falling surface".

I hope that this helps you! :P

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me Brainliest? I'd greatly appreciate it! Arigato~! X3)

Cost of items = $0.25 × 100

= $25.00

Answer: [tex]24\sqrt{3}[/tex]

Step-by-step explanation:

You need to remember that [tex]\sqrt[n]{a}[/tex] can be written in the following for:

[tex]a^{\frac{1}{n}}[/tex]

Knowing this and given the expression [tex](2*6)^{\frac{3}{2}}[/tex], you need to  multiply the numbers inside the parentheses:

 [tex](12)^{\frac{3}{2}}[/tex]

Rewrite it in this form:

[tex]=\sqrt{12^3}==\sqrt{1,728}[/tex]

Descompose 1,728 into its prime factors:

[tex]1,728=2*2*2*2*2*2*3*3*3=2^6*3^3[/tex]

Applying the Product of power property, which states that:

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

You can say that:

 [tex]=\sqrt{1,728}=\sqrt{2^6*3^2*3}[/tex]

Simplifying, you get:

[tex]=2^3*3\sqrt{3}=24\sqrt{3}[/tex]

Answer:

3,4

6,6

9,8

Step-by-step explanation:

Final answer:

The volume of the tilted solid is 1200 cubic feet.

Explanation:

The volume of the cube in the image is given as 1000 cubic feet. Let's call the height of the cube 'h'. The length and width of the cube are also 'h', so the volume of the cube is h x h x h = h³ = 1000. Solving for 'h', we find that h = 10 feet.

The tilted solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. So the length of each slanted side is h + 2 = 10 + 2 = 12 feet.

To find the volume of the tilted solid, we can use the formula for the volume of a rectangular prism: volume = base area x height. The base area is h x h = h², and the height is 12 feet. Therefore, the volume of the tilted solid is h² x 12 = 10² x 12 = 1200 cubic feet.

d = rt ( d = distance, r = rate (speed) and t = time)

14  = 7t

Divide both sides by 7:

t = 14/7

t = 2 hours

1 hour = 60 minutes.

2 hours x 60 = 120 minutes total.

Based on the distance Andrew went and the rate at which he went, Andrew's time in minutes was 120 minutes.

The distance formula is:

Distance = Rate x Time

Andrew's time is therefore:

14 = 7 x Time

Time = 14 / 7

= 2 hours

In minutes this is:

= 2 x 60 minutes per hour

= 120 minutes

In conclusion, Andrew covered that distance in 120 minutes.

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Answer: Second Option

5 to the power of 1 over 6

Step-by-step explanation:

The square root of the cubic root of 5 is written as follows

[tex]\sqrt[2]{\sqrt[3]{5}}[/tex]

Now use the following property of the roots

[tex]\sqrt[m]{\sqrt[n]{x}}=\sqrt[m*n]{x}[/tex]

In this case [tex]m = 2[/tex] and [tex]n=3[/tex] and [tex]x=5[/tex]

So we have that

[tex]\sqrt[2]{\sqrt[3]{5}}=\sqrt[2*3]{5}[/tex]

[tex]\sqrt[2*3]{5}=\sqrt[6]{5}[/tex]

Now use the following property

[tex]\sqrt[n]{x^h}=x^{\frac{h}{n}[/tex]

So we have that:

[tex]\sqrt[6]{5}=5^{\frac{1}{6}}[/tex]

The answer is the second option

5 to the power of 1 over 6

Answer:

5 to the power of 1 over 6

Step-by-step explanation:

Answer:

Its B. y^2 + 3y + 13x - 1

Step-by-step explanation:

It's easy add or subtract the like terms.

Hope my answer has helped you if not i'm sorry in advance.

Answer: [tex]y=-\frac{5}{2}x-1[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Write the equation of the given line in Slope-Intercept form by solving for "y":

[tex]5x + 2y = 12\\\\2y=-5x+12\\\\y=-\frac{5}{2}x+6[/tex]

You can observe that the slope of this line is:

[tex]m=-\frac{5}{2}[/tex]

Since the slopes of parallel lines are equal, then the slope of the other line is:

 [tex]m=-\frac{5}{2}[/tex]

Now, substitute the slope and the point (-2, 4) into  [tex]y=mx+b[/tex] and solve for "b":

[tex]4=-\frac{5}{2}(-2)+b\\\\4=\frac{10}{2}+b\\\\4-5=b\\\\b=-1[/tex]

Then the equation of the line parallel to the given line is:

[tex]y=-\frac{5}{2}x-1[/tex]

Answer:

Domain: All the real numbers

Range: All the real numbers

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable 'x'. That is to say, all the values that 'x' can take:

In this case, f(x)= 2x+1, the independent variable has no restrictions. Meaning that 'x' can take all the Real Values. In set notation: x∈ℝ.

The range of a function is the complete set of all possible resulting values of the dependent variable 'y'. In this case, given that the independent variable has no restrictions, the dependent variable 'y' can take any value. So, the range is: y ∈ ( −∞, ∞ ) - All the real numbers.

Answer: the graph decreases from left to right

Step-by-step explanation:

because the price over time is getting cheaper the graph will decrease from 0 onward

(pls mark me the brainliest)

Answer:

The graph decreases from left to right.

Step-by-step explanation:

Given,

The original cost of the straw, P = $ 150.00,

The rate of decreasing per year, r = 1.5% = 0.015

Thus, the price after x years,

[tex]C(x)=P(1-r)^x[/tex]

[tex]\implies C(x) = 150(1-0.015)^x=150(0.985)^x[/tex]

Which is an exponential function,

∵ An exponential function [tex]f(x) = ab^x[/tex] has,

Decay : if 0 < b < 1,  ( decreasing from left to right )

Growth : if b > 1,  ( increasing from left to right )

Since, 0.985 < 1

Thus, the graph is decreasing from left to right,

if x = 2,

C(2) = [tex]150(0.985)^2[/tex] = 145.53375 ≠ 147.75,

I.e. (2, 147.75) does not lie on the graph,

If x = 3,

C(3) = [tex]150(0.985)^3[/tex] = 143.35 ≠ 141.20

i.e. (3, 141.20) does not lie on the graph.

ANSWER

[tex] \frac{5a}{3} [/tex]

EXPLANATION

The given fractions are:

[tex] \frac{{a}^{3} + {a}^{2} b}{5a} \times \frac{25}{3b + 3a} [/tex]

We factor to obtain:

[tex]\frac{{a}^{2}(a + b)}{5a} \times \frac{25}{3(a + b)} [/tex]

We cancel the common factors to get:

[tex]\frac{{a}(1)}{1} \times \frac{5}{3(1)} [/tex]

We multiply the numerators and also multiply the denominators to get:

[tex] \frac{5a}{3} [/tex]

Therefore the two fractions simplifies to [tex] \frac{5a}{3} [/tex]

Answer:

Choice C)

[tex]\displaystyle \frac{g(7) - g(4)}{7 - 4} = \frac{5}{6}[/tex].

Step-by-step explanation:

The average rate of change of a function is:

[tex]\displaystyle \frac{\text{Change in Function Value}}{\text{Change in Independent Variable}}[/tex].

Note that [tex]\text{Change} = \text{Final Value} - \text{Initial Value}[/tex].

For this question,

As a result,

As a result,

The average rate of change in the value of [tex]g(x)[/tex] between [tex]x = 4[/tex] and [tex]x = 7[/tex] will be:

[tex]\displaystyle \frac{g(7)-g(4)}{7 - 4}[/tex].

Answer:

C

Step-by-step explanation:

Nice work using latex. I admire anyone who has skills with it.

It looks like this question can be grouped using to sets of brackets.

(4r^3 + 10r^2) : Pull out the common factor. 2r^2* (2r + 5)

The second set of brackets is a little bit tricker. Minus signs are not to be ignored.

(-10r - 25) : -5(2r + 5)

Now put both together,

2r^2(2r + 5) - 5(2r + 5)            

Notice that there is a common factor on either side of that isolated minus sign. The common factor is 2r + 5. Use the distributive property to pull it out.

(2r + 5)(2r^2 - 5)

It looks like C will be the answer.

4^(x- 3) = 18

ln[4^(x- 3)] = ln(18)

ln4(x - 3) = ln(18)

ln4x - ln4(3) = ln18

ln4x = ln18 + 3ln4

x = [ln18 + 3ln4]/ln4

x = 5.0849625007

x is approximately 5.085.

To solve the equation 4^x - 3 = 18, isolate the exponential term, take the logarithm of both sides, apply the power rule, and then divide to solve for x. The solution to the nearest thousandth is x ≈ 2.416.

To solve the equation 4^x - 3 = 18, first add 3 to both sides of the equation to isolate the exponential term:

4^x = 18 + 3

4^x = 21

Now, take the logarithm of both sides. You can use any logarithm base, but it's most common to use either the natural logarithm (ln) or the common logarithm (log base 10). For this example, we'll use the common logarithm.

log(4^x) = log(21)

Using the power rule for logarithms, which states that log(a^b) = b * log(a), you can write:

x * log(4) = log(21)

Now, divide both sides by log(4) to solve for x:

x = log(21) / log(4)

Use a calculator to find the value of x. Be sure to round your answer to the nearest thousandth, as the problem instructs. The answer comes out to:

x ≈ 2.416

This value of x solves the original equation when rounded to the nearest thousandth.

Answer:

monomial

Step-by-step explanation:

because it has one variable which in this case is b and one number in this case is 10

Answer:

MONOMIAL

Step-by-step explanation:

Answer: 30+18x C is correct

Step-by-step explanation: You distribute the 6 to both of the values in the parenthesis.

Answer:

C 30 + 18x

Step-by-step explanation:

6(5 + 3x)

Distribute the 6 to both terms inside the parentheses

6*5 +6*3x

30 +18x