What is the value of a in the equation 5a-10b=45 , when b=3 ?

Answer:

-3+4

Step-by-step explanation:

if it's put in parentheses it needs to be done first

The distance traveled by a car and the amount of gas used are directly proportional. The more distance covered, the more gas is consumed. This relationship can be quantified to make estimates for a specific car's fuel needs over given distances.

The relationship between the distance traveled by a car and the amount of gas in the car is directly proportional, that is, the more distance the car travels, the more gas it consumes. This correlation can be quantified for a specific car and then used to estimate gas consumption for given distances based on the car's average speed.

For example, let's say that a 2014 Lamborghini Aventador Roadster travels from Philadelphia to Atlanta, covering a distance of about 1250 km, and uses 213 L of gasoline. This gives us a standard ratio of gas consumption against the distance. We could say that for every 1250 km traveled, the car would need about 213 L of gas. This is a simplified model as there are other variables at play such as traffic conditions, velocity, etc.

Gasoline powers the engine which provides the force needed to move and maintain the car's speed. As the path traced (distance) increases, more fuel is consumed. This relationship of distance traveled and fuel consumed can be defined as a directly proportional relationship.

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[tex]\bf -3~~,~~\stackrel{-3+4}{1}~~,~~\stackrel{1+4}{5}~~,~~\stackrel{5+4}{9}...\qquad \stackrel{\textit{common difference}}{d=4} \\\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common}\\ \qquad \textit{difference}\\ \cline{1-1} d=4\\ a_1=-3 \end{cases}\implies a_n=-3+(n-1)4 \\\\\\ a_n=-3+4n-4\implies a_n=4n-7[/tex]

Answer:

A n = 4n - 7

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The small triangle on the left, the larger triangle on the right, and the overall triangle all have the same angles, and therefore are similar.

Writing a proportion:

4 / 6 = 6 / a

a = 9

Answer:

C. 9 (third option)

Step-by-step explanation:

A proportion sets two ratios equal to each other.

For example of proportion: ⇒ [tex]x*6=y[/tex]

Another example of proportion: ⇒ [tex]\frac{y}{x}=\frac{6\div 2}{2\div2}=\frac{3}{1}=3[/tex]

6/4=4/a

=9 is the correct answer.

Answer:

65 million in 2016

Step-by-step explanation:

Hope this helps you! :)

Answer:

Step-by-step explanation:

2 - 3y + 3t = -x - 2yz

I don't think you can actually solve the equation. You are not given any information about the letters (variables).

Answer:

$9.00

Step-by-step explanation:

4x + 12 = 48         - First, subtract 12 from each side of the equation.

4x = 36                 - Then, divide each side by 4 to get x by itself.

x = 9                     - After dividing by 4, we are left with x = 9, so 1 ticket costs

                              $9.00

For this case we have the following equation:

[tex]4x + 12 = 48[/tex]

Where the variable "x" represents the cost of a performance ticket.

Clear "x" of the equation to know the cost of a ticket.

Subtracting 12 on both sides of the equation:

[tex]4x = 48-12\\4x = 36[/tex]

Dividing between 4 on both sides of the equation:

[tex]x = \frac {36} {4}\\x = 9[/tex]

So, the cost of a ticket is $ 9.00

Answer:

Option C

Answer:

13 inches

Step-by-step explanation:

Your formula for a right circular cylinder's volume is

[tex]V=\pi r^{2} h[/tex]

All you have to do is plug in your variables. Since we know that the volume is 2028pi and the height is 12 inches, we can set up the equation as follows:

[tex]2028\pi =\pi r^{2} 12[/tex]

Next, we simplify. First, we have to divide both sides by pi.

[tex]2028=12r^{2}[/tex]

Once we've divided both sides by pi, we can divide both sides by 12.

[tex]169=r^2[/tex]

Now, to find the radius, we have to find the square root of both sides. This is because the square root of r squared is r.

[tex]13=r[/tex]

Your radius is 13 inches.

In the context of Mathematics, it involves utilizing the volume formula of a right circular cylinder (V = πr²h) and rearranging it to solve for radius. Then, we substitute given values (volume and height of the cylinder) into the rearranged formula to calculate the value of the radius.

The subject of this question is Mathematics. Specifically, it involves using the formula for calculating the volume of a right circular cylinder to determine the radius when given the volume and height. The formula for the volume, V, of a right circular cylinder in terms of its radius, r, and its height, h, is V = πr²h.

To solve this problem, we need to rearrange the formula to solve for r which turns out to be r = √(V/(πh)). Substituting the given details, r becomes √(2028/(3.142*12)), which will give us the value of the radius. This involves use of algebra and geometry concepts.

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Answer:

Option 2) When the x-value is 0, the y-value is 1.

Step-by-step explanation:

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Remember that in a direct variation

For x=0, the value of y is equal to zero too

therefore

The graph is not a direct variation , because

When the x-value is 0, the y-value is 1.

The function f(x) = 4.34 is a constant function, which means it does not change regardless of the value of 'x'. Thus, none of the options provided (A: Decreasing linear, B: Exponential growth, C: Increasing linear, D: Exponential decay) correctly describe the function.

The function represented by f(x) = 4.34 is a constant function.

This is because no matter what value of 'x' you put into the function, the output is always going to be 4.34.

Looking at the options provided:

A. Decreasing linear - This indicates that the function should decrease as 'x' increases, which is not the case here.

B. Exponential growth - This would mean the function increases at an increasing rate, which also does not apply to a constant value.

C. Increasing linear - This suggests that the function's value should increase as 'x' increases, which is not true for a constant function.

D. Exponential decay - This implies the function's values decrease at a decaying rate, which, again, does not match a constant value.

Therefore, none of the options accurately describe f(x) = 4.34.

The function is neither increasing nor decreasing and it is not an exponential function.

[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{3x+2}{3x-5}[/tex]

Answer:

[tex](\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}[/tex] for [tex]x\neq \dfrac{5}{3}[/tex].

Step-by-step explanation:

The given functions are

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

[tex]g(x)=3x-5[/tex]

We need to find the function [tex](\dfrac{f}{g})(x)[/tex].

Using division property of functions.

[tex](\dfrac{f}{g})(x)=\dfrac{f(x)}{g(x)}[/tex]

Substitute the values of functions.

[tex](\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}[/tex]

This function is defined for all values of x, except a value for which 3x-5=0.

[tex]3x-5=0\Rightarrow x=\dfrac{5}{3}[/tex]

Therefore, the required function is [tex](\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}[/tex] for [tex]x\neq \dfrac{5}{3}[/tex].

Answer:

x = 5/2

Step-by-step explanation:

log4(x^2+5x)-log8(x^3)=1/log3(4)

log(x^2 + 5 x) / log(4) - log(x^3) / log(8) = log(3) / log(4)

log(x (x+5))/log(4) - log(x^3) / log(8) = log(3) / log(4)

(3 log(x (x+5)) - 2 log(x^3)) / log(64) = log(3) / log(4)

3 log(x (x+5)) - 2 log(x^3) = 3 log(3)

log((3 x)/(x+5))=0

x=5/2

Answer:

5/2

Step-by-step explanation:

So first of all 1/log_3(4) can be written as log_4(3)...

So everything is base 4 except the log_8(x^3)...

We can play with this to get it so that the base is 4.

Let y=log_8(x^3) then 8^y=x^3

Rewrite 8 as 4^(3/2) so we have

4^(3/2 *y)=x^3

Now rewriting in log form gives: log_4(x^3)=3/2*y

Then solving that for y gives 2/3*log_4(x^3) or log_4(x^2)... let's put it back into the equation:

log_4(x^2+5x)-log_4(x^2)=log_4(3)

log_4((x^2+5x)/x^2)=log_4(3)

Set insides equal:

(x^2+5x)/x^2=3

Cross multiply:

x^2+5x=3x^2

Subtract 3x^2 on both sides:

-2x^2+5x=0

Factor

-x(2x-5)=0

So solutions are 0 and 5/2.  

We have to verify these...

0 isn't going to work because we can't do log of 0

it makes x^2+5x 0 and x^3 0

The only solution is 5/2.

Answer:

x=0, x=-6

Step-by-step explanation:

Answer: -33

Step-by-step explanation:

Final answer:

To find the quotient of x + 4x² divided by 2x, divide each term inside the numerator by the denominator. Simplify the expression by dividing each term by 2x.Simplifying further, we get: 1/2 + 2x

Explanation:

To find the quotient of x + 4x² divided by 2x, we divide each term inside the numerator by the denominator.

This gives us: (x + 4x²) ÷ 2x

Next, we can simplify the expression by dividing each term by 2x:

x ÷ 2x + 4x² ÷ 2x

Simplifying further, we get: 1/2 + 2x

Answer:

m=p*V

Step-by-step explanation:

we have

p=m/V

Solve for m

That means-----> isolate the variable m

Multiply both sides by V

p*V=(m/V)*V

Simplify

p*V=m

rewrite

m=p*V

Answer:

[tex]m=\rho*V[/tex]

Step-by-step explanation:

Note that the formula for density depends on two variables

The mass m

The volume V

[tex]\rho=\frac{m}{V}[/tex]

If we have the density [tex]\rho[/tex] and the volume V and we want to find the mass m then we solve the equation for the variable m

[tex]\rho=\frac{m}{V}[/tex]

Multiply both sides of the equality by the volume V

[tex]\frac{m}{V}*V=\rho*V[/tex]

[tex]m=\rho*V[/tex]

The formula is:

[tex]m=\rho*V[/tex]

Answer:

If two chords intersect each other in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

x² = 12

x = 2√3

The formula x = r0 is used to calculate the length of a circular arc 'x', given the radius 'r' and an angle '0' in radians. For example, for a radius of 0.15m and an angle of 75.4 radians, we find x = 11m.

The problem revolves around the relationship between the radius r and an angle in radians 0, given by the formula x = r0. This applies to questions involving the measurement of a circular arc, where 'x' is the length of the arc. An example calculation would be, if we had a radius of 0.15m and an angle of 75.4 radians, we would multiply these to find 'x', giving us x = 11m. Similarly, for a radius of 0.0450m and an angle of 220 radians, x = 9.90m. Notice that the unit of 'x' will always be in the same unit as the radius (in this case, meters).

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Answer:

y=-2x+14

Step-by-step explanation:

If we are looking for a line parallel to 2x+y=5.

Then we are looking for an equation with the same slope as the equation 2x+y=5.

To obtain the slope of equaiton 2x+y=5 I will put it in slope-intercept form.

Luckily there is only one step which is to subtract 2x on both sides.

y=-2x+5

The slope of this line is -2

The slope of parallel line will also be -2.

So we know our equation is in the form y=-2x+b

To find b we will just use the point (x,y)=(5,4) we know is on the line.

Plug in and solve for b.

4=-2(5)+b

4=-10+b

14=b

So the equation that is parallel to 2x+y=5 and goes through (5,4) is y=-2x+14

Answer:

The standard deviation of the data set is 5.7 to the nearest tenth

Step-by-step explanation:

* Lets explain how to find the standard deviation

# Step 1: find the mean of the data set

∵ The mean = the sum of the data ÷ the number of the data

∵ The data set is 3 , 17 , 18 , 15 , 12 , 21 , 9

∵ Their sum = 3 + 17 + 18 + 15 + 12 + 21 + 9 = 95

∵ They are seven

∴ The mean = 95 ÷ 7 = 13.6

# Step 2: subtract the mean from each data and square the answer

∴ (3 - 13.6)² = 112.36

∴ (17 - 13.6)² = 11.56

∴ (18 - 13.6)² = 19.36

∴ (15 - 13.6)² = 1.96

∴ (12 - 13.6)² = 2.56

∴ (21 - 13.6)² = 54.76

∴ (9 - 13.6)² = 21.16

# Step 3: find the mean of these squared difference

∵ The mean = the sum of the data ÷ the number of the data

∵ The sum = 112.36 + 11.56 + 19.36 + 1.96 + 2.56 + 54.76 + 21.16 = 223.72

∴ The mean = 223.72 ÷ 7 = 31.96

# Step 4: the standard deviation is the square root of this mean

∴ The standard deviation = √(31.96) = 5.6533 ≅ 5.7

* The standard deviation of the data set is 5.7 to the nearest tenth

Answer:

11-3i-4-5i

=11-4-3i-5i

=7-8i

Follow below steps:

The difference of the complex numbers (11-3i) and (4+5i) is computed by subtracting the real and imaginary parts separately. The real parts are 11 and 4, and their difference is 11 - 4 = 7. The imaginary parts are -3i and +5i, and their difference is -3i - 5i = -8i. Therefore, the difference of the two complex numbers is 7 - 8i.

Answer:

tan(x) = 0

Step-by-step explanation:

We know that tan = sin /cos

tan (x) = sin(x)/ cos (x)

Substituting what we know, sin (x) =0 and cos(x) =1

          = 0/1

         =0

Answer:

Its tan(x) = 0 on Edge 2020.

Step-by-step explanation:

On jah.

Answer:I dontvknow

Step-by-step explanation:

Answer:

169

Step-by-step explanation:

Answer:

step 4 it not overdrawn any more it postive 46 not negtive

Step-by-step explanation:

Answer:

Step 4 : the account is overdrawn by $46

Step-by-step explanation:

Please see that when an account is in negative figure , we call it overdrawn. but when it is in positive figure we called is in credit.

Here we see from the calculation that the final balance available in the account of teller is $46, hence the account is having positive balance . hence it is not overdrawn.

So the mistake is in last step.

Answer:

1. A

2. C

Step-by-step explanation:

H in the parent function equations are always negative and k is always positive.

Ex:

[tex]f(x)=2^(x-h)+k[/tex]

So that means when we're adding 4 to the exponent, we're actually subtracting, therefore moving the graph 4 units to the left.

Then, since k is positive, and we're adding 8, we move the graph 8 units up.

Answer:

tree diagram

Step-by-step explanation:

A tree diagram is an organizing tool used to determine the sample space of a compound event.

A compound event is an event that has more than one possible outcomes

[tex]A(7,0)\Longrightarrow\boxed{A'(-7,0)}[/tex]

Hope this helps.

r3t40

Answer:

(- 7, 0)

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

Hence

(7, 0 ) → (- 7, 0 )

Answer:

Step-by-step explanation:

Answer:

= 5.099 i

Step-by-step explanation:

The problem tells us to find the square root of -36 +10

√(-36 + 10)

= √(-26)

Which is an imaginary number

Lets remember that, √(-1) = i

= i*√(26)

= 5.099 i

Please see attached images for more information

For this case we must find the value of the variable "x" of the following expression:

[tex]2 (3x-1) \geq4x-6[/tex]

We apply distributive property to the terms within parentheses: [tex]6x-2 \geq4x-6[/tex]

We subtract 4x on both sides:

[tex]6x-4x-2 \geq-6\\2x-2 \geq-6[/tex]

We add 2 to both sides:

[tex]2x \geq-6 + 2\\2x \geq-4[/tex]

We divide between 2 on both sides:

[tex]x \geq \frac {-4} {2}\\x \geq-2[/tex]

Answer:

[tex]x \geq-2[/tex]

Answer: [tex]x\geq -2[/tex]

Step-by-step explanation:

Given the inequality [tex]2(3x - 1) \geq 4x -6[/tex] you need to solve for "x".

Apply Distributive property on the left side of the equation:

 [tex]6x - 2 \geq 4x -6[/tex]

Now add 2 to both sides:

 [tex]6x - 2+(2) \geq 4x -6+(2)[/tex]

 [tex]6x \geq 4x -4[/tex]

The next step is to subtrac [tex]4x[/tex] from both sides:

 [tex]6x-(4x) \geq 4x -4-(4x)[/tex]

 [tex]2x \geq -4[/tex]

And finally, divide both sides by 2:

[tex]\frac{2x}{2}\geq  \frac{-4}{2}\\\\x\geq -2[/tex]

Answer:

1.56666

Step-by-step explanation:

3.5/2.25=1.555

Answer:

as a decimal its 0.125 as a fraction its 1 5/9

Step-by-step explanation:

All you have to is first change both into a mixed number so 7/2 divided by 9/4 then do keep change flip (KCF) so 7/2 * 4/9 which equals 28/18 and it simply to 1 5/9.