which of the following shows the graphical representation of the solution for the one-variable linear equation 2x-1=3​

Answer:

Following are the statements:

a. logₐb - logₐc = logₐb/logₐc

False.

b. logₐB - logₐc = logₐ(b/c)

True.

c. log₄(5x+16) = log₄5x+log₄16 = 2 +log₄5x

False.

d.  log₄(5x*16) = log₄5x+log₄16 = 2 +log₄5x

True.

e. logₐ(3x)₂ = 2 logₐ3 + logₐx

False.

f. logₐ(3x)₂ = 2 logₐ3 + 2 logₐx

Answer:

a. False

b. True

c. False

d. True

e. False

f. True

Step-by-step explanation:

By properties of logarithms:

a. False: ㏒ₐb-㏒ₐc ≠ (㏒ₐb / ㏒ₐc) does not exists that property

b. True: (㏒ₐb)-(㏒ₐc) = ㏒ₐ(b/c)  Logarithm of a Quotient

c. False: Does not exists the property:  ㏒ₐ(c+b) = ㏒ₐc + ㏒ₐb

so

㏒₄(5x+16) ≠ ㏒₄5x + ㏒₄16 but,  ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x  

because ㏒₄16 = 2.

d. True:  Logarithm of a Product: ㏒ₐ(c×b) = ㏒ₐc + ㏒ₐb

so

㏒₄(16×5x) = ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x

e. False: Logarithm of a Power: ㏒ₐ(c×b)ⁿ = n ㏒ₐ(c×b) = n (㏒ₐc + ㏒ₐb) = n ㏒ₐc + n ㏒ₐb

so

㏒ₐ(3x)² ≠ 2 ㏒ₐ3 + ㏒ₐx

f. Correct use of property in point e.

Answer: It depends on you if it seems easier for you, you should try both and see which one works better for you.

Answer:

Geometry nation helps when you need to go more in depth and need practice problems. While the textbook might give you good definitions it may seem more monotone.

The given compound inequality doesn't have any solutions because it creates a contradictory situation where x needs to be both greater than 9 and less than 0 at the same time, which is not possible.

The given compound inequality is −33 > −3x − 6 ≥ −6. To find the equivalent form, let's solve it step by step.

First, add 6 to all sides, resulting in -27 > -3x > 0.

Then, divide by -3. Remember that when dividing by a negative number, the direction of the inequality changes. So, we get 9 < x < 0.

This indicates that x is greater than 9 but x also needs to be less than 0. This, however, is a contradictory situation because a number cannot be both greater than 9 and less than 0 at the same time. So, there are no solutions for this inequality.

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An equivalent form of the compound inequality −33 > −3x − 6 ≥ −6 is x > 9.5 or x ≤ 0.

To find an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6, we can break it down into two separate inequalities:

−33 > −3x − 6

−3x − 6 ≥ −6

To simplify the first inequality, we can add 6 to both sides: −27 > −3x. Then, we can divide both sides by -3, remembering to flip the inequality sign since we are dividing by a negative number: x > 9.5.

To simplify the second inequality, we can add 6 to both sides: −3x ≥ 0. Then, we can divide both sides by -3, remembering to flip the inequality sign: x ≤ 0.

Therefore, an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6 is x > 9.5 or x ≤ 0.

Answer: 1.587 ounces of sodium chloride

Step-by-step explanation:

We know that 1 ounce is equivalent to 28.35 gr.

So we use this as a conversion factor to find the equivalent amount of sodium chloride in ounces.

If we need 45 grams of sodium chloride then this equals to:

[tex]45\ g* \frac{1\ ounces}{28.35\ gr} = 1.587\ ounces[/tex]

Finally you need 1.587 ounces of sodium chloride

Answer:

1.587 ounces

Step-by-step explanation:

We need to measure out 45 grams of sodium chloride using the bottle mentioning units of measure in units.

We are to find the number of ounces of sodium chloride that we will need.

We know that:

1 ounce = 28.35 grams

So using the ratio method to find the number of ounces of Sodium Chloride needed.

[tex]\frac{1 ounce}{x} =\frac{28.35 g}{45 g}[/tex]

[tex]= \frac{45}{28.35} = [/tex] 1.587 ounces

Answer:

(5e)^4

Step-by-step explanation:

5e•5e•5e•5e

There are 4 sets of 5e being multiplied together

(5e)^4

Answer:

thanks for the points

Step-by-step explanation:

ANSWER

A.

[tex] - \frac{2}{3} [/tex]

EXPLANATION

The given equation is

[tex]y = - \frac{2}{3}x + 3[/tex]

This equation is already in the form:

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

This is called the slope-intercept form.

The slope is

[tex]m = - \frac{2}{3} [/tex]

and the y-intercept is 3.

The correct answer is A.

In a situation where the line is not given in the slope intercept form, then you must rewrite in this form before comparing.

b. state taxes are the most likely to pay for universities and police.

Answer:

B

Step-by-step explanation:

Answer:

multiplication property of equality

Step-by-step explanation:

Given:

[tex]-\frac{1}{2}p = 4[/tex]

The rule is that whatever is done on one side of the equation is done on the other side of the equation two.

In order to isolate p, both sides of equation will be multiplied by -2.

This is called the multiplication property of equality ..

Answer:

angle COD

Step-by-step explanation: vertical angles share the same vertacy and are opposite of each other. They are created by two intersecting lines.

Let

[tex]P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}[/tex]

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

[tex]P(1):\ 1 = \dfrac{1\cdot 2}{2}=1[/tex]

So, the base case is ok. Now, we need to assume [tex]P(n)[/tex] and prove [tex]P(n+1)[/tex].

[tex]P(n+1)[/tex] states that

[tex]P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}[/tex]

Since we're assuming [tex]P(n)[/tex], we can substitute the sum of the first n terms with their expression:

[tex]\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}[/tex]

Which terminates the proof, since we showed that

[tex]P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}[/tex]

as required

Answer: it can’t be converted to a fraction

Step-by-step explanation:

Answer:

Monthly Expense = $270.83

Step-by-step explanation:

The semi-annual premium is paid twice a year so,

Automobile insurance premium for whole year = 650*2

= $1300

Monthly premium will be paid 12 times a year so,

Health insurance premium for whole year = 125*12 = $1500

Annual premium is only paid once a year.

So adding all the premiums will give us the total premiums for whole year.

Total amount of premium for a year = $1300+$1500+$450

= $3250

The premium amount for whole year is $3250. To find the monthly expense, we will divide it by 12.

So monthly expense is:

= 3250/12

= $270.83 ..

To find the monthly expense, calculate the total annual premium for each insurance and divide by 12. The monthly expense is $187.5.

To find the monthly expense, we need to calculate the total annual premium for each insurance and divide it by 12 (since there are 12 months in a year).

For automobile insurance, the semiannual premium is $650, so the annual premium is $650 * 2 = $1300.

The monthly premium for health insurance is $125.

For life insurance, the annual premium is $450.

Now, let's calculate the total monthly expense: ($1300 + $125 + $450) / 12 = $187.5.

So, the monthly expense is $187.5.

Answer:

- [tex]\sqrt{11}[/tex]

Step-by-step explanation:

Radical roots occur in conjugate pairs

Thus if [tex]\sqrt{11}[/tex] is a root then

- [tex]\sqrt{11}[/tex] is also a root

The other root of the given polynomial is  [tex]-\sqrt{11}[/tex].

"Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero."

Given roots of a polynomial f(x) are - 4, 2, 1, [tex]\sqrt{11}[/tex].

We know, for the root of an equation, radical roots are always in pair.

If a polynomial has two roots, one is [tex]\sqrt{x}[/tex] then the other one must be [tex]-\sqrt{x}[/tex].

Similarly, the root of the given polynomial is [tex]-\sqrt{11}[/tex].

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Answer:Quadrilateral TRAP has an area that is one-fourth the area of quadrilateral HELP.

Step-by-step explanation: Because you rearrange the squares and it is 1/4

Answer:

Quadrilateral TRAP has an area that is one-fourth the area of quadrilateral HELP.

Step-by-step explanation:

Answer:

33 feet.

Step-by-step explanation:

Perimeter of a rectangle = 2*width + 2*length.

So here we have:

2*3 + 2*L = 72  where L = the length.

2L = 72 - 6 = 66

L = 33 feet.

Craig has 72 feet or 24 yards of material, with a stated width of 3 feet (1 yard). Subtracting the width of two sides from the total perimeter (24 yards), we find that the length of Craig's fence is 22 yards.

Craig has 72 feet of material to build a fence around a rectangular flower bed, with the width required to be 3 feet. To calculate the length of the fence in yards, we first need to find out the total perimeter in yards. Since Craig is using all 72 feet of material, this is the perimeter of the fence. We know that 1 yard is equal to 3 feet, so we convert 72 feet to yards.

To do this division, 72 feet ÷ 3 feet per yard = 24 yards. So, Craig has 24 yards of fencing material in total.

If one side (width) of the flower bed is 3 feet, which is equivalent to 1 yard, we must subtract the width of the two opposite sides from the total perimeter to find the total length of the fence. 24 yards total perimeter - 2 yards total width = 22 yards total length. Therefore, the length of Craig’s fence in yards is 22 yards.

Answer:

Option 1 and 3 are correct.

Step-by-step explanation:

The corresponding angles are the matching angles when two lines are crossed by another line which is called traversal.

Looking in the figure following are corresponding angles

8 and 6

4 and 2

7 and 5

3 and 1

Now, looking at the options

Option 1  5 and 7

and Option 3  6 and 8 are only given corresponding angles.

So Option 1 and 3 are correct.

Answer:

∠EGF = 65°

Step-by-step explanation:

Since EF = EG the triangle is isosceles and the base angles are equal, that is

∠EGF = ∠GEF

∠EGF = [tex]\frac{180-50}{2}[/tex] = [tex]\frac{130}{2}[/tex] = 65°

Answer:

[tex]\large\boxed{D.\ 2160\pi\ units^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a cylinder:}\\\\V=\pi r^2H\\\\r-radius\\\H-height\\\\\text{We have}\ r=12\ \text{and}\ H=15.\ \text{Substitute:}\\\\V=\pi(12^2)(15)=\pi(144)(15)=2160\pi[/tex]

The volume of the cylinder is [tex]\( 2160 \pi \)[/tex] units³.

To find the volume of the cylinder, we'll use the formula for the volume of a cylinder, which is given by:

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

Where:

- V is the volume of the cylinder,

- r is the radius of the cylinder, and

- h is the height of the cylinder.

Given:

- Height h = 15 units

- Radius r = 12 units

We'll substitute these values into the formula:

[tex]\[ V = \pi \times (12)^2 \times 15 \][/tex]

[tex]\[ V = \pi \times 144 \times 15 \][/tex]

[tex]\[ V = 2160 \pi \][/tex]

So, the volume of the cylinder is [tex]\( 2160 \pi \)[/tex] cubic units.

The correct answer is option D: [tex]\( 2160 \pi \)[/tex] units³.

Answer:

answer is (1,0)

Step-by-step explanation:

Let the coordinates of D be (a,b).The diagonals of a parallelogram bisect each other.The midpoint of AC should be the same as the midpoint of BD.Compare corresponding coordinatesThis implies that:, , , Therefore the coordinates of D are: (1,0)

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Answer: The quotient of 5 & 7 is approximately 0.714

Step-by-step explanation:

First you divide 5 by 7, teachers typically want a simple form so instead of putting the whole answer we can give them a short answer and say it's approximately.714! Hope this helped out!!

Answer:

3

Step-by-step explanation:

There are 13 dots, so we need to find the value of the median, or middle dot. The middle dot is the 7th dot which has the value of 3. The median of the set must be 3

The answer is A. The new weight room has an area of 480 ft.

Since the area of the gym is 4x^2, they are adding 480 ft^2, which is the area of the new weight room.

Hope this helps!

Answer:

A. The new weight room has an area of 480ft^2

Step-by-step explanation:

Area of gym = 4x^2

Area of weight room = 480

Area of gym + weight room = 4x^2 + 480

480 is a constant because its value cannot and will not change whereas x is an unknown

Answer:

Option C.

Step-by-step explanation:

We know that

f(t) = 1.5t + 50

represents the approximate population of trout in Sky Lake

And

g(t) = 0.1t^2 - 4t + 70

represents the approximate population of trout in Lake Cyan

The total trout population in the area is described as

f(t) + g(t)

f(t) + g(t) =  [1.5t + 50] + [0.1t^2 - 4t + 70]

f(t) + g(t) =  [1.5t + 50+ 0.1t^2 - 4t + 70]

f(t) + g(t) =  [0.1t^2 -2.5t + 120]

f(t) + g(t) =  0.1t^2 -2.5t + 120

Option C.

Answer:

Step-by-step explanation:

The variance is the square of the standard deviation.  Here, the variance is 17^2, or 289.

Answer:

[tex]\large\boxed{3x-4y=-48}[/tex]

Step-by-step explanation:

The standard form of an equation of a line

[tex]Ax+By=C[/tex]

We have the eqution in the point-slope form:

[tex]y-4=\dfrac{3}{4}(x+8)[/tex]

Convert it to the standard form:

[tex]y-4=\dfrac{3}{4}(x+8)[/tex]           multiply both sides by 4

[tex]4y-16=3(x+8)[/tex]           use the distributive property

[tex]4y-16=3x+32[/tex]          add 16 to both sides

[tex]4y=3x+48[/tex]           subtract 3x from both sides

[tex]-3x+4y=48[/tex]           change the signs

[tex]3x-4y=-48[/tex]

Answer:

n=40

Step-by-step explanation:

25/n=5/8

25/5=5

n/5=8

n=40

Answer:

N= 40.

Hope that helps!

Answer:

The Graph Should Be Going Down Pretty Sharp and Intersects the Y-Axis at 1

Step-by-step explanation:

There isn't a visual graph so I can't directly pick which one, but I can describe it to you.

Answer: There should be a point at (6, -1), (0, 1), (4, 1)

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

− 5

y-intercept:  

( 0,1)

x   y

0  1

1 −4

Hope this helps!

Please mark brainiest!:)

Answer:

1st graph in edgnuity

Step-by-step explanation:

Answer:

1st graph

Step-by-step explanation:

i got it correct

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

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

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

m - slope

b - y-intercept

The formula of a slope:

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

We have the points A(-3, 0) and B(-6, 5). Substitute:

[tex]m=\dfrac{5-0}{-6-(-3)}=\dfrac{5}{-3}=-\dfrac{5}{3}[/tex]

The line passes through the origin, therefore the y-intercept is equal to 0.

Therefore we have the equation:

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

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

[tex]y=-\dfrac{5}{3}x[/tex]         multiply both sides by 3

[tex]3y=-5x[/tex]                add 5x to both sides

[tex]5x+3y=0[/tex]

The equation of the line parallel to AB passing through the origin is 5x - 3y = 0.

The equation of the line that passes through the origin and is parallel to AB is 5x - 3y = 0.

To find the equation of a line parallel to AB passing through the origin, we first need to find the slope of AB, which is (5 - 0) / (-6 + 3) = 5 / -3 = -5/3.

Since the line passing through the origin and parallel to AB has the same slope, its equation will be of the form y = mx. Substituting the point (0, 0) into y = -5/3x gives us y = -5/3x, which simplifies to 5x - 3y = 0.