solve for x: ㏒(x+3)+㏒x=1

Answer:

To find the prime factorization of 28, you should break the number down into its smallest prime factors:

28 = 2 × 2 × 7

So, the prime factors of 28 are: 2 and 7.

Answer:

1/2 or 50%

Step-by-step explanation:

Numbers on a 6 sided die:

1

2

3

4

5

6

Factors of 28 that are on a 6 sided die:

1

2

4

So you have a 3/6 = 1/2 = 50% chance of rolling a factor of 28

Answer:

5 sides

Step-by-step explanation:

the sum of the interior angle and exterior angle = 180°

sum the parts of the ratio, 2 + 3 = 5 parts , then

180° ÷ 5 = 36° ← value of 1 part of the ratio

exterior angle = 2 × 36° = 72°

the sum of the exterior angles of a polygon = 360°

since the polygon is regular then the exterior angles are congruent , so

number of sides = 360° ÷ 72° = 5

Answer:

Step-by-step explanation:

Answer:

1st one is 14 2nd one is 12 and the 3rd one is 30 your welcome

Answer:

43!

Step-by-step explanation:

i added it up

Answer:

coordinates of P are (2, 1).

Step-by-step explanation:

Let P be the point that partitions the line segment AB such that AP: PB = 2:1.(m:n) Then we can use the line ratio formula:

[tex]\bold{x = \frac{xB * m + xA*n}{m + n}}[/tex]

[tex]\bold{y = \frac{yB * m + yA*n}{m + n}}[/tex]

where (xA, yA) and (xB, yB) are the coordinates of A and B respectively, and m is the ratio of AP to PB, which is 2:1.

Substituting the given values, we get:

[tex]\bold{x = \frac{4*2+ (-2)*1}{2 + 1}}=2[/tex]

[tex]\bold{y = \frac{0 * 2 + 3*1}{2 + 1}= 1}[/tex]

Therefore, the coordinates of P are (2, 1).

Answer:

(2, 1)

Step-by-step explanation:

If the line segment AB is partitioned so that the ratio of AP to PB is 2 : 1, then point P is two-thirds of the way along AB.

Point A is located at (-2, 3) and point B is located at point (4, 0).

Since the difference between the x and y values of points A and B are multiples of 3, we can visually partition AB into 3 sections of equal length by placing points at (0, 2) and (2, 1).

Therefore, as point P is two-thirds of the way along AB, point P is located at (2, 1).

To prove this mathematically, we can use the Section Formula for Internal Division:

[tex]\boxed{\begin{minipage}{8.1 cm}\underline{Section Formula - Internal Division}\\\\\\$P(x,y)=\left(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n}\right)$\\\\\\where:\\\phantom{ww} $\bullet$ $\overline{AB}$ is the directed line segment.\\\phantom{ww} $\bullet$ $A(x_1, y_1)$ and $B(x_2, y_2)$ are the endpoints.\\\phantom{ww} $\bullet$ Point $P$ divides the segment in the ratio $m : n$.\\ \end{minipage}}[/tex]

Given values:

Substitute the values into the formula:

[tex]\begin{aligned}P(x,y)&=\left(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n}\right)\\\\&=\left(\dfrac{1 \cdot (-2)+2 \cdot 4}{2+1},\dfrac{1 \cdot 3+2 \cdot 0}{2+1}\right)\\\\&=\left(\dfrac{-2+8}{3},\dfrac{3+0}{3}\right)\\\\&=\left(\dfrac{6}{3},\dfrac{3}{3}\right)\\\\&=\left(2,1\right)\end{aligned}[/tex]

Hence proving the the location of point P on the coordinate plane is (2, 1).

Answer:

12

Step-by-step explanation:

[tex]18 = \frac{n}{3} + 14[/tex]

[tex]4 = \frac{n}{3} [/tex]

12 = n

The value of variable n in the equation is 54.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Therefore, let's solve the equation as follows:

We will have to find the variable n in the equation. A variable is a number represented with letter in an equation.

18 = n / 3 + 14

subtract 14 from both sides of the equation

18 = n / 3 + 14

18 - 14 = n / 3 + 14 - 14

18 = n / 3

cross multiply

n = 18 × 3

n = 54

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a. The concentration would be 0.5 mg/L at approximately t = 40 hours.

b. The table representing the concentration of the drug in the bloodstream, t hours after administration is shown below.

c. A reasonable domain for this function is t ≥ 0.

d. The patient should receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L at t = 1.25 hour.

e. The concentration of the oral drug and the concentration of the intravenous drug would keep increasing over the first 20 hours after it is administered.

In order to determine the time when the concentration would be 0.5 mg/L, we would substitute the value of the concentration and then solve the quadratic function for time (t);

c(t) = 20t/(t² + 4)

0.5 = 20t/(t² + 4)

0.5(t² + 4) = 20t

0.5t² + 2 = 20t

0.5t² + 2 - 20t = 0

t² + 4 - 40t = 0

t² - 40t + 4 = 0

Time, t = 38.8998 ≈ 40 hours.

Part b

In this context, we would complete the table of values at various time (t) as follows;

t        0    2      4     6       8           10        12        14     16        18      20

c(t)    0    5      4      3     2.35      1.92     1.62     1.4    1.23     1.10    1.00

Part c

Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes zero (0) for any value of time (t), we can reasonably infer and logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.

Part d and e

Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.

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a. The concentration would be 0.5 mg/L at approximately t = 40 hours.

b. The table representing the concentration of the drug in the bloodstream, t hours after administration is shown below.

c. A reasonable domain for this function is t ≥ 0.

d. The patient should receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L at t = 1.25 hour.

e. The concentration of the oral drug and the concentration of the intravenous drug would keep increasing over the first 20 hours after it is administered.

In order to determine the time when the concentration would be 0.5 mg/L, we would substitute the value of the concentration and then solve the quadratic function for time (t);

c(t) = 20t/(t² + 4)

0.5 = 20t/(t² + 4)

0.5(t² + 4) = 20t

0.5t² + 2 = 20t

0.5t² + 2 - 20t = 0

t² + 4 - 40t = 0

t² - 40t + 4 = 0

Time, t = 38.8998 ≈ 40 hours.

Part b

In this context, we would complete the table of values at various time (t) as follows;

t        0    2      4     6       8           10        12        14     16        18      20

c(t)    0    5      4      3     2.35      1.92     1.62     1.4    1.23     1.10    1.00

Part c

Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes zero (0) for any value of time (t), we can reasonably infer and logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.

Part d and e

Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.

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The equation is 3y / 3 = 2y / y. And the value of 'y' will be 2.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The equation is given as,

3y / 3 = 2y / y

Simplify the equation, then we have

3y / 3 = 2y / y

3y / 3 = 2

y = 2

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Answer:

28 cm

Step-by-step explanation:

Just add them all up bloke

Answer:

(-3.464,-2) on edge

Step-by-step explanation:

The senior class can purchase 27 jerseys for $430.

To get number of jerseys that can be purchased for $430, we need to solve for x in the equation.

C = 0.1x² + 2.4x + 25

0.1x²+2.4x+25 = 430

0.1x²+2.4x+25-430 = 0

0.1x²+2.4x-405 = 0

Using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a=0.1, b=2.4, and c=-405.

x = -2.4 ± [tex]\sqrt{(2.4^2 - 4(0.1)(-405))) / 2(0.1)}[/tex]

x = -2.4 ± [tex]\sqrt{838.80}[/tex]

x = -2.4 + 28.96 or -2.4 - 28.96

x = 26.56 or -31.36

x = (26.56, -31.36).

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Answer:

22 1/2

Step-by-step explanation:

Answer:

Sure, here are the steps on how to find a 95% confidence interval for the true proportion of adults who are dissatisfied with the quality of k-12 education:

Find the sample proportion. The sample proportion is the number of people in the sample who are dissatisfied with the quality of k-12 education divided by the total number of people in the sample. In this case, the sample proportion is 54%.

Find the standard error of the sample proportion. The standard error of the sample proportion is a measure of how much the sample proportion can vary from the true proportion. In this case, the standard error of the sample proportion is 1.66%.

Find the 95% confidence interval. The 95% confidence interval is a range of values that is likely to contain the true proportion. To find the 95% confidence interval, we add and subtract 1.96 standard errors from the sample proportion. In this case, the 95% confidence interval is (52.34%, 55.66%).

Interpret the 95% confidence interval. The 95% confidence interval means that we are 95% confident that the true proportion of adults who are dissatisfied with the quality of k-12 education is within the range of values (52.34%, 55.66%).

In other words, if we were to repeat this survey many times, 95% of the time the confidence interval would contain the true proportion of adults who are dissatisfied with the quality of k-12 education.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

B is the equation for a circle.  In a function every input (x value) has only one output (x value).  In a circle, the x values have more than one y value.

Helping in the name of Jesus.

Answer:

your answer is B

Step-by-step explanation:

have a nice day and can you mark me Brainliest.

The calculated value of the probability P(B|A) is  (d) 5/8

From the question, we have the following parameters that can be used in our computation:

Given that the digits are non-zero digits and no two digits are the same, then we have

P(A) = 4/9

Also, we have

P(B) = 5/8

The probabilty is then calculated as

P(B|A)  = P(B)

So, we have

P(B | A) = 5/8

Hence, the value of the probability P(B|A) is  (d) 5/8

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Answer:

5 sides

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° ( n - 2) ← n is the number of sides

given sum is 6 right angles = 6 × 90° = 540° , then

180° (n - 2) = 540° ( divide both sides by 180° )

n - 2 = 3 ( add 2 to both sides )

n = 5

that is the number of sides is 5

The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.

When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.

Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.

We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.

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The volume of the prism is 242 in³

First, we need to know the formula for the volume.

The formula for calculating the volume of a triangular prism is expressed as;

V = Bh

Such that the parameters are expressed as;

From the information given, we have that;

Line DF = 22 in

Line EG = 11 in

Where DF is the base length and EG is the height

Substitute the values

Volume = 22(11)

multiply the values

Volume = 242 in³

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(a) x -5 -3 0 2 4

   y 4 0 -6 -10 -14

(d) x -14 -10 -6 0 4

   y 4 2 0 -3 -5

These tables could be used to verify that the functions they represent are inverses of each other

To verify if two functions are inverses of each other, we need to check if the composition of the two functions gives the identity function.

In other words, if f and g are two functions, then we need to check if f(g(x)) = x and g(f(x)) = x for all x in their domains.

We can create two tables, one for f and one for g, and use them to compute the compositions.

If the compositions give the identity function, then the functions are inverses of each other.

Based on this, the two tables that could be used to verify that the functions are inverses of each other are:

(a) x -5 -3 0 2 4

    y  4 0 -6 -10 -14

(d) x -14 -10 -6 0 4

    y 4    2   0 -3 -5

We can use the values in these tables to compute the compositions f(g(x)) and g(f(x)) and check if they give the identity function.

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The coordinates of the midpoint K of AC are (2,2), the components of vector BC are (5,0), B' has coordinates (6,3), ABCB' is a parallelogram, and K is the midpoint of BB'.

1°) The points A(1,3), B(-2,1), and C(3,1) can be marked on the coordinate system as follows:

2°) To find the coordinates of the midpoint K of AC, we can use the midpoint formula:

K = ((x1 + x2)/2, (y1 + y2)/2) where (x1, y1) and (x2, y2) are the coordinates of A and C, respectively.

K = ((1 + 3)/2, (3 + 1)/2) = (2, 2)

3°) The components of the vector BC can be found by subtracting the components of B from the components of C:

BC = (3, 1) - (-2, 1) = (3 + 2, 1 - 1) = (5, 0)

4°) Let B' have coordinates (x,y). The components of AB' are given by subtracting the components of A from the components of B':

AB' = (x-1, y-3)

We want to find the coordinates of B' such that vector BC is equal to vector AB', or in other words, AB' = BC. This gives us the following system of equations:

x - 1 = 5

y - 3 = 0

Solving for x and y, we get:

x = 6

y = 3

Therefore, B' has coordinates (6, 3), and the components of AB' are (6-1, 3-3) = (5, 0), which is equal to the components of BC.

5°) Quadrilateral ABCB' is a parallelogram, since its opposite sides AB' and BC are equal and parallel. We have shown in part 4°) that AB' = BC, so the sides AB' and CB have the same length and are parallel. Therefore, ABCB' is a parallelogram.

To show that K is the midpoint of BB', we need to show that KB = KB' and that K is on the line segment BB'. Since B' has coordinates (6, 3), the components of vector BB' are (6-(-2), 3-1) = (8, 2).

Therefore, the midpoint of BB' has coordinates (-2+4, 1+1) = (2, 2), which is the same as the coordinates of K. Therefore, K is the midpoint of BB'.

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Answer:

(x - 3)² - 6

Step-by-step explanation:

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 6x

x² + 2(- 3)x + 9 - 9 + 3

= (x - 3)² - 9 + 3

= (x - 3)² - 6 ← in the form (x - a)² + b

It will take them 2.4 hours or 2 hours and 24 minutes to paint the wall working together.

We have,

We can use the formula:

1/Time taken to complete task = Work done / Time

Let's say the work to be done is to paint the whole wall. We can represent the work done by each brother as follows:

Eldest brother's work done in 1 hour = 1/3

Middle brother's work done in 1 hour = 1/4

The youngest brother's work done in 1 hour = 1/6

Now, we can add up their work done in 1 hour:

1/3 + 1/4 + 1/6 = 2/4

Simplifying, we get:

5/12

This means that together, the three brothers can complete 5/12 of the work in one hour.

To find out how long it would take them to complete the whole work

(paint the wall), we can use the same formula:

1/Time taken to complete task = Work done / Time

Let's say the time taken for the three brothers to complete the work is 't'. Then we can write:

1/t = 5/12

Solving for 't', we get:

t = 12/5 hours or 2.4 hours

Therefore,

It will take them 2.4 hours or 2 hours and 24 minutes to paint the wall working together.

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Answer: false

Step-by-step explanation: believe it

Answer:

option D

Step-by-step explanation:

The graph in option D function of y

Graph D

Step-by-step explanation:

The graph in option D is the function of y

The best answer is a. chronological, topical.

the organization type would change from topical to categorical.

In the original outline, the organization of the speech follows a chronological order, where the steps to prepare for a job interview are presented in a sequential manner. Each step builds upon the previous one, creating a logical flow.

If the four main points were changed to part-time job interviews, summer job interviews, college entrance interviews, and full-time job interviews, the organization would still follow a chronological order. Each main point would represent a different type of interview, and within each point, the subpoints would address the specific considerations for that type of interview.

Therefore, the organization type remains chronological, even if the specific content changes.

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Answer:1/25

Step-by-step explanation:

4 percent of 100 is 4.

4 percent of 50 is 4/2, 2.

50x1/25 = 50/25 = 2

let's firstly convert the mixed fraction to improper fraction and proceed from there.

[tex]\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div \left(\cfrac{3}{8}\div \cfrac{1}{2} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{8}\cdot \cfrac{2}{1} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{4} \right) \\\\\\ \cfrac{9}{4}\cdot \left(\cfrac{4}{3} \right)\implies \cfrac{9}{3}\cdot \cfrac{4}{4}\implies 3\cdot 1\implies \text{\LARGE 3}[/tex]

Value of Area of quadrilateral BCDE is,

A = 20 cm².

Now, From the given figure,

AD/DB=AE/EC=2

AD/AB-AD=AE/AC-AE =2

AB-AD/AD=AC-AE/AE=1/2

AB/AD = AC/AE = 1+1/2

=3/2

Therefore, ratio of areas of triangles ABC and ADE will be

ΔABC/ΔADE = (3/2)² = 9/4

If area of ΔABC =36 cm²,

36/ΔADE = 9/4

Then area of ΔADE =36×4/9 = 16 cm²

Now area of quadrilateral BCED = Area of ΔABC - Area of ΔADE

= 36 - 16

= 20 square cm

Therefore, area of quadrilateral BCDE is 20 cm².

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