2/3 (x - 7) = -2 what does x equal

(2/3 is a fraction not dividing)

Answer:

See explanation

Step-by-step explanation:

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest,

P = principal,

r = rate (as decimal),

t = time

In your case,

[tex]P=\$1,539\\ \\r=0.01[/tex]

If [tex]t_1=5[/tex] years, then

[tex]I_1=1,539\cdot 0.01\cdot 5=76.95[/tex] and the whole sum is [tex]\$1,539+\$76.95=\$1,615.95[/tex]

If [tex]t_2=10[/tex] years, then

[tex]I_2=1,539\cdot 0.01\cdot 10=153.9[/tex] and the whole sum is [tex]\$1,539+\$153.9=\$1,692.9[/tex]

If [tex]t_3=15[/tex] years, then

[tex]I_3=1,539\cdot 0.01\cdot 15=230.85[/tex] and the whole sum is [tex]\$1,539+\$230.85=\$1,769.85[/tex]

The solution is x < 3.

Solution:

The given expression is 3x + 4 < 13.

To solve the given inequality.

3x + 4 < 13

Subtract 4 tiles on both sides of the inequality.

⇒ 3x + 4 – 4 < 13 – 4

⇒ 3x < 9

Divide by 3 tiles on both sides of the inequality.

⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]

⇒ x < 3

Hence the solution is x < 3.

Final answer:

To solve the inequality using algebra tiles, represent 3x+4 with tiles on one side and 13 units on the other, remove 4 units from both sides to get 3x < 9 and then divide the remaining 9 units into 3 groups to find x < 3.

Explanation:

To solve the inequality 3x+4<13 using algebra tiles, we follow these steps:

Start by representing the inequality with algebra tiles. Place 3 x-tiles (each representing 'x') and 4 unit tiles (each representing '1') on one side of a mat to model the expression 3x+4.

On the other side, place 13 unit tiles to represent the number 13.

To isolate the variable x, we need to remove the same number of unit tiles from each side. Remove 4 unit tiles from each side of the mat, which corresponds to Subtracting 4 from both sides of the inequality.

After removal, the inequality on the mat now shows 3x tiles on one side and 9 unit tiles on the other, representing the inequality 3x < 9.

Lastly, to find the value of one x-tile, divide the remaining unit tiles into 3 equal groups. Since there are 9 units left, each group will consist of 3 unit tiles, indicating that each x-tile is less than 3. This gives us the final inequality x < 3.

From this process, we've determined that for the original inequality 3x+4<13, the solution is x<3.

Answer:

4 units

Step-by-step explanation:

In triangle DEF, DK is the angle bisector of angle EDF.

Angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.

Hence,

[tex]\dfrac{DE}{DF}=\dfrac{EK}{KF}[/tex]

Thus,

[tex]\dfrac{DE}{10}=\dfrac{2}{5}\\ \\5DE=2\cdot 10\\ \\5DE=20\\ \\DE=4[/tex]

Answer:

0.3 units

Step-by-step explanation:

The ratio of the length of the arc to the circumference of the circle is proportional to the ratio of the central angle to the sum of angle in a circle.

[tex]\frac{l}{6}=\frac{20}{360}[/tex]

This implies that:

[tex]l=\frac{20}{360}*6[/tex]

This simplifies to: [tex]l=\frac{20}{60}[/tex]

[tex]l=\frac{1}{3}=0.3 units[/tex]

Since the circumference of this circle is 6 units, the length of the arc formed is equal to 0.33 units

Given the following data:

Circumference = 6 units.

Central angle = 20°

Mathematically, if you want to determine the length of the arc formed by a circle, you will divide the angle subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle as follows:

20/360 × 6 = 0.33 units.

Read more on circumference here: brainly.com/question/14478195

Answer:

 n (A'  U  B )  = 75

Step-by-step explanation:

Here, given :  n(U)=120, n(A)=45, and n(B)=50

As we know:

n (A ' U B)  =  n(A) − n (A∩B)   ... (1)

Here, n(A) = 45

So, n( A')  = n(U) - n(A)  = 120 - 45  = 75

⇒ n(A')  = 75

Now, as given A and B are disjoint sets.

⇒   n (A ∩ B)   = Ф

So, (A'  U  B )  = A'

So, n (A'  U  B )  =n( A') = 75

⇒  n (A'  U  B )  = 75

Answer:

$47

Step-by-step explanation:

Andy's initial amount was $28.

The question is on subtraction. It is meant to understand your capacity on worded form of subtraction.

After Andy cashed the cheque, his amoussou rose from $28 to $75.

Therefore, to know the amount on the cheque we subtract the initial amount from the total amount.

$75 - $28 = $47

Answer:2

Step-by-step explanation:

Answer:

Laura and Erica will both have made 16 blankets in one more day.

Step-by-step explanation:

i) Erica has made 10 blankets already.

ii) Erica can make 6 blankets more per day

iii) Laura has completed 6 blankets already

iv) Laura can complete 10 more blankets per day.

v) Let x be the number of days to the point when they will have completed the same number of blankets

vi) Therefore the number of blankets that Erica makes till x days is = to the number of blankets that Laura makes till x days

vi) therefore 10 + 6x  = 6 + 10x    ⇒   4x  = 4    ⇒ x = 1 day

vii) Therefore Laura and Erica will both have made 16 blankets in one more day.

Answer:

[tex]\displaystyle x=\frac{5}{2}, x=\frac{2}{5}[/tex]

Step-by-step explanation:

Quadratic Equations

The quadratic equation has the following general form

[tex]ax^2+bx+c=0[/tex]

It can be solved by several methods, including the well-known quadratic formula

[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

The question requires us to find a number that added with its reciprocal results 2 9/10. If x is the required number

[tex]\displaystyle x+\frac{1}{x}=2\ \frac{9}{10}=\frac{29}{10}[/tex]

Operating

[tex]\displaystyle \frac{x^2+1}{x}=\frac{29}{10}[/tex]

Rearranging

[tex]10(x^2+1)=29x[/tex]

[tex]10x^2-29x+10=0[/tex]

Comparing with the general quadratic equation, we have

[tex]a=10,\ b=-29,\ c=10[/tex]

Using the formula

[tex]\displaystyle x=\frac{29\pm \sqrt{(-29)^2-4(10)(10)}}{2(10)}[/tex]

[tex]\displaystyle x=\frac{29\pm \sqrt{441}}{20}=\frac{29\pm 21}{20}[/tex]

It gives us two possible solutions

[tex]\displaystyle \boxed{x=\frac{5}{2}, x=\frac{2}{5}}[/tex]

Both are valid solutions since

[tex]\displaystyle \frac{5}{2}+\frac{2}{5}=\frac{29}{10}[/tex]

Answer:

15. ∠ABE = 50°

16. ∠EBD = 10n - 19

Step-by-step explanation:

If [tex]$ \overline{\textbf{BE}} $[/tex] bisects ∠ABD then we have ∠ABE = ∠DBE

So, we will have: (6x + 2)° = (8x - 14)°

⇒ 6x + 2 = 8x - 14

⇒ 8x - 6x = 14 + 2

⇒ 2x =16

⇒ x = 8

∴ ∠ABE = 6(8) + 2

= 48 + 2

= 50°

∴∠ABE = 50°

16. If [tex]$ \overline{\textbf{BE}} $[/tex] bisects ∠ABD then ∠ABE + ∠EBD = ∠ABD

⇒(12n - 8) + ∠EBD = (22n - 11)

⇒ ∠EBD = 22n - 11 - 12n + 8

⇒ ∠EBD = 10n - 3

Hence, the answer.

Answer:

The number of persons surveyed leaving a movie theater is 150.

Step-by-step explanation:

Science fiction 18% or 0.18 = 27 persons surveyed.

Total of persons surveyed = 2,700/18

Total of persons surveyed = 150

The number of persons surveyed leaving a movie theater is 150.

Answer:

150 people were surveyed.

Answer:

(2.5, -.25)

Step-by-step explanation:

I'm not positive that I know exactly what they want on this one....but since you specifically asked me to look at your other question, I tried.

See pic.

Answer:

8 and 5

Step-by-step explanation:

The sum of 8 and 5 implies

8 + 5 = 13

The difference between 8 and 5 implies:

8 - 5 = 3

Therefore, the sum of two numbers that gives 13 and their difference being 3 are 8 and 5.

Plot the vertices A'(-12, 9), B'(9, 3), and C'(6, -3) on the coordinate plane. Label them as A', B', and C', respectively.

To determine the coordinates of the dilated triangle A'B'C', we can follow these steps:

1. Find the coordinates of the original triangle's vertices: A(-4, 3), B(3, 3), and C(2, -1).

2. Dilate each vertex from the origin by a scale factor of 3. This means we will multiply the x and y coordinates of each vertex by 3.

- For vertex A: Multiply -4 by 3 to get -12 and multiply 3 by 3 to get 9. Therefore, the coordinates of A' are (-12, 9).
- For vertex B: Multiply 3 by 3 to get 9. The y-coordinate remains the same at 3. Therefore, the coordinates of B' are (9, 3).
- For vertex C: Multiply 2 by 3 to get 6 and multiply -1 by 3 to get -3. Therefore, the coordinates of C' are (6, -3).

3. Plot the vertices A'(-12, 9), B'(9, 3), and C'(6, -3) on the coordinate plane. Label them as A', B', and C', respectively.

Note: The original triangle ABC remains unchanged on the coordinate plane.

By following these steps, you will have successfully determined the coordinates of the dilated triangle A'B'C' and plotted it on the coordinate plane.

c = cost of food/med for cats

d = cost of food/med for dog

y = total cost/spent

What you know:

y = 6c + d              [has 6 cats and 1 dog]  

c = 2/3d - 5        [cost for cat is 5 less than 2/3 cost for dog]

y = $195

y = 6c + d    

Substitute/plug in what you know, plug in (2/3d - 5) for c and 195 for y

195 = 6(2/3d - 5) + d        Distribute/multiply 6 into (2/3d - 5)

195 = 4d - 30 + d        Combine like terms

195 = 5d - 30      Add 30 on both sides of the equation

225 = 5d        Divide 5 on both sides

$45 = d            

Answer:

21

Step-by-step explanation:

You know the length of JK 12

you also know the length of GF 2.5*12=30

HL is a mid segment because it cuts both legs it intersects in half.

Using the rule saying that the mid segment is half the bases added up we can figure out that HL = (12+30)/2 = 21

Answer:

21

Step-by-step explanation:

Find attached the solution

Answer: -425

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

An inscribed angle of circle T has a measure of 36°.

The cantral angle subtended on the same arc as this inscribed angle has the measure twice greater than inscribed angle, so the measure of the central angle is

[tex]36^{\circ}\cdot 2=72^{\circ}[/tex]

The measure of the intercepted arc (at which angles are subtended) is the same as the measure of the central angle, so correct option is option A

Answer:

a is the answer

Step-by-step explanation:

Answer:

r = 7

Step-by-step explanation:

Given

r + 15  = 4r - 6 ( subtract 4r from both sides )

- 3r + 15 = - 6 ( subtract 15 from both sides )

- 3r = - 21 ( divide both sides by - 3 )

r = 7

The area of the rectangle is 300 square inches, calculated by multiplying the length (20 inches) by the width (15 inches).

To find the area of the rectangle, we can use the formula for the area of a rectangle, which is [tex]\( \text{length} \times \text{width} \).[/tex] However, we need to find the length of the rectangle first.

We are given that the width of the rectangle is 15 inches. Let's denote the length of the rectangle as [tex]\( l \).[/tex]

We know that the diagonal of a rectangle forms a right triangle with the length and width of the rectangle. Therefore, we can use the Pythagorean theorem to find the length of the rectangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides (the length and the width).

So, we have:

[tex]\[ l^2 + 15^2 = 25^2 \][/tex]

Solving for[tex]\( l \):\[ l^2 = 25^2 - 15^2 \]\[ l^2 = 625 - 225 \]\[ l^2 = 400 \][/tex]

Taking the square root of both sides:

[tex]\[ l = \sqrt{400} \]\[ l = 20 \][/tex]

Now that we have found the length of the rectangle to be 20 inches, we can calculate the area:

[tex]\[ \text{Area} = \text{length} \times \text{width} \]\[ \text{Area} = 20 \times 15 \]\[ \text{Area} = 300 \, \text{square inches} \][/tex]

So, the area of the rectangle is 300 square inches.

Answer:

8.33

Step-by-step explanation:

Answer: 7+3=4+6

Step-by-step explanation: 7+3=10 and so does 4+6

Answer:

2 weeks and 5 days

Step-by-step explanation:

Final answer:

Raphael ran for a total of 5 weeks, calculated by dividing the total number of days he ran (35 days) by the number of days in a week (7 days).

Explanation:

Raphael runs for 35 days in a row, and we need to calculate how many weeks he runs. A week consists of 7 days. To find out the number of weeks Raphael ran, we divided the total number of run days by the number of days in a week.

Number of weeks = Total run days / Days in a week = 35 / 7 = 5

Therefore, Raphael ran for 5 weeks, illustrating the duration of his consistent running routine in terms of weeks. This computation provides a clear understanding of the duration of Raphael's running streak in a familiar time frame, aiding in tracking and planning his exercise regimen.

Answer:

The domain of the function (cd)(x) will be all real values of x except x = 2.

Step-by-step explanation:

The two functions are [tex]c(x) = \frac{5}{x - 2}[/tex] and d(x) = x + 3

So, (cd)(x) = [tex](\frac{5}{x - 2})(x + 3) = \frac{5(x + 3)}{x - 2}[/tex]

Then, for x = 2 the function (cd)(x) will be undefined as zero in the denominator will make the function (cd)(x) undefined.

Therefore, the domain of the function (cd)(x) will be all real values of x except x = 2. (Answer)

Answer:

the answer is b on edg2020

Step-by-step explanation:

Answer:

Proportionality

Step-by-step explanation:

Answer:

  x = y^2 – 7

Step-by-step explanation:

The first step in finding the inverse of y = f(x) can be to write the equation x = f(y). The equation shown above is such an equation.

Answer:

[tex]x= y^2-7[/tex]

Step-by-step explanation:

We have been given an equation [tex]y=x^2-7[/tex]. We are asked to determine that which equation can be simplified to find the inverse of our given equation.

We know that to find inverse of an equation, the x and y-values are interchanged.

Let us interchange x and y values for our given equation.

[tex]x= y^2-7[/tex]

Therefore, the equation [tex]x= y^2-7[/tex] can be simplified to find the inverse of our given equation.

After 28 years, there will be approximately $48,505.29 in the account.

To calculate the amount of money that will be in the account after 28 years with an annual interest rate of 8.25%, we can use the formula for compound interest:

[tex]\[ A = P \times (1 + r)^n \][/tex]

Where:

- A  is the amount of money accumulated after  n years, including interest.

- P  is the principal amount (the initial amount of money), which is $6700 in this case.

- r  is the annual interest rate (in decimal form), which is 8.25% or 0.0825.

- n is the number of years, which is 28 in this case.

Plugging in the values into the formula:

[tex]\[ A = 6700 \times (1 + 0.0825)^{28} \][/tex]

Calculating the value:

[tex]\[ A = 6700 \times (1.0825)^{28} \][/tex]

[tex]\[ A \approx 6700 \times 7.2417 \][/tex]

[tex]\[ A \approx 48,505.29 \][/tex]

For 57 to be a prime number, it would have been required that 57 has only two divisors, i.e., itself and 1. However, 57 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 57 = 3 x 19, where 3 and 19 are both prime numbers.

Answer: No

Step-by-step explanation: For 57 to be a prime number, it would have been required that 57 has only 2 divisors, ie itself and 1. How ever 57 is a semiprime because it is the product of a two non- necessarily distinct prime numbers. inderd, 57= 3×19, where 3 and 19 are prime numbers.