What is the value of x in the attached diagram?

Answer:

Step-by-step explanation:

Use the point-slope formula.

y - y_1 = m(x - x_1)    you have :  x_1 =1  and  y_1 =2

m the slope   m= -2 (same slope for the line : 2x+y-1=0 because this lines are parallel and you can write y=-2x-1

an equation for this line is : y-2 = -2(x-1)

Answer:

dependent

Step-by-step explanation:

This question assumes that we're working with a standard full deck of cards.  There are 52 unique cards in such a deck.

If David picks a card at random and doesn't put it back, then the number of unique cards left in his deck is 51.

These two events are dependent because the withdrawal of 1 card changes the probability of drawing any other of these 51 cards

The length of the side of a cube with a surface area of 390 sq cm is approximately 8.06 cm.

The student's question relates to finding the length of a side of the cube, given the total surface area of the cube. In the case of a cube, all sides are equal in length. Furthermore, a cube has six equal sides. Therefore, to find the length of one side, we can use the formula of the surface area of a cube, which is 6 * side² = Total Surface Area. For our problem, side² = 390 / 6 = 65. Hence, the length of the side would be the square root of 65, which is approximately 8.06 cm.

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The best description of the length of the side of the cube is Option C. between 8 and 9.

To determine the length of the side of a cube given its surface area, we first recall the formula for the surface area (SA) of a cube:

SA = 6s²

where s is the length of one side. We are given a surface area of 390 cm². We substitute this value into the formula and solve for s:

390 = 6s²

s² = 390 / 6

s² = 65

s = √65

To find the exact value of √65, we use a calculator:

√65 ≈ 8.06

Therefore, the length of the side of the cube is approximately 8.06 cm, which falls between 8 and 9. Hence, the correct answer is:

Option C. between 8 and 9

Complete question:

If the surface area of a cube is 390 cm^2. Which best describes the length of the side of the cube?

A. less than 7

B. between 7 and 8

C. between 8 and 9

D. greater than 9

Answer: 0.6 meters cubed.

Step-by-step explanation:

To find the answer to this, first find the volume of the cube.

Volume is equal to the side cubed. In this case, 1 cubed is 1, so the area of the cube is 1 meter cubed.

The depth of the water is 0.4 meters, so the water makes a shape of a rectangular prism, where the length and width are 1 meter, and the height is 0.4 meters.

The volume of a rectangular prism is l*w*h, so the volume of this rectangular prism is 0.4 * 1 * 1, or 0.4 meters cubed.

As such, the volume of the air in the tank is 1 - 0.4, or 0.6 meters cubed.

Answer:

0.6 meters CUBED

Step-by-step explanation:

hope it helps

Answer:

(2x+5)(7x^2+5)

Answer:

x=-2

Step-by-step explanation:

2+3x=-20-8x

22=-11x

x=-2

Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

[tex]2 + 3x = - 4(5 + 2x) \\ 2 + 3x = - 20 - 8x \\ 3x + 8x = - 20 - 2 \\ 11x = - 22 \\ \frac{11x}{11} = \frac{-22}{11} \\ x =- 2[/tex]

Answer:

30% off

Step-by-step explanation:

63 is 70% of 90 which means that 30 percent of the price is off.

Please mark me brainliest. I need it. Hope this helps

Answer:

12

Step-by-step explanation:

12x12=144

Answer:

-3k+10

Step-by-step explanation:

We want to simplify the expression: [tex]\large{-3k-(-8)+2}[/tex]

Step 1:

Open the bracket taking note of the fact that the product of same sign is positive.

[tex]\large{-3k-(-8)+2}=-3k+8+2[/tex]

Step 2:

Simplify

[tex]-3k+8+2=-3k+10[/tex]

Therefore, an equivalent expression to -3k-(-8)+2 is -3k+10.

Answer:

8

Step-by-step explanation:

Ok here's the solution. I'm typing this to get 20+ characters:

2^3 = 2 x 2 x 2

= 8

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{z = 2^3}[/tex]

[tex]\mathsf{2^3 = z}[/tex]

[tex]\mathsf{2^3}[/tex]

[tex]\mathsf{= 2 \times 2 \times 2}[/tex]

[tex]\mathsf{= 4 \times2}[/tex]

[tex]\mathsf{= \bf 8}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Therefore, your answer is: z = \bf 8 (Option A)}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

Answer:

[tex]-18\cdot h^{2} + 85\cdot h - 18[/tex]

Step-by-step explanation:

The polynomial in standard form is:

[tex](-2\cdot h + 9) \cdot (9\cdot h - 2)[/tex]

[tex]-18\cdot h^{2} + 81\cdot h +4 \cdot h - 18[/tex]

[tex]-18\cdot h^{2} + 85\cdot h - 18[/tex]

50% is one half.

One half of 10 miles would be 5 miles.

You can either divide 10 by 2 or multiply 19 by the decimal for 50% which is 0.5 , they will both get you the answer of 5 miles.

Answer:

1) 38

2) 19

3) 1134

Step-by-step explanation:

Answer:

18 meters

Step-by-step explanation:

12 + 6 = 8

Lila travels an absolute altitude difference of 18 meters from home to school, considering she travels from 12 meters below sea level to 6 meters above sea level.

The question presents a situation where Lila travels from an altitude of 12 meters below sea level to an altitude of 6 meters above sea level. Here, instead of adding these two numbers, we consider the absolute values of these heights. Thus, when Lila travels from her home to school, she first climbs up 12 meters to reach sea level and then another 6 meters to reach her school. So, in total, Lila travels 18 meters in altitude when going from home to school.

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Answer:

Answer: False

Step-by-step explanation:

Answer:

False :)

Step-by-step explanation:

It should look like the photo I've attached.

The points that represent the data are of the form (age, height), and the graph can be seen below.

Here we have the table:

Age (years) Height (cm)

11                   140

12                  145

12                   151

13                   160

14                   155

14                    161

15                    170

15                    179

16                    175

16                    179

Then the points that represent the data are of the form (age, height).

So we have 10 points:

(11, 140), (12, 145), (12, 151), (13, 160), (14, 155), (14, 161), (15, 170), (15, 179), (16, 175), (16, 179).

The graph of these 10 points can be seen below:

If you want to learn more about graphing:

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Answer:

9 /16 cups

Step-by-step explanation:

Take the number of cups and divide by the number of servings

2 1/4 ÷ 4

Change to an improper fraction

9/4 ÷4

Copy dot flip

9/4 * 1/4

9 /16

Answer: 9/16

Step-by-step explanation: First, take the number of cups and divide by the number of servings. So we have 2 and 1/4 ÷ 4.

Now, rewrite 2 and 1/4 as the improper fraction 9/4 an 4 as 4/1.

So we have 9/4 ÷ 4/1.

Now, dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction. So 9/4 ÷ 4/1 can be rewritten as 9/4 × 1/4.

Now, multiply across the numerators and denominators to get 9/16.

So there are 9/16 cup of raisins in each serving.

Answer:

s = 13 - x

t = [tex]\frac{18+x}{2}[/tex]

Step-by-step explanation:

To start out with:

s = 18

t = 18

Sue gives Tony x sweets

s = 18 - x

t = 18 + x

Sue then eats 5 of her sweets

s =  18 - x - 5 = 13 - x

t  = 18 + x

Tony eats half of his sweets

s = 13 - x

t = [tex]\frac{18+x}{2}[/tex]

(Possible constraint that [tex]x\mod 2 = 0[/tex])

When Sue gives Tony x sweets, and then eats 5, she has 13 - x sweets left. Tony, having received x from Sue and then eats half of his total, has 9 + 0.5x sweets.

The question begins with Sue and Tony each having 18 sweets. First, Sue gives Tony 'x' sweets which results in Sue having 18 - x sweets and Tony having 18 + x sweets. Sue then eats 5 sweets resulting in her having 18 - x - 5 = 13 - x sweets. Tony then eats half of his sweets, resulting in him having (18 + x) / 2 = 9 + 0.5x sweets. So, the expressions summarizing the number of sweets Sue and Tony have now are 13 - x for Sue and 9 + 0.5x for Tony respectively.

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Answer:

14

Step-by-step explanation:

In mathematics, sum can be defined as the result or answer we get on adding two or more numbers or terms.

(-4)-10=14

Answer:

False

Step-by-step explanation:

Cost of 1 can = $18.95

Cost of x cans = 18.95x

Cost of paintbrushes = $55

Total cost = 18.95x+55

Let y be the total cost

y=18.95x+55

So, Equation that can be used : y=18.95x+55

We are given that Martina can use the equation x = 18.95y + 55 to find the total cost, y, of her order.

So, It is False

Answer:

Outside of probability, Pascal's Triangle is also used for: Algebra, where coefficient of polynomials can be used to find the numbers in Pascal's triangle.  Pascal's Triangle is an arithmetical triangle you can use for some neat things in mathematics.

The entries in Pascal's triangle are actually the number of combinations of N take n where N is the row number starting with N = 0 for the top row and n is the nth number in the row counting from left to right where the n = 0 number is the first number.

The mathematical formula for the number of combinations without repetition is N!/(n!(N-n)!).

Step-by-step explanation:

To construct Pascal's triangle, start with a 1. Then, in the next row, write a 1 and 1. It's good to have spacing between the numbers. In the third row, we have 1 and 1 on the outside slopes. The 2 comes from adding the two numbers above and adjacent. Thus, we are adding the number on the left, 1, with the number on the right, 1, to get 1 + 1 = 2.

In the next row, the 3 comes from adding the 1 and the 2. This particular Pascal's triangle stopped at 1 5 10 10 5 1, but we could have continued indefinitely.

Answer:

96

Step-by-step explanation:

Multiply 8 and 12.

Answer:

$120.1355

Step-by-step explanation:

We can model this as an exponencial function:

P = Po * (1+r)^t

Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.

For this case, we have that Po = 900, r = -25% = -0.25 and t = 7, so we can find the value of P

P = 900 * (1 - 0.25)^7 = $120.1355

The price after 7 years will be $120.1355.

To calculate the value of Dan's computer after 7 years of 25% annual depreciation, we use the exponential decay formula. The approximate value of the computer after 7 years is $120.14.

To calculate the approximate value of Dan's computer after 7 years with a depreciation rate of 25% per year, we can use the formula for exponential decay:

[tex]V = P(1 - r)^t[/tex]

Plugging in the values, we get:

[tex]V = $900(1 - 0.25)^7[/tex]

[tex]V = $900(0.75)^7[/tex]

V = $900 * 0.1334838867

Therefore, the approximate value of the computer after 7 years is:

V = $120.14

Dan can expect the computer to be worth approximately $120.14 after 7 years.

Perimeter is the sum of the outside dimensions:

4 + 5 + 1 + 5 + 9 = 24 inches.

Answer:

Tenth term=14

Step-by-step explanation:

The nth term of a sequence=2n-6

Find the 10th term

If 2n-6= nth term

Then,

Tenth term=2(10)-6

=20-6

=14

Therefore,

Tenth term =14

Answer:

  x = ±√3

Step-by-step explanation:

In order to avoid extraneous answers, I like to work these by transforming to an expression equal to zero.

  [tex]\dfrac{x^2}{2x-6}=\dfrac{9}{6x-18}\\\\\dfrac{x^2}{2(x-3)}-\dfrac{9}{6(x-3)}=0\\\\\dfrac{x^2-3}{2(x-3)}=0\\\\x^2=3\\\\\boxed{x=\pm\sqrt{3}}[/tex]

__

If you do this the usual way, by clearing fractions to start, you will get an extraneous solution of x=3.

Answer:

2

Step-by-step explanation:

f'(x) is an odd function (symmetrical about the origin), therefore f(x) is an even function (symmetrical about the y-axis).  So f(x) = f(-x).

Since f(-4) = 2, f(4) = 2.

We can also show this using integrals:

f(-4) = ∫₀⁻⁴ f'(x) dx + C

2 = ½ (-4)(-2) + C

2 = 4 + C

C = -2

f(4) = ∫₀⁻⁴ f'(x) dx − 2

f(4) = ½ (4)(2) − 2

f(4) = 4 − 2

f(4) = 2

Final answer:

After 30 years of monthly $250 contributions to a 401(k) with a 2% annual growth rate, the interest earned on the account is approximately $65,961.73.

Explanation:

To calculate the amount of interest earned in the 401(k) after 30 years with a 2% annual growth rate, we first need to figure out the future value of the account. We use the formula for the future value of an annuity, as the investments are made at regular intervals (monthly).

The formula is: FV = P *rac{(1 + r)^n - 1}{r}

Where:

FV is the future value of the annuity.

P is the payment amount per period.

r is the interest rate per period.

n is the total number of payments.

Since contributions are made monthly, the annual interest rate (2% or 0.02) is divided by 12 to get the monthly rate, and the total number of contributions is multiplied by 12 to account for monthly contributions over 30 years.

For an investment of $250 per month at a monthly rate of 0.02/12, over 360 months (30 years), we get:

FV = $250*  rac{(1 + 0.02/12)^{360} - 1}{0.02/12}

Now we calculate the future value:

FV ≈ $250 *  rac{(1 + 0.0016667)^{360} - 1}{0.0016667}

FV ≈ $250 *  rac{(1.0016667)^{360} - 1}{0.0016667}

FV ≈ $250 *  rac{2.0398873 - 1}{0.0016667}

FV ≈ $250 * 623.8469386

FV ≈ $155,961.73

The total amount invested over 30 years is $250 * 12 *30 = $90,000.

The interest earned is therefore:

Interest = FV - Total amount invested

Interest ≈ $155,961.73 - $90,000

Interest ≈ $65,961.73

So the interest earned on the account after 30 years is approximately $65,961.73.

Answer:

triangle LMN is similar to triangle RST

Step-by-step explanation: