Student A is 5 years old. Student B is three times as old as Student A. When Student A is 20, how old will Student B be?

The mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg

Let's denote the mass of one art book by "a" and the mass of one biology book by "b".

From the given information, we have two equations:

6a + 4b = 7.2 (equation 1)

2a + 3b = 3.4 (equation 2)

We can solve for "a" and "b" by using any method of solving linear equations, such as substitution or elimination.

Here, we'll use elimination method. Multiplying equation 2 by 3 and subtracting it from equation 1 multiplied by 2, we get:

12a + 8b - (6a + 9b) = 14.4 - 10.2

6a - b = 4.2 (equation 3)

Multiplying equation 2 by 2, we get:

4a + 6b = 6.8 (equation 4)

Multiplying equation 3 by 6, we get:

36a - 6b = 25.2 (equation 5)

Adding equations 4 and 5, we get:

40a = 32

a = 0.8 kg

Substituting this value of "a" in equation 2, we get:

2(0.8) + 3b = 3.4

1.6 + 3b = 3.4

3b = 1.8

b = 0.6 kg

Therefore, the mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg.

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Answer:

✔️2a + 6 + 7a

✔️2a + 7a + 6

✔️9a + 6

Step-by-step explanation:

Given:

2(a + 3) + 7a

Required:

3 equations equivalent to the given expression

Solution:

2(a + 3) + 7a = 2a + 6 + 7a = 2a + 7a + 6

= 9a + 6

From the above, we can pick 3 expressions that are equivalent to 2(a + 3) + 7a. They are:

✔️2a + 6 + 7a

✔️2a + 7a + 6

✔️9a + 6

Answer:

Volume = (24x⁵ + 78x⁴ - 147x³ - 624x² - 360x)

Step-by-step explanation:

Container given in the picture is in the shape of a cuboid.

And volume of a cuboid is measured by the expression,

Volume of a cuboid = Length × width × height

Now substitute the measure of the container's dimensions given in the picture

Volume = (4x² + 3x)(x²- 8)(6x + 15)

             = [(4x² + 3x)(x²- 8)](6x + 15)

             = [4x²(x² - 8) + 3x(x² - 8)](6x + 15)

             = (4x⁴ - 32x² + 3x³ - 24x)(6x + 15)

             = (4x⁴ + 3x³ - 32x² - 24x)(6x + 15)

             = 6x(4x⁴ + 3x³ - 32x² - 24x) + 15(4x⁴ + 3x³ - 32x² - 24x)

             = 24x⁵+ 18x⁴ - 192x³ - 144x² + 60x⁴ + 45x³ - 480x² - 360x

             = 24x⁵ + 78x⁴ - 147x³ - 624x² - 360x

Answer:

V = 24x⁵+78x⁴-147x³-624x²-360x

Step-by-step explanation:

Answer: 2 pages

Step-by-step explanation:

Answer:

2.55555555555555555555555555556

Answer:

1. 5 cups of yellow paint.

2. 15 cups of yellow paint to 3 cups of blue paint.

3. 1:5 is the proportional relationship.

4. 5 is the constant of proportionality, it represents the . of yellow cups of paint.

Step-by-step explanation:

sorry if 4 is wrong

Answer:

Sure, I'd be happy to help you with that!

To calculate Dan's earnings with simple interest, we can use the following formula:

I = P * r * t

where:

I = interest earned

P = principal amount (initial investment)

r = interest rate (as a decimal)

t = time period (in years)

We know that Dan invests £2500 and receives 5% simple interest per year, so:

P = £2500

r = 0.05

t = 2 years

Plugging these values into the formula, we get:

I = £2500 * 0.05 * 2

I = £250

This means that Dan will earn £250 in interest over the 2-year period.

To calculate Dan's total earnings, we simply add the interest earned to the initial investment:

Total earnings = £2500 + £250

Total earnings = £2750

Therefore, Dan will have £2750 in his bank account after 2 years.

Answer:

Its green

Step-by-step explanation:

In here wehn they don't say or it means that the line is going to be attached

Answer:

a) 293 units

b) 5795p

Step-by-step explanation:

First, determine how many units used

Take the new reading and subtract the old reading

6538 - 6245

293 units

The first 200 is at 22p

200 * 22 p =4400p

293 -200 = 93 units at the remaining unit price.

93 * 15 p =1395p

Add the two totals together

4400p + 1395p =5795p

Answer:

\( 379 \: {units}^{2} \)

Step-by-step explanation:

Area of the composite figure

= Area of rectangle with dimensions 17 & 11 units + Area of trapezoid with length of parallel sides 11 and 21 units and height (29 - 17 = 12) 12 units.

\( = 17 \times 11 + \frac{1}{2} (11 + 21) \times 12 \\ \\ = 187 + 32 \times 6 \\ \\ = 187 + 192 \\ \\ = 379 \: {units}^{2} \)

Answer:

1st add 2x+25 then 3x+1 then 5x-2 what answer you get thats the answer of this question......

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Answer:

they ate 7/12 of the pizza I think but sry if I am wrong

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

\(x=4+5i\\\\x=4-5i\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}\)

Given quadratic equation:

\(x^2-8x+41=0\)

Solve using the quadratic formula.

Therefore:

Substitute the values of a, b and c into the quadratic formula and solve for x.

\(\implies x=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(1)(41)}}{2(1)}\)

\(\implies x=\dfrac{8 \pm \sqrt{64-164}}{2}\)

\(\implies x=\dfrac{8 \pm \sqrt{-100}}{2}\)

\(\implies x=\dfrac{8 \pm \sqrt{100 \cdot -1}}{2}\)

\(\implies x=\dfrac{8 \pm \sqrt{100} \sqrt{-1}}{2}\)

\(\implies x=\dfrac{8 \pm10i}{2}\)

\(\implies x=4 \pm5i\)

Therefore, the solutions to the given equation are:

Answer:

-2 ≤ x ≤ 5

Step-by-step explanation:

x is greater than or equal to -2 and less than or equal to 5

⇒ x ≥ -2 and x ≤ 5

⇒ -2 ≤ x ≤ 5

From eq(1) and (2)

Combine them

\(\\ \rm\hookrightarrow -2\leqslant x\leqslant 5\)

\(\\ \rm\hookrightarrow x\in [-2,5]\)

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Answer:

146, 146

Step-by-step explanation:

\(AB^2 = (-4-4)^2 + (11-8)^2 = 73 \\ \\ BC^2 = (4-1)^2+ (8-0)^2 =73 \\ \\ \therefore AB^2 + BC^2 = 146 \\ \\ \\ AC^2 = (-4-1)^2 + (11-0)^2 = 146\)

The instantaneous rate of change of y = √x at x = 2 is √2 / 2.

To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.

Taking the derivative of y = √x using the power rule for differentiation, we have:

dy/dx = (1/2) × x^(-1/2)

Now, substituting x = 2 into the derivative expression:

dy/dx = (1/2) × 2^(-1/2)

= (1/2) × √2

= √2 / 2

Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.

None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.

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Answer:

The rectangular equation equivalent to the polar equation r = 4 is x^2 + y^2 = 16.

Step-by-step explanation:

The polar equation r = 4 can be transformed into an equation in rectangular coordinates by using the following relationships between polar and rectangular coordinates:

x = r cos(theta)

y = r sin(theta)

Substituting r = 4 into these equations, we get:

x = 4 cos(theta)

y = 4 sin(theta)

Therefore, the rectangular equation equivalent to the polar equation r = 4 is:

x^2 + y^2 = (4 cos(theta))^2 + (4 sin(theta))^2 = 16(cos^2(theta) + sin^2(theta)) = 16

The required inequality for the price of a 2-pack shopkin should not be more than $4 is  ≤ 4.

The price of a 2-pack shopkin should not be more than $4. Inequality in the situation is to be determined.

Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

The price of a 2-pack shopkin should not be more than $4.
Let the price of 2 - pack shopkin is x and it should not be more than $4 it impise the price of 2 pack shopkin canno be set up more than 4 but it could be 4 or less so, Inequality for 4 or less of price of 2 pack shopkin is given by,
x  ≤ 4.

Thus, the required inequality for the price of a 2-pack shopkin should not be more than $4 is  ≤ 4.

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The total number of people want in all is 531.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of buses = 9

Number of buses that has 63 people = 5

Number of buses that has 54 people = 4

The total number of people in all the buses.

= 5 x 63 + 4 x 54

= 315 + 216

= 531

Thus,

The total number of people want in all is 531.

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9514 1404 393

Answer:

  (5x -8) +96 +(5x +2) +4x +4x = 540

  x = 25

Step-by-step explanation:

It usually works to follow directions. The sum of angles is ...

  (5x -8) +96 +(5x +2) +4x +4x = 540 . . . . An equation

  18x +90 = 540 . . . . . . . . . collect terms

  x +5 = 30 . . . . . . . . . divide by 18

  x = 25 . . . . . . . . subtract 5

The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.

The basic mathematical operations include addition, subtraction, division, and multiplication.

In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).

The quantity of ribbon attached to the rearview mirror = 2/7

The remaining quantity of ribbon after the attachment = 10/21

The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)

Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.

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The probability that at least 2 of the colors will be the same, the following is the best simulation is Option D Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

Given, Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. We have to find the probability that at least 2 of the colors will be the same. There are 5 colors in the pack of clay, and 7 colors are possible in total.

So, the probability of picking any color at random is

P(picking a color) = 5/7 = 0.7143Let P(X = 2) be the probability that exactly 2 of the colors are the same.

Then, the probability that at least 2 of the colors are the same can be calculated by using the formula:

P(X ≥ 2) = 1 - P(X < 2).

The simulation method that can be used to find the probability of at least 2 of the colors will be the same in the mystery pack is option D.

Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

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The angle sum property of a triangle and the angle formed between a tangent and a radius of a circle indicates.

m∠ADC = 58°

A tangent to a circle is a straight line which touches the circumference of a circle at only one point.

The vertical angles theorem indicates that we get;

∠1 ≅ ∠2

Therefore; m∠1 = m∠2

The tangent to a circle indicates that we get;

The angle formed at vertex B and Q are 90 degrees angles and the triangles ABP and AQP are right triangles, which indicates that the acute angles of each of the right triangles are complementary, therefore;

m∠1 + 26° = 90°

m∠1 = 90° - 26° = 64°

Therefore, m∠2 = m∠1 = 64°

m∠2 = m∠CAD = 64°

The segments AC and AD are radial lengths therefore, the triangle ΔACD is an isosceles triangle.

m∠ADC ≅ m∠ACD (Base angles of an isosceles triangle)

The angles ∠ADC and ∠ACD are therefore;

m∠CAD + m∠ADC + m∠ACD = 180° (Angle sum property of a triangle)

m∠CAD + m∠ADC + m∠ADC = 180°

m∠CAD + 2 × m∠ADC = 180°

64° + 2 × m∠ADC = 180°

m∠ADC = (180° - 64°)/2 = 58°

m∠ADC = 58°

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Answer:

[See Below]

Step-by-step explanation:

✦ \(\sqrt{95} =9.74679434\)

~Hope this helps Mate. If you need anything feel free to message me.

-I have included a number line as well...