the only way to learn maths is to do maths, explain why we do maths​

Answer:

Percent rate of change per unit, t ≈ 10.99%

Step-by-step explanation:

The percent rate of change per unit, t, for a function is equal to the derivative of the function with respect to t, divided by the function value at t.

For the given function g(t) = 200(1.12)^t, the derivative with respect to t is:

g'(t) = ln(1.12) * 200(1.12)^t

The function value at t is:

g(t) = 200(1.12)^t

Therefore, the percent rate of change per unit, t, is:

g'(t) / g(t) = [ln(1.12) * 200(1.12)^t] / [200(1.12)^t] = ln(1.12) ≈ 0.1099

Multiplying by 100 to express the answer as a percentage, rounded to the nearest tenth of a percent, we get:

Percent rate of change per unit, t ≈ 10.99%

Answer: The answer is the letter B

Step-by-step explanation:

Mean is the overall average of numbers or books and range is the length from greatest to least

Answer:

x = 3

y = -10

Step-by-step explanation:

  5x + y = 5                                                                    y = 3x - 19

  5x + 3x - 19 = 5

  8x - 19 = 5

  8x = 24

   x = 3

Now put x in to solve for y

y = 3(3) - 19

y = 9 - 19

y = -10

Let's check

5(3) - 10 = 5

15 - 10 = 5

5 = 5

So, x = 3 and y = -10 is the correct answer.

Answer:

Step-by-step explanation:

40-20 =20 then times 3 which is 60.

The domain of a function is all the possible input values for which the function is defined.

Function is a block of code that performs a specific task. It is a reusable piece of code that can be called from other parts of the code, reducing the amount of code that needs to be written and making the code easier to read and maintain. Functions can take in parameters and return values, allowing for increased flexibility and reusability. Functions can also be used to break up large programs into smaller, more manageable pieces.

In this case, the reasonable domain for the function f(x) = 4x³-50x²+150x would be all real numbers. This is because the function is a polynomial, which is continuous, meaning that it is defined for all real numbers.

The input of the function is a width, and the output is a volume. Therefore, the domain of the function should include all reasonable widths that could produce a volume. This means that the domain should include all positive real numbers, as any negative value would produce a negative volume, which is not reasonable. Thus, the reasonable domain for the function f(x) = 4x³-50x²+150x is all positive real numbers.

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Answer:

3.3.1 Approximations for trigonometric functions. 3.3.2 ... 7.2.1 Consistency for three simultaneous linear equations in two unknowns ... x : y : z =5:4:3;.

The number line graph A is correct, thus, option C is true.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, an inequality x ≥ -5.

The inequality x ≥ -5 means that x is greater than or equal to -5.

In other words, any value of x that is equal to or greater than -5 satisfies the inequality.

For example, x = -5, x = 0, x = 10, and x = 100 all satisfy the inequality x ≥ -5 because they are greater than or equal to -5.

On a number line, the solution set for this inequality would include all the values of x to the right of -5, including -5 itself,

because the dot at -5 would be filled in to indicate that it is included in the solution set.

The part of the number line to the left of -5 would not be included because those values of x are less than -5, which does not satisfy the inequality.

Therefore, the Option C is correct.

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If the bacteria in a dish that contains 2 bacteria quadruple every 16 minutes can be represented by the expression 2×4t/16, an equivalent expression for the number of bacteria in the dish for any time, t, in minutes is B. 8t/16.

An equivalent expression depicts two algebraic expressions that have the same value when the values for the variables are plugged in.

An algebraic expression is the combination of variables, values, constants, and numbers using mathematical operands without the equal symbol (=).

2×4t/16 = 8t/16

2×4t/16 ≠ 4t8

2×4t/16 ≠ 2×2t8

2×4t/16 ≠ 4×2t16

Thus, 2×4t/16 = 8t/16 as equivalent expressions.

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We can see that the scale factor is 0.5, which means that the image got smaller, and that the values are:

b' = 4

c = 14.

If k is the scale factor applied, all the sides are modified by the same scale factor, so we know that:

a' = k*a

Here we know that:

a =  6

a' = 3

Then:

3 = k*6

3/6 = k

1/2 = k

now.

If b = 8, then:

b' = (1/2)*8 = 4

if c' = 7, then:

7 = (1/2)*c

2*7 = c

14 = c

Finally, the scale factor is smaller than 1, then the image got smaller, and the scale factor is 1/2 = 0.5

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On  the number line, the points that represent the values of x in - 1 < x < 3 are:

The expression given is - 1 < x < 3 which means that x is any whole number that is greater than - 1 but less than 3. This means that on the number line given, the value of x would be any number that is more than - 1 but less than 3.

These numbers will include 0, 1, and 2. The line should therefore begin at -1 and go to 3 to show the values of x in - 1 < x < 3 . The line to use should be the open circle which shows greater than or less than

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72 items were checked to work correctly.

What is the solution of algebraic expression?

Finding the value of the variable is part of solving an algebraic statement. We must do certain algebraic operations to determine the value of one of the variables in the linear equations before we can substitute that value to get the value of another variable.

Then the percentage of defective items in the checked batch is x + 3%.

We know that out of 300 items, this percentage represents the number of defective items. So we can write:

(x + 3%) * 300 = number of defective items

Simplifying this equation, we get:

3x + 9 = number of defective items

number of items checked - number of defective items = number of items checked to work correctly

Substituting the equation we derived above for the number of defective items, we get:

300 - (3x + 9) = number of items checked to work correctly

Simplifying this equation, we get:

291 - 3x = number of items checked to work correctly

3x = number of defective items in a batch of 300 items with the normal percentage of defects

Substituting this expression for the number of defective items in our previous equation, we get:

291 - 3x = number of items checked to work correctly

Now we can solve for x:

3x = number of defective items in a batch of 300 items with the normal percentage of defects = x/100 * 300

3x = 3 * (300 - number of items checked to work correctly - number of defective items)

3x = 900 - 3(3x + 9)

3x = 900 - 9x - 27

12x = 873

x = 73

So the normal percentage of defective items is 73%.

Now we can find the number of items checked to work correctly:

291 - 3x = 291 - 3(73) = 72

Therefore, 72 items were checked to work correctly.

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The equation which represents a proportional relationship from the given set of equations is y = 4x.

What is meant by a proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. y= k x, where k is the proportionality constant, is the equation that depicts a directly proportional relationship, or a line. y = k(1/x) or xy = k, where k is the proportionality constant, is the equation that depicts an indirectly proportional relationship, or a line. One can argue that two variables are in a proportional relationship if one variable is always equal to a constant multiplied by the other variable.

So according to the above explanation, we can say that the equation y = 4x is an example of a proportional relationship.

This is because the ratio y/x is always a constant 4.

Therefore the equation which represents a proportional relationship is y = 4x.

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The only solution to the system of inequalities y < −x+5 and y ≥ 3x+1 is (1,3).

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

For the inequality y < -x + 5, any point below the line y = -x + 5 will satisfy the inequality. For the inequality y ≥ 3x + 1, any point on or above the line y = 3x + 1 will satisfy the inequality.

To find the solutions that satisfy both inequalities, we can shade the region that is below the line y = -x + 5 and also on or above the line y = 3x + 1. This region is the shaded triangle bounded by the lines y = -x + 5, y = 3x + 1, and the x-axis.

Therefore, the solutions to the system of inequalities are the points in this shaded triangle. To check which options are solutions, we can substitute the values of x and y given in each option into both inequalities and check if they satisfy both.

Hence, the only solution is (1,3).

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Complete question:

Which of the following are solutions to the system of inequalities y < −x+5 and y ≥ 3x+1?

Select all that apply.

a. (0,2)

b. (1,3)

c. (2,1)

d. (3,6)

Answer: I dont understand the answer that much but off of what i understand i think the answer is A

Step-by-step explanation: I am not sure but i think so

A spinner which can be use to simulate this probability is shown in figure.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

The weather forecast says there is a 75% chance it will rain later today.

Now, We can simplify the number is,

⇒ 75%

⇒ 75/100

⇒ 3/4

Thus, We can draw A spinner which can be use to simulate this probability as shown in figure.

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Answer:

Step-by-step explanation:

5*x+11=36

5*x=36-11

x=25/5

x=5

5 is the answer

Hey there!

Guide to follow

• Product = multiply/multiplication
• Sum = add/addition
• Quotient = divide/division
• Difference = subtract/subtraction

• Is = equal to/equivalent to

Question reads….
“The product of a 5 and a number plus 11 is 36”

We are not sure what the unknown number is, so we will label it as “w”

Your equation:

5 * w + 11 = 36

SOLVING for the answer to the equation:

5 * w + 11 = 36
5w + 11 = 36

SUBTRACT to both sides

5w + 11 - 11 = 36 - 11

SIMPLIFY it

5w = 25

DIVIDE 5 to BOTH SIDES

5w/5 = 25/5

SIMPLIFY it

w = 25/5

w = 5

Therefore, your unknown number should be: 5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Employing the identity (a+b)² = a² + 2ab + b², where a and b are any real numbers.

Substituting  a and b with a and x/y, respectively:

(a + x/y)² = a² + 2a(x/y) + (x/y)²

(a + x/y)² = (a + x/y)(a + x/y)

= a² + ax/y + ax/y + x²/y²

= a² + 2ax/y + x²/y²

add a² to both sides of the equation:

a² + (a + x/y)² = a² + 2ax/y + x²/y² + a²

a² + (a + x/y)² = (a² + x²/y²) + 2ax/y + a²

xy = a² substitute a² for xy in the last term:

a² + (a + x/y)² = (a² + x²/y²) + 2axy/xy + a²

a² + (a + x/y)² = (a² + x²/y²) + 2a + a²

We have that  x²/y² = (xy)/(y²) = a/y, and substituting this back into the equation:

a² + (a + x/y)² = (a² + a/y + a/y) + 2a + a²

= 2a² + (2a/x) + (2a/y)

A real number is described as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

Therefore from the mathematical expression shown above, we have shown that:

a² + (a + x/y)² = 2a² + (2a/x) + (2a/y)

This is the mathematical expression we wanted to prove.

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Answer:

  40% (high)

Step-by-step explanation:

You want to know the percentage error when an actual value of 1.5 L is estimated to be 2.1 L.

The percentage error is given by ...

  (percent error) = (estimate/actual - 1) × 100%

  percent error = (2.1/1.5 -1) × 100%

  = (1.40 -1.00) × 100% = 0.40 × 100%

  = 40%

The student's estimate is 40% too high.

Answer:

See below.

Step-by-step explanation:

We are asked to simplify the expression provided.

An easy way to simplify this expression is by Combining Like Terms.

Combining Like Terms means adding terms that are similar, whether that's natural numbers, or variables.

For example, 8x + 9x are like terms since they both have the same variables. There's no exponents or any other variables that make these terms different from each other.

Using what we've learned, let's combine like terms for our problem now.

Combine Like Terms:

[tex]7h+6.3d-15+4d-3.4h[/tex]

[tex]7h - 3.4h = 3.6h[/tex]

[tex]6.3d + 4d = 10.3d[/tex]

-15 has no like terms.

We should have;

[tex]10.3d-15+3.6h[/tex]

This will be our final answer. There's no more like terms to combine and we can't simplify this expression further.

Answer:

[tex]\cos \dfrac{\theta}{2}(1-\cos \theta)=\sin \dfrac{\theta}{2} \sin \theta[/tex]

Step-by-step explanation:

[tex]\textsf{To show that}\;\;\cos \dfrac{\theta}{2}(1-\cos \theta)=\sin \dfrac{\theta}{2} \sin \theta:[/tex]

[tex]\textsf{Let}\;\;u=\dfrac{\theta}{2} \implies 2u=\theta[/tex]

Therefore:

[tex]\implies \cos \dfrac{\theta}{2}(1-\cos \theta)=\cos u(1-\cos 2u)[/tex]

 cos(A±B) = cosA cosB ∓ sinA sinB

 cos(2θ) = cos²θ - sin²θ

 cos(2θ) = 2cos²θ - 1

 cos(2θ) = 1 - 2sin²θ

Use the cos double angle identity cos(2θ) = 1 - 2sin²θ to rewrite cos(2u) in terms of sin:

[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1-\cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\end{aligned}[/tex]

Simplify:

[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1- \cos \theta)&=\cos u(1- \cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&=\cos u(1-1+2 \sin^2 u)\\&= \cos u(2 \sin^2 u)\\&=2 \sin u \cos u \sin u\end{aligned}[/tex]

 sin(A±B) = sinAcosB ± cosAsinB

 sin(2θ) = 2sinθcosθ

Using the sine double angle identity to rewrite 2sin(u)cos(u) as sin(2u):

[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1- \cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&= \cos u(1-1+2 \sin^2 u)\\&= \cos u(2 \sin^2 u)\\&=2 \sin u \cos u \sin u\\&= \sin(2u) \sin u\end{aligned}[/tex]

Finally, substitute u = θ/2 back in:

[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1-\cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&=\cos u(1-1+2 \sin^2 u)\\&= \cos u(2\sin^2 u)\\&=2\sin u\cos u \sin u\\&=\sin(2u) \sin u\\&=\sin\left(2 \cdot \dfrac{\theta}{2}\right) \sin \dfrac{\theta}{2}\\&=\sin \theta \sin \dfrac{\theta}{2}\\&=\sin \dfrac{\theta}{2} \sin \theta \end{aligned}[/tex]

If you don't want to substitute u = θ/2, the full calculation using the same double angle identities is:

[tex]\begin{aligned}\implies\cos\dfrac{\theta}{2}(1-\cos\theta)&=\cos\dfrac{\theta}{2}\left(1-\left(1-2\sin^2\dfrac{\theta}{2}\right)\right)\\\\&=\cos\dfrac{\theta}{2}\left(1-1+2\sin^2\dfrac{\theta}{2}\right)\\\\&=\cos\dfrac{\theta}{2}\left(2\sin^2\dfrac{\theta}{2}\right)\\\\&=2\sin \dfrac{\theta}{2}\cos \dfrac{\theta}{2} \sin \dfrac{\theta}{2}\\\\&=\sin\left(2\cdot\dfrac{\theta}{2}\right)\sin\dfrac{\theta}{2}\\\\&=\sin\theta\sin\dfrac{\theta}{2}\\\\&=\sin\dfrac{\theta}{2}\sin\theta \end{aligned}[/tex]

Answer:

[tex]x[/tex] = 100 , [tex]y[/tex] = 100 , [tex]z[/tex] = 80

Step-by-step explanation:

Information we need to know:

Opposite angles in a rhombus are equal

Angles in a quadrilateral equal to 360

1) Find any angles that we can

We already know that opposite angles are 80. This means that we can easily see that [tex]z[/tex] is 80.

The total we have at the moment is 160

2) Find the remaining angles

If we know that all angles in a quad add up to 360, we can easily find [tex]x[/tex] and [tex]y[/tex] by taking 160 from 360 and the dividing by 2!

TOP TIP:

To make sure our answer is correct we can add all our answers up and check that they add up to 360

Our answer is correct!

Hope this helps, have a great day! :)

Answer:

x = 100

y = 100

z = 80

Step-by-step explanation:

The properties of a rhombus are:

Two angles are said to be adjacent when they share a common vertex.

Therefore, both angle x and angle y are adjacent to the angle that measures 80°.

Since adjacent angles in a rhombus are supplementary:

⇒ x° + 80° = 180°

⇒ x° = 100°

⇒ x = 100

Similarly:

⇒ y° + 80° = 180°

⇒ y° = 100°

⇒ y = 100

As opposite angles in a rhombus are equal:

⇒ z° = 80°

⇒ z = 80

Answer: N′(−7, −2), M′(−4, −1), O′(−7, −5)

Step-by-step explanation:

im right and youre wromng

Based on the four options, Brianna should choose to invest her summer earnings in the Account 4 (compounded continuously) because interest is at highest in the account after like 3 years.

Interest is higher in compounded continuously because it is calculated more frequently than in other compounding methods, such as annually or semi-annually. In continuous compounding, interest is calculated and added to the principal an infinite number of times over a given period, which results in a higher effective interest rate than other compounding methods.

This means that the amount of interest earned on an investment or loan increases more rapidly, which can result in greater returns for investors or higher costs for borrowers. Continuous compounding is often used in financial markets where small changes in interest rates can have significant impacts on returns, such as in the case of short-term bonds or options trading.

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Answer:

C) x < 19

Step-by-step explanation:

It is an open circle pointing in the negative direction starting at 19.

We can calculate the value of {x} as 63.2°.

There are six major trigonometric functions as -

We can write the relation between them as -

Also the following trigonometry relations hold true -

Given is that -

cos{x} = 0.4505

We have -

cos{x} = 0.4505

{x} = cos⁻¹(0.4505)

{x} = cos⁻¹{cos(63.2)}

{x} = 63.2°

Therefore, we can calculate the value of {x} as 63.2°.

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The value of a discriminant determines the kind of roots in a quadratic equation, and the sign of a discriminant indicates whether the roots were real or complex, unique or recurring.

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd quadratic formula in a single variable. a 0. It has at most one solution since it is a 2nd quadratic problem, which is guaranteed by the algebraic basic theorem. The solution could be straightforward or difficult.

To put it another way, if a twice the square of a expression that comes after b plus b times the same expression never squared plus c equals 0.

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The quadratic functiοn in standard fοrm that wοuld represent the data in the table is y = 2x² + x - 9.

A quadratic functiοn is a type οf pοlynοmial functiοn that can be written in the fοrm οf f(x) = ax² + bx + c, where a, b, and c are cοnstants, and x is an unknοwn variable. The graph οf a quadratic functiοn is a parabοla, and the rοοts οf the equatiοn (the x-intercepts) are the pοints where the parabοla crοsses the x-axis. Quadratic functiοns are used tο mοdel a variety οf natural phenοmena, such as the trajectοry οf a prοjectile οr the grοwth οf a pοpulatiοn οver time.

This can be determined by putting the given values intο the standard fοrm equatiοn: y = ax²  + bx + c  and sοlving fοr a, b and c.

When x = 2, y = 3. Therefοre, 3 = 2a + b - 9, which gives b = 11.

When x = 4, y = 1. Therefοre, 1 = 8a + 11 - 9, which gives a = -1/4.

When x = 6, y = 3. Therefοre, 3 = 18a - 1/4 + 11 - 9, which gives c = -5/4.

The quadratic equatiοn in standard fοrm, y = 2x²  + x - 9, can then be written using the values οf a, b and c fοund.

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ΔQRS ≅ ΔTUV and ΔTUV ≅ ΔXYZ then ΔXYZ  ≅ ΔQRS by Transitive Property.

ΔEFG ≅ ΔJKL then ΔJKL ≅ ΔEFG using Symmetric Property.

The transitive property of congruence states that “ if two shapes are congruent to the third shape, then all the shapes are congruent to each other.

This is the transitive property at work: if a=b and b=c, then a=c.

First, ΔQRS ≅ ΔTUV and ΔTUV ≅ ΔXYZ

The property of Transitivity shows for any angle <A, <B and <C.

So, <A = <B and <B = <C then <A = <C

Second, The property of Symmetry shows or any angle <A, <B

if  <A≅ <B then <B≅ <A

So, ΔEFG ≅ ΔJKL then ΔJKL ≅ ΔEFG using Symmetric Property.

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They are intersecting

a) Not parallel because they share different slopes

b) Not perpendicular, they dont intersect creating a right angle. This is because neither of the slopes are a reciprocal of each other.

The angle measures are given as follows:

Two angles are called supplementary when the sum of their measures is of 180º.

On a trapezoid, consecutive interior angles are supplementary, hence the pairs of supplementary angles are given as follows:

Hence the value of y is obtained as follows:

y + 145 = 180

y = 35º.

(as the two angles are supplementary we know that the sum of their measures is of 180º).

The value of x is obtained as follows:

x + 62 = 180

x = 118º.

(as the two angles are supplementary we know that the sum of their measures is of 180º).

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