Tommy looks around at an assembly. He notices his younger sister to his right and his older brother 4 meters ahead of him. If Tommy's brother and sister are 5 meters apart, how far apart are Tommy and his younger sister?

Answer:

-----------------------------

Given sequence:

If t(n) = 200, we can try to find the value of n:

There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.

The sequence should include integer numbers, so there is no solution.

Given function:

Solve for x if f(x) is 200:

Answer:

1.  No

[tex]\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)[/tex]

Step-by-step explanation:

Given sequence:

[tex]t(n)=5 \cdot 2^n[/tex]

To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:

[tex]\implies 5 \cdot 2^n=200[/tex]

[tex]\implies 2^n=40[/tex]

[tex]\implies \ln 2^n=\ln 40[/tex]

[tex]\implies n\ln 2=\ln 40[/tex]

[tex]\implies n=\dfrac{\ln 40}{\ln 2}[/tex]

[tex]\implies n=5.3219280...[/tex]

In a sequence, n is a positive integer.  Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.

Given function:

[tex]f(x)=5 \cdot 2^x[/tex]

To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:

[tex]\implies 5 \cdot 2^x=200[/tex]

[tex]\implies 2^x=40[/tex]

[tex]\implies \ln 2^x=\ln 40[/tex]

[tex]\implies x=\dfrac{\ln 40}{\ln 2}[/tex]

[tex]\implies x=5.3219280...[/tex]

Therefore, it is possible for the function to have an output of 200 when:

[tex]x=\dfrac{\ln 40}{\ln 2}[/tex]

The domain is x < 2 or x ≥ 3 and the range y > - 3

The domain of a function is the interval of valid inputs to the function.

The range of a function is the interval of valid outputs to the function.

Since we have the function

To find the domain of the function, we see that the values of x are between x < 2 or x ≥ 3.

So, the domain is x < 2 or x ≥ 3.

To find the range of the function, since

f(x) = -x/2 - 2 if x < 2 and f(x) = 2x - 4 if x ≥ 3.

Using the first function f(x) = -x/2 - 2 if x < 2 and substituing x = 2, we have that

f(2) = -2/2 - 2 = - 1 - 2 = -3

Since f(x) cannot be less than f(2), then

f(x) > - 3

So, y > - 3

Also, using the second function f(x) = 2x - 4 if x ≥ 3. and substituting x = 3 into the equation since this is the minimum value of x, then

f(3) = 2(3) - 4

= 6 - 4

= 2

Since this is the minimum value of f(3) = 2

So, y > 2

Since y > -3 and y > 2, combining both expressions, we have that

y > - 3

So, the range is y < -3

So, the domain is x < 2 or x ≥ 3 and the range y > - 3

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The value of 1/8 = 0.125 and 3/6 = 0.5.

To simplify an expression, you can use algebraic rules such as combining like terms, using the distributive property, and applying the order of operations (PEMDAS). Additionally, you can use properties of exponents, logarithms, and trigonometric functions to simplify expressions that involve those operations.

For example, you can simplify the expression 2x + 3x by combining the like terms 2x and 3x to get 5x. Another example, you can simplify the expression (3x + 2)(4x - 1) by using the distributive property to get 12x^2 + x - 8.

According to question:-

To simplify 1/8 * 3/6, you can first convert the fractions to have a common denominator. In this case, the least common multiple of 8 and 6 is 24. So you can convert 1/8 to 3/24 and 3/6 to 12/24.

Then, you can multiply the numerators and denominators separately:

(1/8) * (3/6) = (3/24) * (12/24) = 3/24 * 12/24 = 3/24 * 1 = 3/24

So the simplified form of the expression is 3/24.

As a side note, if you want to further simplify, you can divide the numerator and denominator by their greatest common divisor, which is 1 in this case, then you will get 3/24 equals to 1/8.

Hence, the value of 1/8 = 0.125 and 3/6 = 0.5.

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Answer:

Step-by-step explanation:

[tex]\mathrm{Slope=\cfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\mathrm{\left(x_1,\:y_1\right)=\left(-5,\:7\right)}[/tex]

[tex]\mathrm{\left(x_2,\:y_2\right)=\left(0,\:4.5\right)}[/tex]

[tex]\mathrm{m=\cfrac{4.5-7}{0-\left(-5\right)}}[/tex]

[tex]\mathrm{m=-\cfrac{2.5}{5}}[/tex]

[tex]\mathrm{m=-0.5}[/tex]

-Hope this helps!

The equation of the line in the slope-intercept form will be y = 5x + 5.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

A line passes through the points (0, 5) and (1, 10). Then the equation of the line is given as,

(y - 5) = [(10 - 5) / (1 - 0)] (x - 0)

y - 5 = 5x

y = 5x + 5

The equation of the line in the slope-intercept form will be y = 5x + 5.

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Answer:

The other leg is 19.6cm

Step-by-step explanation:

Use Pythagorean Theorem to set up an equation and solve.

The Pythagorean Thm is:

leg^2 + leg^2= hypotenuse^2

Let's fill in what we know:

4^2 + leg^2 = 20^2

(let's use a variable)

4^2 + b^2 = 20^2

simplify

16 + b^2 = 400

subtract 16

b^2 = 384

squareroot both sides.

b = sqrt384

use a calculator to find the squareroot.

b = 19.5959179

round to the nearest tenth.

b = 19.6

don't forget units!

The other leg is 19.6cm

Continental tropical (cT) air masses can be characterized by hot and dry air. The correct answer would be option (D).

Continental tropical air masses, on the other hand, are most common in the summer and are characterized by dry and hot air. They will be most common in Mexico's southwestern and northern regions.

These air masses frequently move into the northeast, bringing more dry and hot weather to the Great Plains, but they typically have a much smaller range than other air masses.

Therefore, the correct answer would be option (D) hot and dry air.

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On solving the provided question, we can say that Principal = 21,000, interest = 0.4% and time = 4 yrs => SI = $336

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.

here,

Principal = 21,000

interest = 0.4%

time = 4 yrs

SI = Principal X Interest X time / 100

SI = 21000*0.4*4/100 = $336

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Answer: 480 and 300

Step-by-step explanation:

240 divided by 0.50 = 480

240 divided by 0.80 = 300

Answer:

(2,2)

Step-by-step explanation:

The middle point of (-4,8) and (8,-4) is (2,2)

On solving the provided question, we can say that we know that all angles of a parallelograms  are 360 => x = 23

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

as we know that all angles of a parallelograms  are 360

then, 3j +6k +(k+10) + (5j-9) = 360

3x + 6x + x +10 + 5x -9 = 360

15x = 349

x = 349/15

x = 23.2666666667 = 23

x = 23

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Answer:

10

Step-by-step explanation:

The length of the slant height will be 4 units. Then the correct option is A.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Let 's' be the slant height. Then the length of the slant height will be given as,

5² = s² + (6/2)²

25 = s² + 9

s² = 25 - 9

s² = 16

s = 4 units

The length of the slant height will be 4 units. Then the correct option is A.

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The missing diagram is given below.

When you are using the plane mirror, the image is going to have to be the same in size as you are.

When using the plane mirror and trying to get a reflection from the plane mirror, it would be found that the image that we are looking at in the mirror would turn out to be the same as the object that is being reflected. That is, your image is going to be exactly the same way.

The reason for this is because, the plane mirror is known to reflect light at the same angle that it received the light. This would cause the distance and the size of the object to be replicated in that image that has been reflected.

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On solving the provided question we cans ay that the value of the function will be x(x−2)=0 => x=0,2

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given functions are -

f(x)=x^2, g(x)=2^x

Find the value for -

fog(x)= gof(x)....equation 1

f(g(x)={g(x)}^2

First find solution for function f(g(x) -

⇒ f(g(x)={2^x}^2=2^2x

Now find solution for function g(f(x)) -

g(f(x))=2^f(x)

⇒g(f(x))=2^x^2

Now, substitute the values in equation 1 -

gof(x)=fog(x)

2^x^2=2^2x

⇒x^2=2x

x^2−2x=0

Therefore, the solution set is obtained as x=0,2.

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The value of x would be -3/2.

What is the linear equation in one variable?

A linear equation in one variable is an equation in which the highest power of the variable is 1. A linear equation in one variable can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear equation in one variable is a straight line.

6 + 3/(x + 1) = 0

3/x+1 = -6

3 = -6(x + 1)

3 = -6x - 6

-6x= 9

x = -9/6

x = -3/2

Hence, the value of x would be -3/2.

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Answer:

18x - 9 = 72

3(6x - 3) = 72

x = 4.5

Step-by-step explanation:

Given equation:

[tex]\dfrac{3}{5}\left(30x-15\right)=72[/tex]

Separate the fraction:

[tex]\implies 3 \cdot \dfrac{1}{5}\left(30x-15\right)=72[/tex]

Multiply the terms inside the parentheses by 1/5:

[tex]\implies 3\left(\dfrac{1}{5}\cdot30x-\dfrac{1}{5}\cdot 15\right)=72[/tex]

[tex]\implies 3\left(6x-3\right)=72[/tex]

Expand the brackets:

[tex]\implies 3\cdot6x-3\cdot3=72[/tex]

[tex]\implies 18x-9=72[/tex]

Add 9 to both sides of the equation:

[tex]\implies 18x-9+9=72+9[/tex]

[tex]\implies 18x=81[/tex]

Divide both sides pf the equation by 18:

[tex]\implies \dfrac{18x}{18}=\dfrac{81}{18}[/tex]

[tex]\implies x = 4.5[/tex]

Therefore, the three equations that have the same value as the given equation are:

Therefore , the solution of the given problem of system of inequalities comes out to be option a.

This system of inequalities defines a region in the x-y plane. The first inequality represents all the points below a line with the equation y = 2 - x, and the second inequality represents all the points above a line with the equation y = x - 1. The solution to the system is the set of points that lie in the intersection of these two regions, which is a certain area of the x-y plane.

Here,

Given : This riddle can be represented by the following system of inequalities:

x + y < 2 (the sum of two numbers is less than 2)

x - y > 1 (if we subtract the second number from the first, the difference is greater than 1)

Where x and y are the two numbers.

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The net worth of the surf shop would be $572,922.

Option (B) is correct.

What is the net worth?

Net worth is a financial metric that represents the value of an individual or a company, and it is calculated by taking the total assets and subtracting the total liabilities.

To calculate this, you would add up all of the assets (property value, long term investments, cash, savings account, owned inventory, and owned equipment) and subtract all of the liabilities (building mortgage, other debt, small business loan, and long term liabilities).

In this case, the assets total:

$130,284 (property value) + $106,987 (long term investments) + $208,634 (cash) + $172,839 (savings account) + $38,671 (owned inventory) + $38,291 (owned equipment) = $731,109

And the liabilities total:

$78,280 (building mortgage) + $21,987 (other debt) + $28,950 (small business loan) + $48,970 (long term liabilities) = $178,187

So,

$731,109 (assets) - $178,187 (liabilities) = $572,922 (net worth)

hence, The net worth of the surf shop would be $572,922.

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The standard form of a linear equation is Ax + By = C where A and B are not both zero and A, B and C are integers whose GCF is 1.

To convert the equation y = 9x - 1 to standard form, we need to rearrange it as:

9x - y = 1

We can divide both sides by -1 to get

-9x + y = -1

Which is the standard form of the equation.

So the standard form of the equation is:

-9x + y = -1

The typical oil to vinegar ratio is three parts oil to one part vinegar/acid, though this ratio might change depending on the vinegar/acid you use.

One part vinegar to three parts oil is the general ratio for vinaigrettes. I learned this general principle from French culinary school, which results in a somewhat acidic dressing that goes well on salads. This implies that if you start with a cup of vinegar, you would need one cup of oil.

The typical oil to vinegar ratio is three parts oil to one part vinegar or acid, however this ratio might change based on the vinegar or acid you choose and your preferences. Less oil is required the less acidic the vinegar or acid.

Salad dressing mixing involves a physical alteration. Shaking the bottle creates a transient emulsion and suspension since the dressing's constituents are layered and immiscible.

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Answer:

t=-2

Step-by-step explanation:

5t-26=18t

5t-26+26=18t+26

simplify and subtract 18t from both sides

Answer:

C. 1/4 (-x + 2)

Step-by-step explanation:

-1/4x + 1/2

1/4 (-x + 2)

The factors of x² - 9 is +3 , -3.

What is factors ?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics.

The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.

x² - 9 = 0

x² = 9

x = √9

x = ± 3

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Answer:

See below

Step-by-step explanation:

Obviously, as h ==> 0 it becomes very small

  I would pick a very small number for h   .....  say -.001

then the equation becomes

[   f (-1.001)  - f(-1)  ] / (-.001)                where f(x) = x^5

= [ (-1.001)^5  - (-1)^5  ]  / ( -.001)         For the point that has x = -1

                       = 5.01     <==== approximation for the slope at x = - 1

Now we need line with slope = 5.01    and point  (-1,-1)

   Using point slope form :

  y - -1  = 5.01 (x - -1)     re-arrange to:

y = 5.01x - 4.01  <==equation of line with slope = 5.01 and tangent at (-1,-1)

Here is a graph: (and it looks like a good approximation !)

Answer:

y=(-10x+9)/11

Step-by-step explanation:

10x+11y=9

11y=9-10x

y=(9-10x)/11

y=(-10x+9)/11

From the equation y = 25x + 72, the initial temperature is 72°F, the rate of change in the oven temperature is 25 degrees Fahrenheit per minute

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the temperature of the oven in degrees Fahrenheit after x minutes.

Given the equation:

y = 25x + 72

This means that the rate of change is 25 degrees Fahrenheit per minute.

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Therefore , the solution of the given problem rate of interest comes out to be he get commission of 4.9%.

Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.

Here,

Given :

Gross pay = $680

Sales = $13,600

To find the what rate of commission he get on sale:

=> 680/13800 * 100

=> 0.049 * 100

=> 4.9%

Thus , he get commission of 4.9%

Therefore , the solution of the given problem of interest comes out to be

he get commission of 4.9%.

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Answer: x = 10

Step-by-step explanation:

triangle shows angles are 38°, (7x+1)°, (10x+9)°(outside of the triangle)

total angle of the triangle is 180°

then

        38°+ (7x+1)°+ [180-(10x+9)°] = 180°

Simplifying

38 + (7x + 1) + [180 + -1(10x + 9)] = 180

Reorder the terms:

38 + (1 + 7x) + [180 + -1(10x + 9)] = 180

Remove parenthesis around (1 + 7x)

38 + 1 + 7x + [180 + -1(10x + 9)] = 180

Reorder the terms:

38 + 1 + 7x + [180 + -1(9 + 10x)] = 180

38 + 1 + 7x + [180 + (9 * -1 + 10x * -1)] = 180

38 + 1 + 7x + [180 + (-9 + -10x)] = 180

Combine like terms: 180 + -9 = 171

38 + 1 + 7x + [171 + -10x] = 180

Remove brackets around [171 + -10x]

38 + 1 + 7x + 171 + -10x = 180

Reorder the terms:

38 + 1 + 171 + 7x + -10x = 180

Combine like terms: 38 + 1 = 39

39 + 171 + 7x + -10x = 180

Combine like terms: 39 + 171 = 210

210 + 7x + -10x = 180

Combine like terms: 7x + -10x = -3x

210 + -3x = 180

Solving

210 + -3x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-210' to each side of the equation.

210 + -210 + -3x = 180 + -210

Combine like terms: 210 + -210 = 0

0 + -3x = 180 + -210

-3x = 180 + -210

Combine like terms: 180 + -210 = -30

-3x = -30

Divide each side by '-3'.

x = 10

Simplifying

x = 10

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Due to the fact that parallel lines produce congruent alternate interior angles, ADB = CBD by ASA.

A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pains involve using freshly baked sorrowful bread. Prior to, before, ahead of The angles of 30 and 60 degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary angle is two angles combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary.

given

∠CDB = ∠ABD

and

∠ADB = ∠CBD

∠RQP = ∠SQP

since perpendicular lines form congruent right angles. PQ || PQ by reflexive so ∠PQR = ∠PQS by AAS.

Due to the fact that parallel lines produce congruent alternate interior angles, ADB = CBD by ASA.

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Answer: E⁢C=B⁢C; property of isosceles triangle

Step-by-step explanation: Got it right on Edmentum/Plato