Charlie and Hayden are standing outside. Charlie is 64 inches tall and casts a shadow of 30 inches. If Hayden is 68 inches tall, approximately how long is his shadow? 28 inches 32 inches 145 inches 31 inches

The product of (X + A) + (X + B) is- [tex]x2 + xb + ax + ab[/tex]

The information provided in the question,

The outcome of multiplying two numbers together is known as the product. 12 is the result of the addition of 3 and 4, 20 is the sum of 4 and 5, and so on. Discovering the Product A multiplication problem has a solution in the product.

We must determine the of (x + a) and (x + b).

The product is the result of multiplying two numbers, as we all know.

So,

[tex]( x+ a)[/tex]   x  [tex]( x + b)[/tex]

[tex]x( x+b) + a( x + b)[/tex]

[tex]x[/tex]²[tex]+ bx + ax + ab[/tex]

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The y-intercept of the linear function is: C. 15.

The y-intercept of a linear function is defined as the starting or initial value, which is also the point on the y-axis where the line of the equation crosses.

In a given function represented as y = mx + b, the y-intercept is the value of b.

From the information given above, we have:

Initial value/y-intercept (b) = flat rate = $15

Slope/unit rate (m) = $10

Therefore, the y-intercept of the function is: C. 15.

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The area of the Temasa's doll house is 31.5 square feet.

What is the scale factor?

The scale factor is a ratio that compares the measurements of an object on a drawing or map to the actual measurements of that same object in real life. It is usually expressed as a ratio in the format 1:n (or 1/n) where n is the scale factor.

We can start by using the scale factor of 1:10 to find the actual dimensions of the doll house.

Since the scale factor is 1:10, this means that for every 1 inch on the drawing, the actual measurement is 10 inches. So, to find the actual length and width of the doll house, we can multiply the measurements on the drawing by 10.

7 1/5 inches * 10 = 71 inches + 2 inches

4 4/5 inches * 10 = 44 inches + 8 inches

So, the actual length of the doll house is 71 inches + 2 inches = 73 inches, and the actual width is 44 inches + 8 inches = 52 inches.

To find the area of the doll house, we can multiply the length and width:

73 inches * 52 inches = 3788 square inches

To convert this to square feet, we can divide by 12^2, since 1 foot = 12 inches:

3788 square inches / (12 inches)^2 = 31.5 square feet (rounded to the nearest square foot)

Hence, the area of the Temasa's doll house is 31.5 square feet.

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Answer:

the numbers are 13 and 17

Step-by-step explanation:

let the first number be a

let the second number be b

a+b=30.......a=30-b

a-b=4

substitute the first eq into the second one

30-b-b=4

30-2b=4

30-4=2b

26=2b

13=b

a=30-b

a=30-13

a=17

Answer:

9

Step-by-step explanation:

The pre-image is larger than the image because the scale factor is 1/3.  That means that the scale factor going from the image to the pre-image is 3.  

3 x 3 = 9

Answer:

[tex]\frac{5\sqrt{11} }{11}[/tex]

Step-by-step explanation:

To cancel out a square-rooted number at the denominator, we can multiply the square-rooted number by multiplying the square root number over again:

[tex]\frac{5}{\sqrt{11}}[/tex] * [tex]\frac{\sqrt{11}}{\sqrt{11}}[/tex]

Now, any same number of square root times another same number of a square root will cancel out the root. So [tex]\sqrt{11}[/tex] * [tex]\sqrt{11}[/tex] will equal 11.

With this information, we can now go back to the problem, so we will get:

[tex]\frac{5\sqrt{11}}{11}[/tex]

The dimensions for the scale drawing of the flag is 20 cm by 23 cm

A scale is a set of levels or numbers which are used in a particular system of measuring things or are used when comparing things.

Given that, A rectangular flag is 80 centimeters by 92 centimeters. we need to find dimensions of a scale drawing of the flag using the scale 1:4,

Therefore,

80 / 92 = 20 / 23

Hence, the dimensions for the scale drawing of the flag is 20 cm by 23 cm

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Answer:

20cm by 23cm

Step-by-step explanation:

To solve a complex fraction, which is a fraction that contains one or more fractions in its numerator and/or denominator, you can follow these steps:

Factor the numerator and denominator of the complex fraction if possible. This will make it easier to cancel common factors.

Multiply both the numerator and denominator by the reciprocal of the fraction(s) in the denominator. This will eliminate the fraction(s) in the denominator, leaving a simplified expression.

Simplify the resulting expression by combining like terms, if possible.

Check your work by multiplying the numerator and denominator of the original complex fraction by the reciprocal of the fraction(s) in the denominator, and verifying that the simplified expression you obtained is equivalent.

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The percent of the games that was lost is 26.7%.

Percentage is the ratio of two numbers expressed as a number out of 100. The sign that is used to represent percentage is %.

Percentage of the games lost = (number of games lost / total number of games) x 100

Number of games lost = total number of games - number of games won

75 - 55 = 20

Percentage of the games lost = (20 / 75) x 100 = 26.7%

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Step-by-step explanation:

fog(x)=f(x-3)

=(x-3)²+2

=x²-6x+9+2

=x²-6x+11

The coordinates of the vertex for f(x) = 3x²+6x+3 are (-1, 0).

For any equation of the type y=ax²+bx+c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is y = 3x²+ 6x+3

Here, a = 3, b = 6 and c = 3

So, h = -6/2(3)

h = -6/6

h = -1

4ac = 4(3)(3)

4ac = 36

So, k = [36 - (6)2]/4(3)

k = (36 - 36)/12

k = 0

Therefore, the coordinates of the vertex are (h,k) = (-1, 0).

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a) The numeric value at x = 4 is given as follows: f(4) = 64.

b) The logarithmic expression is given as follows: x = log2(16).

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 4(2)^x.

At x = 4, the numeric value is found replacing the lone instance of x by 4, hence:

f(4) = 4(2)^4 = 64.

For the logarithmic expression, we obtain the inverse function, hence:

64 = 4(2)^x.

2^x = 16

x = log2(16).

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Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

Using Composition of functions, the value of g(h(24)) = 1158.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

The new function h is created by combining the two functions f and g, where h(x) = f(g(x)) for all x in g's domain where g(x) is in f's domain. Function composition is denoted by the notation h = f • g, also written as h(x) = (f • g)(x), which can be interpreted as "f of g of x."

Given,

g(x) = 2x + 4, h(x) = x² +1

Using composition of functions,

⇒ h(24) = 24² + 1

⇒ g(h(24)) = 2 (24² + 1) + 4

⇒ g(h(24)) = 2 × 577 + 4

⇒ g(h(24)) = 1158

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The amount left in the container by Alice is solved to be 3/8 tsp

To find the amount left in the container the amount used to feed the fish in each case will factored and then used for subsequent feeding. of the fish.

From the problem it can be deduced that the initial amount in the container was 2 tsp

The routine feeding of the fish include:

Alice fed her fish 1/4 tsp, of food before school = 1/4 * 2 = 1/2

The 2 tsp has reduced to 1/2, this is further used as shown below

Alice fed her fish 3/4  tsp, of food after school = 3/4 * 1/2 = 3/8 tsp

We can therefore say that the amount left in the container is 3/8 tsp

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Answer:

(5n + 1)(3n - 2)

Step-by-step explanation:

Find what number multiplies into -7 and adds into -2, including the coefficient in 15n^2

The scale factor is equal to 2.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

as given, K =(5,0) (10,0)

Solution:

Initial Coordinates=(5,0)=(xi,yi)→xi=5, yi=0

Final Coordinates=(10,0)=(xf,yf)→xf=10, yf=0

Scale factor=xf/xi=yf/yi

We divide the final coordinates by the initial coordinates. In this case the ordinates (yf and yi) are zero and we can't divide by zero, but the abscissas (xf and xi) are different of zero, then we can use them:

Scale factor=xf/xi=10/5

Scale factor=2

Therefore, the scale factor is equal to 2.

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The value of X of the vertical angles would be = 1.36

The vertical angles are the type of angles that are known to be directly opposite each other which are also equal angles.

The given vertical angles are ZA and ZB.

If m A = (8x – 20)°

m B = (3x – 5)º

The vertical angles are equal, to find X;

mA = mB

8x -20 = 3x - 5

Bring the like terms together;

8x + 3x = 20- 5

11x = 15

X= 15/11

X= 1.36

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Complete question:

ZA and ZB are vertical angles. If m A = (8x – 20)° and m B = (3x – 5)º, then find the value of x.

Here you go mate!

7x + 10 = -11

answer : x = -3

-12(x + 5) = -144

Answer : x = 7

-9x - 9 = 27

Answer : x = -4

x/4 + 2 = 10

Answer : x = 32

Solving systems of linear equations in two variables by substitution involves isolating one of the variables and substituting its value into the other equation.

This can be done by adding or subtracting the same term from both sides of one equation and then using that result to substitute into the other equation.

For example, consider the system of equations below:

2x + 3y = 8

3x + 2y = 7

Start by solving for x in the first equation by subtracting 3y from both sides:

2x + 3y = 8

2x = 8 - 3y

x = (8 - 3y)/2

Now substitute this expression for x in the second equation:

3(8 - 3y)/2 + 2y = 7

24 - 9y + 2y = 7

11y = 17

y = 17/11

Finally, solve for x, add y = 17/11 to the first equation as follows:

2x + 3(17/11) = 8  

2x + 51/11 = 8  

2x = 8 - 51/11  

x = (8 - 51/11)/2  

x = 21/22

The solution is x=21/22 and y=17/11.

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After solving, the remainder when [tex]x^4 + x^3 - 2x^2 + x + 1[/tex]  is divided by x − 1 is 2.

In the given question, we have to find the remainder when [tex]x^4 + x^3 - 2x^2 + x + 1[/tex]  is divided by x − 1.

The given polynomial is [tex]x^4 + x^3 - 2x^2 + x + 1[/tex].

We have to find the remainder of the polynomial when we divide this polynomial x - 1.

To find the polynomial we equate x - 1 equal to zero to find the value of x.

x - 1 = 0

x = 1

Now putting x = 1 in the given equation [tex]x^4 + x^3 - 2x^2 + x + 1[/tex].

P(x) = [tex](1)^4 + (1)^3 - 2(1)^2 + 1 + 1[/tex]

P(x) = 1 + 1 - 2×1 + 1 + 1

P(x) = 2 - 2 + 2

P(x) = 2

Hence, the remainder when [tex]x^4 + x^3 - 2x^2 + x + 1[/tex]  is divided by x − 1 is 2.

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The complete question is:

What is the remainder when [tex]x^4 + x^3 - 2x^2 + x + 1[/tex]  is divided by x − 1?

Answer:

The length of the shorter leg of the triangle can be calculated using the Pythagorean Theorem. The formula is a^2 + b^2 = c^2, where a is the length of the shorter leg, b is the length of the longer leg and c is the length of the hypotenuse. In this case, a^2 + 52^2 = c^2. The hypotenuse can be calculated by using the sine formula. c = (52/sinA). Substituting this value into the Pythagorean Theorem equation, a^2 + 52^2 = (52/sinA)^2. Solving for a, a = sqrt(52^2 - (52/sinA)^2).

A triangle is a three-sided polygon with three angles, each angle is formed by the intersection of two sides of the triangle and these angles are labeled with the corresponding vertex.

There are three angles in a triangle ABC. A triangle is a three-sided polygon and it has three angles. Each angle is formed by the intersection of two sides of the triangle.

In a triangle, the angle between two sides is measured in degrees and these angles are formed by the intersection of the two lines that represent the sides of the triangle. The three angles in a triangle are labeled with the corresponding vertex, for example, angle A, angle B, and angle C.

In a triangle, the sum of the three angles is always 180 degrees. This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.

Therefore, In short, a triangle is a three-sided polygon with three angles, each angle is formed by the intersection of two sides of the triangle and these angles are labeled with the corresponding vertex. The sum of the three angles in a triangle is always 180 degrees.

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For given functions for zombies and vampires,  zombies will reach 50,000 first.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

Initial numbers, 100 Zombies and 100 Vampires.

In function z(t), the zombies increase in population by 1000 per day,

and in function V(t), the vampire population increases by 25% each day,

Therefore, z(t)=100+1000t where t=no, of days and

v(t)=100+25t where t= no. of days

for z(t)=50000

100+1000t=50000

t=49900/1000=49.9≈50days

for v(t)=50000

100+25t=50000

t=49900/25=1996 days

Hence,

          zombies will reach 50,000 first.

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For given functions for zombies and vampires,  zombies will reach 50,000 first.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

Initial numbers, 100 Zombies and 100 Vampires.

In function z(t), the zombies increase in population by 1000 per day,

and in function V(t), the vampire population increases by 25% each day,

Therefore, z(t)=100+1000t where t=no, of days and

v(t)=100+25t where t= no. of days

for z(t)=50000

100+1000t=50000

t=49900/1000=49.9≈50days

for v(t)=50000

100+25t=50000

t=49900/25=1996 days

Hence,

         zombies will reach 50,000 first.

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Answer: 6 divided by 2/3 = 9

Step-by-step explanation:

For division always take the first number in the word problem so in this question the answer would be 6 then you take the 2/3 and divide it by 6. So it would be 6 divided by 2/3. then you take the 9 from the word problem  and do 6 divided by 2/3 equals 9. So in this question the answer would be option 2 or could also be called option B. And if this is it that means the answer is, 6 divided by 2/3 = 9.

The division equation which representant this situation is 6 ÷ 2/3 = 9.

Division equations are mathematical equations with the division operator in them. Division equations are useful not only in math class, but in everyday life as well. For example, if we wanted to evenly distribute a bag of candies among our friends, we could use division to find our answer. Assume we have 100 candy bars and four friends. Divide 100 by 4 to find out how many candies each person gets. We discover that our answer is 25, which means that each of our friends receives 25 candies.

It's our job to figure out what the division equals. This can be represented by a variable, such as x. As a result, our total division equation will be: 100/4=x. On both sides of the equals sign, we have things.

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Answer:

sorry its so long

Step-by-step explanation:

We multiply the entire equation by the number

6

6 in order to get rid of the fractions.

2

�

+

3

�

=

6

5

�

=

6

�

=

6

5

=

1

1

5

1

1

5

ℎ

=

1

hour

12

minutes

2x+3x

5x

x

1

5

1

​

h

​

=6

=6

=

5

6

​

=1

5

1

​

The events from "Let George Do It!" in the right sequence will be:

From 1946 to 1954, Owen and Pauline Vinson produced the radio drama series Let George Do It in the United States.

In 1954, Olan Soule voiced the role of private eye George Valentine, which was portrayed by Bob Bailey. The scripts by David Victor and Jackson Gillis were directed by Don Clark.

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Answer:

[tex]x\sqrt{x}[/tex]

Step-by-step explanation:

Use Exponent Power rule:

[tex]b^{1/n} =\sqrt[n]{b}[/tex]

Given [tex]\sqrt{x^3}[/tex] also known as [tex]\sqrt[2]{x^3}[/tex], rewrite with exponent power rule as [tex]x^{3/2}[/tex].

Factor [tex]x[/tex] from [tex]x^{3/2}[/tex] = [tex]x(x^{1/2})[/tex]

Rewrite as [tex]x\sqrt{x}[/tex]

Answer:

follow me first

Step-by-step explanation:

i will answer that in 60 sec

Answer:

B

Step-by-step explanation:

1. Before anything, figure out the inequality symbol. Why? In the solutions, all of the inequalities are different so you narrow it down by figuring out the inequality sign.

2. "At most 50 pounds" means we can't go over 50 pounds, but the package can still equal 50, that's just the most it can be. This means we will have a line underneath because it includes the maximum number, 50, in the solution.

3. "At most" also means the package (x) cannot be over 50. The sign opening must face 50 because that shows x has to be less than. But it can equal 50, so the sign is [tex]x\leq 50[/tex]. That would be B.

4. About the numbers, the box weighs 2 pounds. This means it is x+2 because weight is not negative and it is ADDING weight to what we don't know. To isolate x, just do 50-2, and you get 48. That again proves b is the answer.

Answer: The median is 19

Step-by-step explanation:

To find the median you have to arrange the numbers from lowest to highest.
It would go like this: 13, 15, 16, 22, 24, 28

Pick the number that is in the middle. In this case, it would be 16 and 22. The median of these numbers is the mean of these 2.

To find the mean you add 16 and 22 together to get 38 and divided it by 2 to get 19.

I hope this was able to help you :D