a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 8feet from the base of the building. How high up does the ladder reach?

Answer:

53

Step-by-step explanation:

The Pythagorean theorem rounding of 16 and 18 would be = 24 (approximately)

Pythagorean theorem is defined as the theorem that expresses the relationship that exists between the three side of a right angle triangle.

The relationship states that the square of the longest side is equal to the sum of the square of the other two sides.

That is, c² = a² + b²

Where, a = 16

b = 18

c² = 16²+18²

c² = 256 + 324

c² = 580

C =√580

C = 24.1

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Answer:Don't know

Step-by-step explanation:

Answer:

[tex](x,y)\rightarrow(1,2)[/tex]

Step-by-step explanation:

Multiply first equation by 3 to help cancel out the "y" variable:

[tex]\displaystyle \left \{ {{x+y=3} \atop {x-3y=-5}} \right.\\\\\rightarrow \left \{ {{3x+3y=9} \atop {x-3y=-5}} \right.[/tex]

Combine system of equations on both sides:

[tex](3x+3y)+(x-3y)=9+(-5)\\4x=9-5\\4x=4\\x=1[/tex]

Thus,

[tex]x+y=3\\1+y=3\\y=2[/tex]

Time taken to cross the field will be 3.36 seconds.

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. There are four different types of speed. constant speed, varying speed, an average rate, instantaneous speed.

Solution,

Given,

speed=60 mph

length of football field=0.056 miles

time taken to cross it = distance/speed

time=0.056/60=0.00093 hour = 3.36 seconds.

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The equivalent expression would be; function G(t) = 86,400•3^t

What is a function in simple definition?

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 codomain or range.

The number of views on a viral video can be modeled by the function

G(t) = 2500(5) 2-4.

we have to find out an equivalent function of the form G(t) = ab.

Here, we want to make a transformation

From what we have;

G(t) = 2500(5)^(t - 4)

From indices, we know that;

x^(a + b) = x^a•x^b

Thus, we have it that;

G(t) = 2500•3^t•3^2

G(t) = (9 * 9600) * 3^t

G(t) = 86,400•3^t

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Even though this relationship is proportional, not all of these ratios are equal.

Verify that the ratios provided are equal. The ratios of 3:5 and 15:25 are both equal. Because the first ratio 3: 5 can be derived by multiplying the ratio 15: 25 by 5 on both the numerator and denominator. The initial ratio of 3: 5 can be multiplied by 5 to get the ratio 15: 25, and vice versa.

This indicates that you would require an 8 fl oz can (a quarter of a quart) of Part B if you were ordering a quart of Part A. You will have 1.25 after combining Parts A and B.

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Answer: Values; 6,8,10

Step-by-step explanation:

❌ 2 + 5 > 10

❌ 4 + 5 > 10

✔️ 6 + 5 > 10

✔️ 8 + 5 > 10

✔️ 10 + 5 > 10

The value of x in the give trigonometrical question is 10.6 when hypotenuse is 13 in the right angled triangle.

Trigonometry is the branch of mathematics that deals with particular functions of angles and how to use them in calculations. There are six common trigonometric uses for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their respective names and acronyms.

The figure illustrates these six trigonometric functions in relation to a right triangle. For instance, the triangle has an angle A, and the sine of A, or sin A, is defined as the ratio between the side opposite to A and the side opposite to the right angle (the hypotenuse).

Cos 35° = x/13

0.819152 = x/13

x = 0.819152 × 13

x = 10.6

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The piecewise function represented by the graph is:

f(x) = 2x when -3 ≤ x < 0

f(x) = 3 When 1/2 < x < 3/2

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Let f(x) = y = mx + c

From the graph, when -3 ≤ x < 0.

(-3, -6) and (-1, -2)

m = (-2 + 6) / (-1 + 3) = 4 / 2 = 2

(-1, -2) = (x, y)

-2 = 2 x (-1) + c

-2 = -2 + c

c = 0

f(x) = 2x

From the graph, When 1/2 < x < 3/2.

It is a horizontal line of y = 3.

f(x) = 3

Thus,

f(x) = 2x when -3 ≤ x < 0

f(x) = 3 When 1/2 < x < 3/2

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The area of the actual gymnasium is 25,650 square feet.

We know that the scale factor of the blueprint to the actual gymnasium is 1 in 15 ft, which means that every 1 inch on the blueprint represents 15 feet in the actual gymnasium. To find the area of the actual gymnasium, we can use the formula:

Area of actual = (Area of blueprint) x (Scale factor)²

We know that the area of the floor on the blueprint is 114 square inches, so we can plug that into the formula:

Area of actual = 114 in² x (15 ft/1 in)² = 114 in² x 225 ft² = 25,650 ft²

Therefore, the area of the actual gymnasium is 25,650 square feet.

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An inverse does not exist for a parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

An inverse does not exist for a parabola.

One definition of a parabola includes a line and a point (the focus) (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, an inverse does not exist for a parabola.

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a. The system of equations is given as follows:

35x = 15 + 32x.

The solution is given as follows:

x = 5.

b. The meaning of the solution is that the cost to purchase 5 jackets in each company is the same.

c. Gabriela should choose Anastasia's Monogram, as the function has a lower numeric value when x = 10.

The cost per jacket for each company is constant, hence a linear function is used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Hence the functions for each company are given as follows:

The system of equations is used to find when both will have the same cost, as follows:

35x = 32x + 15

3x = 15

x = 5 jackets.

For 10 jackets, the costs are given as follows:

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2170 toys Jamal assemble altogether during his first 20 days.

What is the arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Here, we have

Given: Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he assembled 137 toys. He noticed that since he started, every day he assembled 3 more toys than the day before.

We have to find how many toys did Jamal assemble altogether during his first 20 days.

We apply the arithmetic sequence formula and we get

tₙ = t₁ + (n-1)d

137 = t₁ + (20-1)(3)

t₁ = 80

To calculate the total number of toys that Jamal assemble in his first 20 days,

S₂₀ = (20/2)(2×80 + (20-1)(3))

S₂₀ = 2170

Hence, 2170 toys Jamal assemble altogether during his first 20 days.

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The process to solve 3 equations with 3 unknown  is explained below.

The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign.

The process of 3 equation with 3 unknown variable is explained step by step as follows:

First of all we have to write all the equations in standard form cleared of decimals or fractions.

And then we have to choose a variable to eliminate them then we have to choose any two of the three equations and eliminate the chosen variable.

After that we have to select a different set of two equations and eliminate the same variable as in Step 2.

Now, we have to solve the two equations from steps 2 and 3 for the two variables they contain.

And then we have to substitute the answers from Step 4 into any equation involving the remaining variable.

And then finally we have to check the solution with all three original equations.

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Answer:

e-5

Pretty simple

The smallest distance it has to go to get back to the starting tree is [tex]3\sqrt{5}[/tex]when traveling 6 miles to the south before turning 3 miles to the east.

According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool.

given

by pythagoras theorem :-

shortest distance = [tex]c^{2} = a^{2} + b^{2} \\[/tex]

[tex]c^{2} = 6^{2} + 3^{2} \\c^{2} = 36 + 9\\c^{2} = 45\\c = 3\sqrt{5}[/tex]

The smallest distance it has to go to get back to the starting tree is [tex]3\sqrt{5}[/tex]when traveling 6 miles to the south before turning 3 miles to the east.

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The length of the 3rd side cannot be determined without at least one more side length.

In order to calculate the length of the third side of a triangle, we must also have the lengths of the other two sides. This is because the sum of the three sides of a triangle must equal 180°, so the length of one side can be determined from the other two. For example, if two sides have lengths of 4 and 8, then the third side must have a length of 8, as

4 + 8 + 8 = 180°.

Without knowing the lengths of the other two sides, it is impossible to calculate the length of the third side.

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Answer:

c) 16 cm²

Step-by-step explanation:

Given information,

→ Base = 4 cm

→ Height = 8 cm

Area of triangle formula,

→ Area = ½ × b × h

Now the area of triangle is,

→ ½ × b × h

→ ½ × 4 × 8

→ 2 × 8

→ 16 cm²

Hence, the area is 16 cm².

Answer:

around 18%

Step-by-step explanation:

14.30/80=0.17875

0.17875*100=17.875

18%

Answer:

Step-by-step explanation:

the answer is [tex]\frac{14.30}{80}[/tex]=17.875%

Answer:

Degree: 4

Number of terms: 4

Leading Coefficient: 4

Constant: -20

Step-by-step explanation:

1) Expand (x+3)(x-4) into x^2 - x - 12

2) Combine like terms; equation becomes 4x^4 + x^2 + 4x - 20

3) Degree is looking for the highest exponent; in this case, it's 4

4) Number of terms is looking for how many terms there are in this equation; there are 4 terms

5) Leading Coefficient is looking for the coefficient of the term with the highest exponent, so the answer is 4

6) Constant is looking for the term without a variable

Hope this helps!

These are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.

A parent function is the simplest form that a function can be. Its basic shape is not in any way altered. In mathematics, you see certain graphs over and over again. For that reason, these original, common functions are called parent graphs, and they include graphs of quadratic functions, square roots, absolute values, cubics, and cube roots.

For instance, when you see a u-shaped graph that is inverted and vertically stretched, you should still recognize that it is a parabola which has undergone different transformations.

We can take a few examples to understand this concept further.

Now, there are 6 parent functions:

Hence, these are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.

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Answer:

2 pie over r

Step-by-step explanation:

Step-by-step explanation:

the circumference is given by:

[tex]2\pi(radius)[/tex]

in this case x is the radius hence the circumference would be:

[tex]2\pi(x)[/tex]

hope this helps :)

The function graph is Linear Constant. Option C

We know that when we plot a graph, there would be the vertical and the horizontal axis. We can be able to deduce the nature of the graph when we look at how the graph is going.

In this case, we can see that the graph is flat. The flatness of the graph would show us that there is neither an increase nor a decrease in the function that we have in view. The increase or the decrease can be seen from the direction of the line that is drawn across the graph.

Hence, the fact that the line is flat on the graph shows that it is linear constant.

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Which statement.........

The speed of Ana is in miles per hour 7.5mph

By dividing the distance Ana covered by the amount of time she spent running, one may calculate her speed in miles per hour. Since the question asks for the speed to be calculated in miles per hour, an hour rather than a minute would be utilized as the unit of time.

Speed = distance ÷ time

Distance =  3/4

Time =  1/10

Speed = 3/4  ÷  1/10

Speed =  3/4   x 10 = 15/2 miles per hour

or, 7.5mph

Divide the distance Ana covered by the time she ran to get her speed.

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The question is incomplete

Ana runs 3/4 mile in 6 minutes or 1/10 hour. Assuming she runs at a constant rate, what is her speed, in miles per hour