the base of a triangular pyramid is a right-angled triangle with a hypotenuse of 6 cm and an acute angle of 30°. all side faces form 60° with the base. calculate the exact volume of the pyramid​

The graph of the function f(x) = −15|x−40|+8 will be a piecewise linear function.

Graph explain: What is it?

A graph is defined as a mathematical structure that connects a collection of points to express a specific function. A pairwise relationship between the objects is established using it. The edges that connect the graph's vertices (also known as nodes) are its vertices (lines).

It will be a V-shape, with the vertex at x = 40 and y = 8.

On the left side of the vertex, the function will be decreasing, representing Tyra moving away from home.

On the right side of the vertex, the function will be increasing, representing Tyra moving towards home.

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

Key features of the graph in the context of the situation:

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

The left side of the vertex represents the time period when Tyra is moving away from home, and the right side represents the time period when Tyra is moving towards home.

The slope of the graph on the left side of the vertex is negative, indicating that Tyra is moving away from home at a decreasing rate, while the slope of the graph on the right side of the vertex is positive, indicating that Tyra is moving towards home at an increasing rate.

The y-intercept is at 8, which means Tyra starts 8 miles away from home.

The graph is symmetric about the y-axis because for every time x on the left side of the vertex, there is a corresponding time on the right side of the vertex.

The graph is not a function because for every x value, there are two y values, one for when Tyra is moving away from home and one for when Tyra is moving towards home.

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(a). The values of x for which f(x) = 8, are x = (-1 + √17) / 2 and x = (-1 - √17) / 2.

(b). The equation has no real roots, and f(x) never equals 5.

(c). The equation has no real roots, and f(x) never equals -5.

(d). The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

What is algebraic value?

A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x.

a.

To find the values of x for which f(x) = 8,

we need to solve the equation x² +10x +32 / x+5 = 8.

We can start by multiplying both sides of the equation by (x+5) to get rid of the fraction:

x² + 10x + 32 = 8(x + 5)

Expanding the right side:

x²  + 10x + 32 = 8x + 40

Subtracting 8x from both sides:

x²  + 2x + 32 = 40

Subtracting 32 from both sides:

x² + 2x = 8

Dividing both sides by 2:

x² + x = 4

Subtracting 4 from both sides:

x² + x - 4 = 0

We can use the quadratic formula to solve this equation:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -4.

So,

x = (-1 ± √(1² - 4 * 1 * -4)) / 2 * 1

x = (-1 ± √(1 + 16)) / 2

x = (-1 ± √17) / 2

Thus, the two solutions are x = (-1 + √17) / 2 and x = (-1 - √17) / 2. These are the values of x for which f(x) = 8.

b. To show that f(x) never equals 5, we need to show that there is no solution to the equation (x² + 10x + 32)/(x + 5) = 5.

Suppose there is such a solution, say x = a.

Then,

5(x + 5) = x² + 10x + 32

5x + 25 = x² + 10x + 32

-x² + 5x - 7 = 0

This is a quadratic equation and can be solved using the quadratic formula. However, we can see that the equation has no real solutions because the discriminant, b² - 4ac, is negative. Therefore, the equation has no real roots, and f(x) never equals 5.

c. To determine whether f(x) ever equals -5, we can follow a similar approach as in part b.

Suppose there is a solution to the equation (x² + 10x + 32)/(x + 5) = -5. Then,

-5(x + 5) = x² + 10x + 32

-5x - 25 = x² + 10x + 32

x² - 15x + -57 = 0

This is a quadratic equation and can be solved using the quadratic formula. However, we can see that the equation has no real solutions because the discriminant, b² - 4ac, is negative. Therefore, the equation has no real roots, and f(x) never equals -5.

d. To confirm the results of parts a, b, and c, we can plot the graph of the function f(x) = (x² + 10x + 32)/(x + 5) and sketch the result.

The graph of the function will show the x-intercepts and the y-intercepts and will also show any asymptotes.

The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

Hence, (a). The values of x for which f(x) = 8, are x = (-1 + √17) / 2 and x = (-1 - √17) / 2.

(b). The equation has no real roots, and f(x) never equals 5.

(c). The equation has no real roots, and f(x) never equals -5.

(d). The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

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For greatest integer function,

domain :  set of all real numbers (ℝ)

range : set of all integers (ℤ)

We know that the greatest integer function of any real number n is the integer which is less than or equal to the given number n.

The mathematical definition of greatest integer function is :

f(x) = minimum { p ∈ Z ; p ≤ x }

where Z is the set of integers.

A greatest integer function is also known as the floor function.

The symbol to represent greatest integer function is  ⌊ ⌋.

We can write greatest integer function for x as ⌊x⌋

The for x = 1.98,

⌊1.58⌋ = 1

From above definition of floor function, we can say that the domain of greatest integer function is the set of all real numbers (R) whereas the range of  is the set of all integers (Z).

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Answer:

y = 10 and x = 5

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5\sqrt{3} }{y}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

y × [tex]\sqrt{3}[/tex] = 10[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

y = 10

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

using Pythagoras' identity in the right triangle

x² + (5[tex]\sqrt{3}[/tex] )² = y² = 10²

x² + 75 = 100 ( subtract 75 from both sides )

x² = 25 ( take square root of both sides )

x = [tex]\sqrt{25}[/tex] = 5

The ideal utilization would be $150but he can choose to borrow $1050

A credit card is a type of credit facility, provided by banks that allow customers to borrow funds within a pre-approved credit limit. It enables customers to make purchase transactions on goods and services.

Given here: Bob's credit limit is $3500 and he has a balance of $2200

Therefore available credit is equal to $3500-$2200=$1300

Thus if he spends more than $1300 then he goes over his limit.

But ideal utilization ratio is 30% and therefore 30%×3500=$1050

Thus ideal credit usage would be = 3500-1050

                                                        =2450

Then $2450-$2200=150

Hence, The ideal utilization would be $150but he can choose to borrow $1050

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The rules of multiplication are Associative Property, Commutative Property, Distributive Property, and Identity Property, and the rules of addition are Addition of two positive numbers is always positive, and the addition of two negative numbers is always negative.

The properties of multiplication are particular rules that are used while multiplying numbers. These properties help simplify expressions easily and, hence, have a significant role in solving all kinds of mathematical expressions, whether algebraic expressions, fractions, or integers.

Associative Property: (P × Q) × R = P × (Q × R)

For example, (4 × 5) × 3 = 4 × (5 × 3) = 60.

Commutative Property: P × Q = Q × P

For example, 3 × 4 × 2 = 2 × 3 × 4 = 24.

Distributive Property: P(Q + R) = PQ + PR; P(Q - R) = PQ - PR

For example, 3(2 + 4) = (3 × 2) + (3 × 4) = 6 + 12 = 18.

Identity Property: P × 1 = P

For example, 4 × 1 = 4, or 1 × 27 = 27.

The addition means summing up two or more numbers or values to get another number.

Positive + Positive  Addition (Sign will be Positive)  3 + 4 = 7

Negative + Negative  Addition (Sign will be negative)  – 3 + (-4) = -7

Positive + Negative  Subtraction (Sign of greater number)  3 + (-4) = -1

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1,40,000 Rs. is his original Salary.

Let the original Salary of the man be = X

His New Salary =  1,54,000 Rs.   (given)

X + (10/100 × X ) = 154000

X + (X/10) = 154000

11X / 10 =154000

X = 154000 × (10/11)

x = 140000

Hence we can say that his original Salary was 1,40,000 Rs.

Answer:

a=7300, b=1.0108.

L(t) = 7300(1.0108)^t

Step-by-step explanation:

First, we can see that L(t) = 7300(1.012)^(4t) can be rewritten as L(t) = 7300e^(4tln(1.012))

Using the properties of logarithms, we can simplify this to L(t) = 7300e^(4t(ln(1.012))

Now, we can see that the function L(t) is in the form L(t) = ab^t, where a = 7300 and b = e^(ln(1.012))

Therefore, we can write the equivalent function as L(t) = 7300e^(0.048t)

The final values rounded to 4 decimal places are a=7300, b=1.0108.

L(t) = 7300(1.0108)^t

Answer

L(t)=

7300

1.0489

7300(1.0489)

Step-by-step explanation:

The 2nd step when solving for systems of equations using the elimination method is explained below.

Equations in math is defined as a mathematical statement that shows that two mathematical expressions are equal.

Here we need to find the steps to the 2nd step when solving for systems of equations using the elimination method.

Here first we need to find Enter the equations.

And then multiply each equation by a number to get the lowest common multiple for one of the variables.

And then add or subtract the two equations to eliminate that variable .

Now we have to substitute that variable into one of the equations and solve for the other variable.

Finally we have to check by substituting your answer into one of the equations,

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Answer:

Step-by-step explanation:

Answer:

KS24 add K27ab4 6b3r1b olps

i have the awnser in the box

Part A:

The graph of the function g(x) = |x - 7| is a V-shaped graph that opens upwards and has a vertex at x = 7. The vertex is the midpoint of the graph and occurs at the value of x where the absolute value changes from positive to negative. The domain of the function is all real numbers and the range is all non-negative numbers.

Part B:

The transformation from f(x) to h(x) occurs by shifting the graph of the parent function up by 2 units along the y-axis. In other words, every y-coordinate in the graph of f(x) is increased by 2 in the graph of h(x). The vertex of the parent function is (0,0) and is shifted to (0,2) in the transformed function. The range of h(x) is all non-negative numbers greater than or equal to 2.

Answer:

50/30, 25/15, 10/6, 5/3

Step-by-step explanation:

To answer the question, you need to decompose the numerator and denominator into simple factors and see what combinations are possible.

50:2 = 25
25:5 = 5
5:5 = 1
Multipliers for 50: 2, 5, 5

30:2 = 15
15:3 = 5
5:5 = 1
Multipliers for 30: 2, 3, 5

Common multipliers for dogs and cats: 2 and 5
So we can divide the our ratio by 2, by 5 and by their product 2 x 5 = by 10.

We get the following series:
50/30, 25/15, 10/6, 5/3

Answer:

x > -1 1/3

Step-by-step explanation:

-9x + 5 < 17

Subtract 5 on each side

-9x < 17

divide by -9 on each side, which causes for the greater than sign to flip because we are dividing by a negative

x > -1 1/3

Answer:

90-99=86x45[80[

Step-by-step explanation:

Answer:

The function g(x) = √(x - 3) is defined for all real numbers x such that x - 3 ≥ 0, since the square root of a non-negative number is a real number.

Solving for x, we have:

x - 3 ≥ 0

x ≥ 3

Therefore, the domain of the function is D: [3, ∞).

Since the square root of a non-negative number is always non-negative, the range of the function is R: [0, ∞).

Therefore, the correct answer is: A. D: [3, ∞) and R: [0, ∞).

The price of the Pie will be $12 and the price of the cake will be $15.

We will solve this problem with the help of equations.

Let the price of Pie be $X and the price of Cake be $Y.

According to a given question in November, they sold 400 Pie and 250 Cake and the total amount is $8550.

So our first equation will be,

400X + 250Y = 8550.

And in December they sold 300 pies and 500 cakes respectively totaling $11100.

So our second equation will be:

300X + 500Y = 11100.

Taking the value of X from our first equation we get:

X = (8550-250Y)/400

Putting it in our second equation we get:

300(8550-250Y)/400 + 500Y = 11100

On solving this:

3/4(8550-250Y)+500Y = 11100

25650/4 - 750/4 Y + 500Y = 11100

1250/4 Y = 18750/4

Y = 15

So the price of the Cake is $15.

Similarly, we can find the price of Pie as (8550-250*15)/400 = 12

So the price of the pie is $12.

Therefore the price of the pie is $12 and the cake price is $15.

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Since 3* + 4x + 2k equals the value of k= -2, the polynomial's zero is 2. A polynomial is an equation with variables, constants, and other terms.

A polynomial is a mathematical expression made up of variables (also known as indeterminates) and coefficients. It can be expressed using only the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that contains variables, constants, and exponents and is based on the operations of addition, subtraction, multiplication, and division of numbers (No division operation by a variable).

Given that -2 is a zero in the equation

f(x)=3a*+4x+2

k, f(-2)=0 :3(-2) +4 (-2) +2k=0\s

=>12-8+2k=0\s

=>2k=-4\s

=>k=-2

Since 3z + 4x + 2k is the value of k = -2, the polynomial's zero is 2.

Complete question:

What is the value of k in the quadratic polynomial 3x². The polynomial 3x2 4x 2k has a zero for what value of k(-2).

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The quadratic polynomial 3x² does not include a term with the variable k.

The expression 3x² is a second degree polynomial, also known as a quadratic, but it does not include a term with the variable k. The general form of a quadratic polynomial is ax² + bx + c, where a, b, and c are coefficients and x is the variable.

In this case, the coefficient of x² is 3, the coefficient of x is 0, and the constant term is 0. The variable k is not present in the expression 3x², so it is not possible to determine its value.

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Complete Question:

What is the value of k in the quadratic polynomial 3x²?.

well the bottom number the bigger the number means it's small The small the number the bigger it is

so 5/8 and 3/8 They're the smallest again the bigger the number means it's small now we will look at the top 5 is bigger than 3 so 3/8 is first and 5/8 is next. The rest I let you solve.

The longest side c of an acute triangle is the one opposite the largest angle γ. To determine its length, use the law of cosines: c = √(a²+ b² - 2ab cos(γ)), where a and b are the two shorter sides of the triangle.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Answer:

10 1/8

Step-by-step explanation:

good luck to you :)

Answer:

10 1/8

Step-by-step explanation:

hope this helps good luck!

The value of {b} is equivalent to 4.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given are two intersecting lines.

The two intersect to create two pairs of vertically opposite angles. We can write -

(5b + 16)° = (b + 32)°

5b - b = 32 - 16

4b = 16

b = 4

Therefore, the value of {b} is equivalent to 4.

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{Question in english is given below -

The figure shows two lines cut by a transversal. (5b + 16)° (b + 32)°.​}

The set of all possible solutions to a linear equation with two variables is called the solution set. Specifically, the collection of all ordered pairs that are equivalent to the equation.

A region always appears on the graph of the solution to a linear inequality. However, that set might not always include the boundary. The "or equal to" part of the inclusive inequality made the line a part of the solution set in the previous example.

Any value of a variable that makes the equation true is a solution. The set of all variables that makes the equation true is called a solution set. Because 2(4) + 6 = 14, the solution set for 2y + 6 = 14 is 4.

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The wrapping paper Marcus have left is 5 5 / 12 feet.

Marcus buys 7 3/4 feet of wrapping paper. He lets his sister use 2 1/3 feet of the wrapping paper to wrap a gift.

The amount of wrapping paper Marcus have left can be calculated as follows:

The amount of wrapping paper Marcus have left is the subtraction of the paper used by the sister by the wrapping paper he had initially.

Hence,

wrapping paper Marcus have left = 7 3 / 4 - 2 1 / 3

wrapping paper Marcus have left = 31 / 4 - 7 / 3

wrapping paper Marcus have left = 93 - 28 / 12

wrapping paper Marcus have left = 65 / 12

Therefore,

wrapping paper Marcus have left = 5 5 / 12 feet

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The statement with the correct value is C. 9

Simple substitution is a topic which are mathematical expressions with variables whose value/s has been given. Thus it is just required to solve the question by simple substitution of the given value in the expression. Example, given that a = 2, determine the value if a + 6.

This can be solved by substituting 2 for a in the question, so that;

a + 6 = 2 + 6

          = 8

Therefore, it can be deduced from the given question that;

-2z + 1, but z = -4

Thus,

-2z + 1 = -2(-4) + 1

          = 8 + 1

          = 9

To complete the statement, the correct value is 9. Option C.

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The final graph is given below in the image.

The equation is [tex]y = -\frac{3}{4}x - 2[/tex]

The graph of a linear equation in two variables is a line (that's why they call it linear).

If you know an equation is linear, you can graph it by finding any two solutions

(x1,y1) and (x2,y2)

plotting these two points, and drawing the line connecting them.

You can find two solutions, corresponding to the x-intercepts and y-intercepts of the graph, by setting first x=0 and then y=0.

To graph the line [tex]y = -\frac{3}{4}x - 2[/tex] we are going to take advantage of the fact that its y-intercept is -2 when x = 0, so our first point is (0,-2). To find our second point, we are going to find the x-intercept; to do it, we are going to set y = 0 and solve for x:

[tex]y = -\frac{3}{4}x - 2\\0 = -\frac{3}{4}x - 2\\2 = -\frac{3}{4}x \\x = -\frac{8}{3}[/tex]

Now, we have our second point (0, -8/3), we just need to join the 2 points with a straight line.

The final graph is given below in the image.

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The Required Equations are y=2(x+3) and y=3x-2

Given:

'y' represents the larger number and

'x' represents the smaller number

Consequently, a greater number is double the sum of three, and a smaller number is larger no = double of ( 3 and smaller number)

The necessary equation for the first condition is y=2(x+3).

The bigger figure is now two less than three times the smaller one.

For the first condition, the equation is larger number Equals three times smaller number and two less, or y=3x-2.

Therefore, y=2(x+3) and y=3x-2 are the Required Equations.

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The midpoint of the line segments with

1) (-4,-2), (3, 3) is ( -1/2 , 1/2).

2) (−1, −6), (−6, 5) is ( -7/2 , -1/2 ).

3) (2, 4), (1, −3) is ( 3/2 , -1/2).

In geometry, the midpoint is defined as the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. To determine the midpoint, just add the two X-values, then divide by 2 and add the two Y-values, then divide by 2. Mathematically, let (xm , ym) be coordinates of mid point of line segment ents with end points ( x₁, y₁) , (x₂, y₂). Then, xₘ =( x₁ + x₂)/2 and yₘ = ( y₁ + y₂)/2

We have , the line segments with coordinates

1) (-4,-2), (3, 3)

Midpoint = ( (-4 + 3)/2 , (-2 + 3/2) )

= ( -1/2 , 1/2)

2) (−1, −6), (−6, 5)

Midpoint = ( ( -6 +(-1))/2 , ( -6 + 5)/2)

= ( -7/2 , -1/2 )

3) (2, 4), (1, −3)

Midpoint = ((2 + 1)/2 , (4+(-3))/2)

= ( 3/2 , -1/2)

Hence, we got all midpoints for line segments.

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Complete question:

Geometry - Clark Midpoint and Distance Formulas

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Find the midpoint of the line segment with the given endpoints.

1) (-4,-2), (3, 3)

2) (−1, −6), (−6, 5)

3(2, 4), (1, −3)