Solve (t-3)^2=6. The arrow is at a height of 48ft after approximately ____s and after ___s

The Vales of x in the equations are : 1) 3 (2) 1  (3) 5  (4) 14  (5) 10 respectively

A linear equation in one variable is that in which the highest power of its variable is 1

The given equations and their solutions are

2x +1 = 7

By collecting like terms we have

2x = 3

x = 3

2) The given equation is 4x +7 = 11

By collecting like terms we have

4x = 4

Making x the subject we have

x = 1

3) 2x -3 = 7

By collecting like terms we have

2x = 10

Making x the subject we have

x = 5

4) 1/2 x - 3 = 7

By collecting like terms we have

1/2x = 7

x= 14

5) The given equation is 3x - 11 = 19

By collecting like terms we have

3x= 30

Therefore x= 10

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Answer:

Step-by-step explanation:

It is a vertical parabola. The equation of a vertical parabola can be written in the form y = a(x-h)² + k, where a>0 and (h,k) is the vertex.

You can eliminate G and I because the leading coefficient is negative.

The graph isn't marked with units, but both F and H say that the vertex is at (0,-2), so you know that each square on the graph is one unit.

Now look for another clue.

The x-intercepts are at (-1,0) and (1,0). Plug one of the points into F and H.

F: 0 = 2·1² - 2

H: 0 ≠ 1² - 2

So, F represents the graph.

Answer:

-88

Step-by-step explanation:

another solution:

x-3=0→x=3

r = f(3) = 3³ - 14(3)² + 7×3 - 10 = 27 - 126 + 21 - 10 = -88

Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.  

To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.

The factor corresponding to x = 3 is (x - 3).

The factor corresponding to x = -4 is (x + 4).

The factor corresponding to x = 5 is (x - 5).

To obtain the polynomial, we multiply these factors together:

P(x) = (x - 3)(x + 4)(x - 5)

Expanding this expression gives us:

\(P(x) = (x^2 - 3x + 4x - 12)(x - 5)\)

\(= (x^2 + x - 12)(x - 5)\)

\(= x^3 - 5x^2 + x^2 - 5x - 12x + 60\)

\(= x^3 - 4x^2 - 17x + 60\).

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Answer:

the length of the rectangle is 19 inches.

Step-by-step explanation:

Let's start by setting up equations based on the information given.

Let L be the length and W be the width of the rectangle. We know that:

L = 3W + 7 (because the length is 7 inches more than 3 times the width)

Area of rectangle = LW = 76

Now we can substitute the first equation into the second equation to get:

(3W + 7)W = 76

Simplifying, we get:

3W^2 + 7W - 76 = 0

We can solve for W by using the quadratic formula:

W = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = 7, and c = -76. Plugging in these values, we get:

W = (-7 ± sqrt(7^2 - 4(3)(-76))) / 2(3)

W ≈ 4 or W ≈ -6.33

We can ignore the negative solution since the width cannot be negative. So the width of the rectangle is approximately 4 inches.

To find the length, we can use the first equation we set up:

L = 3W + 7

L = 3(4) + 7

L = 19

So the length of the rectangle is 19 inches.

Answer:

......................................................

......................................................

in LMNP rectangle

LN and MP are diagonals

so, LN and MP are Equal

x = 2x - 2

2 = 2x - x

2 = x

The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

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Answer

There were 15 oranges initially.

There were 45 apples initially.

Hence, there were (15 + 45) = 60 fruits there initially.

Explanation

Let the number of oranges be x

Let the number of apples be y

The ratio of the number of oranges to the number of apples is 1 : 3 implies:

If 21 oranges were added and the ratio became 4 : 5, this implies:

To know how many fruits were there initially, solve the system of the equations:

x = 15 implies there were 15 oranges initially.

To get y, substitute x = 15 into equation (i):

y = 45 implies there were 45 apples initially.

Hence, there were (15 + 45) = 60 fruits there initially.

Answer:

c(10) = 4

Step-by-step explanation:

The polygon has 21 sides whose interior angle are in Arithmetic Progression (A.P.)

The interior angles of a polygon are in an arithmetic progression (A.P) if the difference between any two consecutive angles is constant. To find the number of sides in a polygon given its smallest angle and the common difference of its interior angles, we can use the formula:

n = (180° - smallest angle) / common difference + 1, where n is the number of sides in the polygon.

In this case, the smallest angle is 100° and the common difference is 4°, so the number of sides can be calculated as follows:

n = (180° - 100°) / 4° + 1 = (80°) / 4° + 1 = 20 + 1 = 21.

Therefore, the polygon has 21 sides. It is important to note that a polygon with 21 sides is called an icosikaihenagon, which is a highly unusual and exotic shape, as most polygons have a smaller number of sides.

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The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer:

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

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

1/48

Step-by-step explanation:

Reduce the the expression by cancelling the common factors.

Answer:

The first step is to divide all the terms by the coefficient of \(x^{2}\) which is 2.

The solutions to the quadratic equation \(2x^2\:-\:5x\:+\:67\:=\:0\) are:

\(x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}\)

Step-by-step explanation:

Considering the equation

\(2x^2\:-\:5x\:+\:67\:=\:0\)

The first step is to divide all the terms by the coefficient of \(x^{2}\) which is 2.

so

\(\frac{2x^2-5x}{2}=\frac{-67}{2}\)

\(x^2-\frac{5x}{2}=-\frac{67}{2}\)

Lets now solve the equation by completeing the remaining steps

Write equation in the form: \(x^2+2ax+a^2=\left(x+a\right)^2\)

Solving for \(a\),

\(2ax=-\frac{5}{2}x\)

\(a=-\frac{5}{4}\)

\(\mathrm{Add\:}a^2=\left(-\frac{5}{4}\right)^2\mathrm{\:to\:both\:sides}\)

\(x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{67}{2}+\left(-\frac{5}{4}\right)^2\)

\(x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{511}{16}\)

Completing the square

\(\left(x-\frac{5}{4}\right)^2=-\frac{511}{16}\)

Since, you had required to know the first step in completing the square for the equation above, I hope you have got the point, but let me quickly solve the remaining solution.

For \(f^2\left(x\right)=a\) the solution are \(f\left(x\right)=\sqrt{a},\:-\sqrt{a}\)

Solving

\(x-\frac{5}{4}=\sqrt{-\frac{511}{16}}\)

\(x-\frac{5}{4}=\sqrt{-1}\sqrt{\frac{511}{16}}\)

\(x-\frac{5}{4}=i\sqrt{\frac{511}{16}}\)       ∵ Applying imaginary number rule \(\sqrt{-1}=i\)

\(x-\frac{5}{4}=i\frac{\sqrt{511}}{\sqrt{16}}\)

\(-\frac{5}{4}=i\frac{\sqrt{511}}{4}\)

\(x=\frac{5}{4}+i\frac{\sqrt{511}}{4}\)

Similarly, solving

\(x-\frac{5}{4}=-\sqrt{-\frac{511}{16}}\)

\(x-\frac{5}{4}=-i\frac{\sqrt{511}}{4}\)    ∵ Applying imaginary number rule  \(\sqrt{-1}=i\)

\(x=\frac{5}{4}-i\frac{\sqrt{511}}{4}\)

Therefore, the solutions to the quadratic equation are:

\(x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}\)

The percentage of the data values are between 110 and 170 = 37.5%

We know that in the box plot, the first quartile is nothing but 25% from smallest to largest of data values.

The second quartile is nothing but between 25.1% and 50% (i.e., till median)

The third quartile: 51% to 75% (above the median)

And the fourth quartile: 25% of largest numbers.

In the attached box plot, we can observe that between two numbers on the number line there are 5 equal parts.

So, each unit length measures 10 units.

Also, the median of the data = 110

We need to find the percentage of the data values are between 110 and 170.

i.e., the percentage of the data values are in the third quartile.

The range of this box plot is: 190 - 30 = 160

The data values are between 110 and 170 = 60

Using percentage formula,

P = (60/160) × 100

P = 37.5%

This is the required percentage.

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Find the complete question below.

Answer:

1. true

2. Associative

Step-by-step explanation:

Answer:

\( 105 \: {m}^{3} \)

Step-by-step explanation:

Volume of swimming pool

\( = 1 \frac{1}{2} \times 10 \times 7 \\ \\ = 1.5 \times 70 \\ \\ = 105 \: {m}^{3} \)

Answer: The volume is 105 m3.

Step-by-step explanation:

V= l*w*h

V= 10* 1 1/2* 7

V= 105

Answer:

Step-by-step explanation:

wheres the diagram?

Answer:B

Step-by-step explanation:

The domain of the function is real numbers.. The value is x-1 = is a real number

The domain of a function is the set of values that we are allowed to enter into our function. This set consists of the x values for a function like f. (x). The set of values that a function can accept as input is known as its range. Once we enter an x value, the function returns this list of values.

Think about the equation y = f(x), where x and y are the independent and dependent variables. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

A positive number has a positive cubic root.

Zero has a cubic root of zero.

A negative number has a negative cubic root.

Given ,

This implies that any real number's cubic root is also a real number.

y =   ³√x-1

³√x-1 = x-1 is a cubic root

x-1 = is a real number

Therefore The value of real number is x-1 = is a real number

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Answer for A it’s 24

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

The Quotient and remainder of the polynomial is  x² + x -6 and 2 respectively

Synthetic division method is one of the method used to divide the polynomial equations.

The polynomial equation given here is

x³ + 3x² - 4x - 10

We need to divide this polynomial equation with x - 2

Thus by dividing the polynomial x³ + 3x² - 4x - 10 with x - 2, we get

the quotient as x² + x -6 and

     Remainder as 2

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The area of the second similar object which is shape D would be = 255.5 m²

The shape C is similar to shape D.

This shows that the both shapes looks alike but has difference dimensions.

The area of shape C = 8942.5 m²

Shape C has a side length = 175m

Shape D has a side length = 5m

The scale factor that shows the difference = 175/5 = 35

Therefore the area of shape D;

= 8942.5/35

= 255.5 m²

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Answer:

9yx

Step-by-step explanation:

product means multiply.

nine, y and x

9yx

The required solution is 5+39e.

What is arithmetic?

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications

Given :

Write down the question as an algebra problem, with the unknown as X

The unknown is a number plus 5, so we write it as (X+5). The product is four times (X+5), so we write it as 39(X+5). Set it equal to e, as per the question, 5+39e

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The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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