Determine the area of the composite figure to the nearest whole number

For this case we have that by definition, a polynomial in its standard form is given by:

[tex]P (x) = ax ^ {n} + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f[/tex]

Where:

a, b, c, d, e, f: They are the coefficients

n, n-1,3,2,1: They are the exponents. The degree of the polynomial is "n" because it is the largest exponent.

x: It is the variable

The given polynomial is:

[tex]4m-2m ^ 4-6m ^ 2 + 9[/tex]

Rewriting it in its standard form:

[tex]P (x) = - 2m ^ 4-6m ^ 2 + 4m + 9[/tex]

It is a polynomial of degree 4

ANswer:

[tex]P (x) = - 2m ^ 4-6m ^ 2 + 4m + 9[/tex]

Answer:

For this case we have that by definition, a polynomial in its standard form is given by:Where:a, b, c, d, e, f: They are the coefficientsn, n-1,3,2,1: They are the exponents. The degree of the polynomial is "n" because it is the largest exponent.x: It is the variableThe given polynomial is:Rewriting it in its standard form:It is a polynomial of degree 4ANswer:

Step-by-step explanation:

Answer:

option D

Lines a and b are parallel and lines c and d are parallel.

Step-by-step explanation:

Given in the question four lines a , b, c, d.

If two parallel lines (a,b) are cut by a transversal(d), then corresponding angles m<7 and m<15 are congruent.

They are know as corresponding angles.

Hence lines a and b are parallel.

If two parallel lines (c,d) are cut by a transversal(d), then corresponding angles m<13 and m<15 are congruent.

They are know as corresponding angles

Hence lines c and d are parallel

Answer:

Final answer is [tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex].

Step-by-step explanation:

Given problem is [tex]\sqrt[3]{x}\cdot\sqrt[3]{x^2}[/tex].

Now we need to simplify this problem.

[tex]\sqrt[3]{x}\cdot\sqrt[3]{x^2}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}[/tex]

Apply formula

[tex]\sqrt[n]{x^p}\cdot\sqrt[n]{x^q}=\sqrt[n]{x^{p+q}}[/tex]

so we get:

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{1+2}}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{3}}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex]

Hence final answer is [tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex].

The original expression ∛x * ∛[tex]x^2[/tex] simplifies to x.

This means that the cube root of x times the cube root of [tex]x^2[/tex] is equal to x.

To simplify the expression ∛x * ∛[tex]x^2[/tex], we can apply the rules of exponents and radicals.

The cube root of x is equivalent to raising x to the power of 1/3.

Similarly, the cube root of [tex]x^2[/tex]  is equivalent to raising [tex]x^2[/tex] to the power of 1/3.

So, we have:

∛x = [tex]x^{(1/3)[/tex]

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

Now, let's multiply these two expressions:

[tex]x^{(1/3)}\times x^{(2/3)[/tex]

To simplify, we add the exponents when multiplying like bases:

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

So, the simplified expression is just x.  

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Answer:

no

Step-by-step explanation:

the first 7, 7000, is 1000 times greater than the first 7. If the first seven is the one in the ones value and the second is in the 7, than it it 1000 smaller.

The value of the first 7 is a thousand times as great as the value of the second 7 in 7,027.

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

Given, a number 7,027 that has two 7 we need to compare the values of 7 in the form of place values.

thus,

Place value of first seven (right to left) = 1

Place value of 2 = 10

place value of 0 = 100

place value of second 7(right to left) = 1000

the first 7 or 7000, is 1000 times greater than the first 7. If the first seven is the one in the one's value and the second is in the 7, then it is 1000 times smaller.

therefore, The first 7's value is 1,000 times more than the second 7's value of 7,027.

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ANSWER

9.7 units

EXPLANATION

According to the Pythagoras Theorem, the square of the hypotenuse is equal to the sum of the squares of the two shorter legs

[tex] {x}^{2} + {7}^{2} = {12}^{2} [/tex]

This implies that,

[tex] {x}^{2} + 49= 144[/tex]

Group similar terms,

[tex] {x}^{2} = 144 - 49[/tex]

[tex] {x}^{2} = 95[/tex]

[tex]x = \sqrt{95} [/tex]

[tex]x = 9.7 \: units[/tex]

to the nearest tenth.

Answer:

2.50

Step-by-step explanation:

The average rate of change over the interval −2≤x≤2 is:

(f(2) − f(-2)) / (2 − -2)

From the table, we see that f(2) = 14 and f(-2) = 4.

(14 − 4) / (2 − -2)

10 / 4

2.50

Answer:

2.50

Step-by-step explanation:

Answer:

45°

Step-by-step explanation:

Each corner of a square is a right angle. That is 90° which divided by 2 equals 45°

Answer:

14

Step-by-step explanation:

2k - 1 is linear, so this is an arithmetic series.  The sum of an arithmetic series is:

S = (n/2) (a₁ + an)

Here:

S = 196

a₁ = 2(1) - 1 = 1

an = 2n - 1

Solving:

196 = (n/2) (1 + 2n - 1)

196 = (n/2) (2n)

196 = n²

n = 14

Answer:

48

Step-by-step explanation:

12x8=96

96/2=48

you can check this on a calculatot

they threw in the angel to confuse you

Here is the answer, you can use the formula to find the area

Answer:

The volume of the smaller solid is [tex]339\ yd^{3}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the larger solid

y----> surface area of the smaller solid

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]x=361\ yd^{2}[/tex]

[tex]y=121\ yd^{2}[/tex]

substitute

[tex]z^{2}=\frac{361}{121}[/tex]

[tex]z=\frac{19}{11}[/tex]

step 2

Find the volume of the smaller solid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> volume of the larger solid

y----> volume of the smaller solid

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{19}{11}[/tex]

[tex]x=1,747\ yd^{3}[/tex]

substitute

[tex](\frac{19}{11})^{3}=\frac{1,747}{y}\\ \\(\frac{6,859}{1,331})=\frac{1,747}{y} \\ \\y=1,331*1,747/6,859\\ \\y=339\ yd^{3}[/tex]

Answer:

7.7%

Step-by-step explanation:

To find the percent error, take the absolute value of (actual amount - estimate) and divide it by the actual amount).  Then multiply it by 100 %

percent error = | actual - estimate|

                          -------------------------- * 100%

                             actual          

                      = | 2.6 -2.4|

                        ----------------- * 100%

                                  2.6

                      = .2 * 100%

                         -----------

                            2.6

                       =7.69230769%

To the nearest tenth percent

                      =7.7%

In the equation: -6x - 19 - 4x replace x with -2

-6(-2) - 19 - 4(-2)

Use your rules of PEMDAS to evaluate

12 - 19 + 8

-7 + 8

1

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer

1

Step-by-step explanation:

Step 1: Replace all x's with -2

-6(-2)-19-4(-2)

Step 2: Multiply

12-19+8

Tip: Remember that a double negative is a positive.

Step 3: Add and Subtract

12-19+8

-7 + 8

1

Answer: 1 Triangle weighs as much as 2 marbles.

Step-by-step explanation: Since we know there balanced, we can figure out using equations whatever we do to the first side so to the other.

The student's question relates to the point P with the polar coordinates (3, -π/3). Polar coordinates are not unique, so we can find all coordinates of point P by adding multiples of 2π to the angle part of the coordinate, that is, (3, -π/3 + 2πn) where n is an integer.

The polar coordinates system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from the origin (point O) and an angle measured anti-clockwise from an arbitrary direction, usually the x-axis.

Each point is represented by the ordered pair (r, θ). Our point P has the polar coordinates (3, -π/3). However, polar coordinates are not unique for a given point. To find all polar coordinate pairs for point P, we add multiples of 2π to the angle part of the coordinate pair, as a complete revolution is 2π in radians. Therefore, alternative polar coordinate pairs for point P would include (3, -π/3 + 2πn) where n is an integer.

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Answer:

1) vertex = (-2,4)

2) Focus = (-0.5,4)

3) x= -3.5

   y= 4

4)  y=4

Step-by-step explanation:

General equation of parabola that is parallel to a-axis and vertex at (h,k) is given as

(y - k)^2 = 4p (x - h)

where

vertex of parabola is at (h,k)

focus of parabola is given at (h + p, k)

the directrix of parabola is given as x = h - p.

Now

1)

finding vertex of parabola:

Given equation of parabola

(y-4)^2=6(x+2)

Comparing with the general form, we get

h=-2 ,k=4 and 4p=6

hence vertex = (-2,4)

2)

Finding focus

Comparing with the above standard form we get

k=4, h=-2, p=3/2

Since the given parabola is parallel to x-axis and also p is positive hence it will opens to the right.

As focus is inside the parabola and it is p units to the right of the vertex:

hence

focus of parabola (h + p, k)=(-2+3/2 , 4)

                                            =(-0.5,4)

3)

Comparing with the above standard form we get

k=4, h=-2, p=3/2

Since the given parabola is parallel to x-axis and also p is positive hence it will opens to the right.

As directrix is outside the parabola and it is p units to the left of the vertex:

hence

directrix x=h-p

                = -2-3/2

                =-7/2

                = -3.5

             y= 4

4)

Finding Axis of symmetry:

as the vertex is (-2,4) also the given parabola is parallel to x-axis so

the axis of symmetry is a horizontal straight line passing through the vertex  at y=4 !

Answer:

a(n) = 3*(2)^(n-1)

Step-by-step explanation:

Each new term is found by multiplying the previous term by 2.  The first term is 3.  Using the standard explicit formula for a geometric series, we get:

a(n) = a(1)*r^(n-1).  In this particular case we have a(n) = 3*(2)^(n-1).

Answer:

The volume of the prism = 300 units³

Step-by-step explanation:

* Lets study the triangular prism

- The triangular prism has 6 faces

- Two right triangular bases

- Four rectangular side faces

- The volume of the prism = area of its base × its height (altitude)

* Now lets solve the problem

∵ The base is a right triangle with a hypotenuse of 13 units and

   a leg of 12 units

∵ The area of the right triangle = 1/2 × leg1 × leg2

- You can find the length of other leg by using Pythagoras theorem

∵ (hypotenuse)² = (leg1)² + (leg2)²

∵ hypotenuse = 13 units

∵ leg1 = 12 units

∴ (13)² = (12)² + (leg2)²

∴ 169 = 144 +  (leg2)² ⇒ subtract 144 from both sides

∴ 25 =  (leg2)² ⇒ take √ for both sides

∴ leg2 = 5 units

- The area of the right triangle = 1/2 × leg1 × leg2

∴ The area of the base = 1/2 × 12 × 5 = 30 units²

∴ The volume of the prism = 30 × 10 = 300 units³

Answer:

3/2x

Step-by-step explanation:

Find the slope of the original line.

3x + 2y = 19

2y = -3x + 19

y = -2/3x + 19

Use the reciprocal with the opposite sign.

3/2x

Final answer:

To find the slope of a line perpendicular to 3x+2y=19, first find the original line's slope (-1.5) and then calculate its negative reciprocal, which is 2/3.

Explanation:

The question asks about the slope of a line perpendicular to the given line 3x + 2y = 19. To find this, we first need to find the slope of the given line. We rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope. For 3x + 2y = 19, subtract 3x from both sides and divide by 2 to get y = -1.5x + 9.5. Thus, the slope of the given line is -1.5. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the slope of the line perpendicular to the given line is 2/3.

Answer:

5x+y=-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = 5x - 3   it's a slope-intercept form

y = 5x - 3         subtract 5x from both sides

-5x + y = -3          change the signs

5x - y = 3     it's a standard form

5x - y = 3          subtract 3 from both sides

5x - y - 3 = 0         it's a general form

Answer:

15 yards, 45 feet and 540 inches are equal.

Step-by-step explanation:

To know if the measurements are equal, we first need to convert all the measures to the same unit. In this case, I will convert them all to feet.

a.6 feet

b.15 yards ≈ 45 feet

c.45 feet

d.600 inches ≈ 50 feet

e. 12 feet

f. 540 inches  ≈ 45 feet

Therefore, b, c and f are equal.

Answer:

[tex]\frac{\tan 60\degree}{\cos45 \degree}= \sqrt{6}[/tex]

Step-by-step explanation:

We want to evaluate

[tex]\frac{\tan 60\degree}{\cos45 \degree}[/tex]

We use special angles or the unit circle to obtain;

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\frac{\sqrt{3}}{\frac{\sqrt{2}}{2}}[/tex]

This implies that;

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\sqrt{3}\div \frac{\sqrt{2}}{2}[/tex]

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\sqrt{3}\times \sqrt{2}[/tex]

[tex]\frac{\tan 60\degree}{\cos45 \degree}= \sqrt{6}[/tex]

Answer:

[tex]\sqrt{6}[/tex].

Step-by-step explanation:

[tex]\frac{tan(60)}{cos(45)}[/tex]

[tex]= \frac{\frac{sin(60)}{cos(60)}}{cos(45)}[/tex]

[tex]= \frac{sin(60)}{cos(60)*cos(45)}[/tex]

[tex]= \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}*\frac{\sqrt{2}}{2}}[/tex]

[tex]= \frac{\frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{4}}[/tex]

[tex]= \frac{4\sqrt{3}}{2\sqrt{2}}[/tex]

[tex]= \frac{2\sqrt{3}}{\sqrt{2}}[/tex]

[tex]= \frac{2\sqrt{3}\sqrt{2}}{2}[/tex]

[tex]=\sqrt{3}\sqrt{2}[/tex]

[tex]=\sqrt{6}[/tex].

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It is the radius of the cylinder

h: It is the height of the cylinder

We have as data, observing the figure, that they give us the radio. Then, the height is missing.

Answer:

Option B

Answer:

The correct answer is -

2. the height of the cylinder  

Step-by-step explanation:

The volume of the cylinder is given as :

[tex]V= \pi r^{2} h[/tex]

In the given figure, we have the radius. So, we need the height in order to calculate the volume.

So, the correct answer is -

2. the height of the cylinder  

Answer:

distribution of numerical data. It is an estimate of the probability distribution of a continuous variable it is different then a bar graph

Step-by-step explanation:

Answer:5

Step-by-step explanation:

To solve the expression 2 + 3x16 - 2x21 - 3, we apply the order of operations rule (PEMDAS) without any parentheses or exponents to handle. The expression simplifies to 5.

The student is asking to solve a mathematical expression using the correct order of operations. The proper order to solve math expressions is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This rule is often remembered by the acronym PEMDAS.

Let's solve the expression step by step:

First calculate any operations inside parentheses. In the given problem, there are none.

Next, perform all multiplication and division operations from left to right. 3x16 equals 48, and 2x21 equals 42.

Subtract and add from left to right. So, 2 + 48 - 42 - 3 = 5.

Therefore, the expression

2 + 3x16 - 2x21 - 3= 5

.

Answer:

S=546 [tex]ft^{2}[/tex]

Step-by-step explanation:

The equation for the volume of a sphere and the surface area of a sphere are as follows

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

[tex]S=4\pi r^{2}[/tex]

As we know that V=1200 we can use the volume equation to solve for r

[tex]1200=\frac{4}{3} \pi r^{3}\\900=\pi r^{3} \\[/tex]

Now we can plug r into the surface area equation

[tex]S=4\pi (\sqrt[3]{\frac{900}{\pi } })^{2} \\\\S=546.09\\S=546 ft^2[/tex] }

Answer:

The length of the hypotenuse is [tex]h = 6.71\ units[/tex]

Step-by-step explanation:

For a straight triangle it is true that

[tex]h = \sqrt{a ^ 2 + b ^ 2}[/tex]

Where has is the hypotenuse of the right triangle and a and b are the lengths of the other two sides.

In this case we know that:[tex]a = 3\\b = 6[/tex]

So the hypotenuse is:

[tex]h = \sqrt{3 ^ 2 + 6 ^ 2}[/tex]

[tex]h = \sqrt{3 ^ 2 + 6 ^ 2}[/tex]

[tex]h = 3*\sqrt{5}[/tex]

[tex]h = 3*\sqrt{5}[/tex]

[tex]h = 6.71[/tex]

ANSWER

The hypotenuse is 3√5 units.

EXPLANATION

We use the Pythagoras Theorem.

Let h be the hypotenuse.

The Pythagoras Theorem says that, the hypotenuse square is equal to the sum of the squares of the two shorter legs.

[tex] {h}^{2} = {3}^{2} + {6}^{2} [/tex]

[tex]{h}^{2} = 9+ 36[/tex]

[tex]{h}^{2} = 45[/tex]

Take positive square root.

[tex]h = \sqrt{45} [/tex]

[tex]h = 3 \sqrt{5} units[/tex]

Answer: SECOND OPTION

Step-by-step explanation:

The area of a parallelogram can be calculated with this formula:

[tex]A=bh[/tex]

Where "b" is the of one base and "h" is the height.

You can observe in the figure that "b" and "h" are:

[tex]b=AB=4\sqrt{2}ft\\\\h=AX=3ft[/tex]

Then, substituting these values into the formula, you get that the area of the given parallelogram is:

[tex]A=(4\sqrt{2}ft)(3ft)\\\\A=12\sqrt{2}ft^2[/tex]

This matches with the second option.

Answer:

12√2 sq. ft.

Step-by-step explanation:

Hope this helps.

Answer:divide the diameter by 2 and plug the values for volume, pi, and radius into the formula for volume of a cylinder. Next, square the radius and multiply the values together. Then, divide both sides by 200.96 for the answer, remembering to include the appropriate unit of measurement

Step-by-step explanation:

Finding A Diameter Of A Cylinder Is Easy.

If You Know The Radius, Multiply The Radius By 2 To get Your Diameter,

Have A Great Day!

If you have 1 nickle, how many quarters do you have? (3)

If you have 4 nickles, you have 3 times as many quarters (3)(4) = 12

If you have n nickles, then you have 3n quarters so 3n = q, you have  a slightly different equation.

If you fix this equation and use substitution like you did, you can get the right answer; you can also try to work in the other information that you have - converting all coin values to cents

    5n + 10d + 25q = 460

This problem can be solved by setting up and solving a system of linear equations. After setting up the equations n+d+q=30, 5n+10d+25q=460, and d=q+2, you substitute and simplify to find that there are 10 nickels, 12 dimes, and 8 quarters.

Let's denote the number of nickels as n, dimes as d, and quarters as q. We have the following three equations based on the information given:

Solving these equations simultaneously will give you the numbers of each coin. If you substitute the third equation into the first and second equation, you get:

Simplify these equations to determine the values of n, q, and d. You would find that n=10, d=12, and q=8. So you have 10 nickels, 12 dimes, and 8 quarters.

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[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{5}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{8+5}{2}~~,~~\cfrac{2+6}{2} \right)\implies \left( \cfrac{13}{2}~,~\cfrac{8}{2} \right)\implies \left(6\frac{1}{2}~,~4 \right)[/tex]