...................what is 30 + 5?

Answer:

-2

Step-by-step explanation:

9+n/4= -15

cross multiply

9+4-15=n

13-15=n

n=-2

Answer:

4) 8+2i

Step-by-step explanation:

When you expand you get 3+4i+5-2i

when you add the like terms you get 8+2i

Answer:

3

Step-by-step explanation:

The answer is 3 3+4 is 7 and 5-2 is 3

Answer:

464 ft

Step-by-step explanation:

How to find out volume:

Length x Width x Height

= Volume

--

8 x 4 x 14.5 = 464 ft

Equation of the line  that passes through the midpoint and is perpendicular to PQ is 2x - y +1 = 0.

One way to describe a perpendicular bisector is as a line segment that cuts through another line segment at a 90 degree angle. Simply said, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle. Measuring a line segment that needs to be bisected will help you discover a perpendicular bisector.

The midway of the measured length can then be determined by dividing it by two. From this center, extend a line at a 90-degree angle. All you need to do to determine the perpendicular bisector of two points is to discover their midpoint and negative reciprocal, then enter these results into the slope-intercept form of the equation for a line.

Here points are P( -4 ,3 ) and Q ( 4,-1)

Mid -point of PQ :

\(=(\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )\\\\=(\frac{-4+4}{2} ,\frac{3-1}{2} )\\\\=(0,1)\\\)

Slope of PQ:

\(m = \frac{y_{2}{-y_{1} } }{x_{2}{-x_{1} }} \\\\m =\frac{-1-3}{4+4}\\\\ m= \frac{-4}{8} \\\\m = \frac{-1}{2}\)

The slope of the line is Perpendicular to PQ

so, slope 2= -1/m

slope 2 = -1/(-1/2)

slope 2 = 2

Equation of the line  that passes through the midpoint and is perpendicular to PQ

\(y-y_{1} =m(x-x_{1}) \\y-1 =2(x-0}) \\\\y-1=2x\\\)

2x - y +1 = 0.

Learn more about perpendicular bisector visit: brainly.com/question/1761937

#SPJ4

Correct Question:

Find the midpoint of PQ with endpoints P (-4, 3) and Q (4,-1) . Then write an equation of the line that passes through the midpoint and is perpendicular to PQ. This line is called the perpendicular bisector.

Answer:

2.6667

Step-by-step explanation:

you divide 8 by 3

Answer: X=2

Step-by-step explanation: its pretty hard to explain i dont think i can explain

Answer:

\(x-6\)

Step-by-step explanation:

We can let the 'number' in the expression be equal to \(x\). Something 6 less than x would x minus 6, or \(x-6\).

Answer:

x-6

Step-by-step explanation:

Let the number be x

Less than means subtract from

x-6

Answer:

angle 1 = 45° because vertical angles

angle 2 = 135° because supplementary angles

Step-by-step explanation:

∠1 = ∠a, ∠a = 45°

∠2 + ∠a (45°) = 180°

180° - 45° = 135°

Answer:

Angle 1= 45 degrees, angel 2= 135

Step-by-step explanation:

you know that line b has a 45 degree angle on a 180 total, so to find angle 1 you just move the 45 as they are the same, to find angle b you substract 45 from 180 getting 135

The equation of the parabola whose vertex is (2, 5) and focus (2, 2) is:y = (1/8)(x - 2)² + 5.

The equation of the parabola whose vertex is (2,5) and focus (2,2) is: y = (1/8)(x - 2)² + 5.

Step-by-step explanation:

Given the vertex of the parabola is (2, 5)and the focus is (2, 2).The parabola is said to be opening downwards because the focus lies below the vertex. We know that, if (a,b) is the vertex and the parabola opens downward, then the equation of the parabola can be given by: (y - b) = - (1/4a)(x - a)²

This is the required equation of the parabola. The parabola is opening downwards. The distance from the vertex to the focus is 5 - 2 = 3. Therefore the distance from the vertex to the directrix is also 3.

Hence, the equation of the directrix is y = 5 + 3 = 8. (Since the parabola opens downwards). The equation of the parabola with the given vertex and focus is: (y - 5) = - (1/12)(x - 2)²4a = - 12a = - 3

The value of 'a' is - 3 in the above equation. Let's simplify it by substituting the value of 'a' in the equation.(y - 5) = - (1/12)(x - 2)²- 36(y - 5) = (x - 2)² We get the above equation by simplifying.

To Know more about parabola visit:

https://brainly.com/question/11911877

#SPJ11

Solving for v in the given equation is performed by making v the equation's

subject.

The statement that describes where the error was made is option;

v can be solved for from the  given expression as follows;

\(\displaystyle k = \mathbf{\frac{1}{2} \cdot m \cdot v^2}\)

\(\displaystyle k \div m = \mathbf{\left(\frac{1}{2} \cdot m \cdot v^2 \right) \div m}\)

\(\displaystyle \frac{k}{m} \times 2 = \left( \frac{1}{2} \cdot v^2 \right) \times 2\)

\(\displaystyle \frac{2 \cdot k}{m}= \mathbf{v^2}\)

Taking the square root of both sides of the equation gives;

\(\pm \sqrt{\displaystyle \frac{2 \cdot k}{m}} = \mathbf{\sqrt{v^2}}\)

Therefore;

\(\displaystyle \pm \sqrt{\frac{2 \cdot k}{m} } = v\)

Therefore, the error was made in the step, \(\displaystyle \pm \frac{2 \cdot \sqrt{k} }{m} = \sqrt{v^2}\) , which is by

applying the square root property was applied to only some of the

variables on the left hand side of the equation, rather than the combined

expression on the left hand side of the equation.

Learn more about making a variable the subject of the formula here:

https://brainly.com/question/8481791

Answer:

The square root property should have been applied to both complete sides of the equation instead of to select variables.

or D

Step-by-step explanation:

I found the answer and just gave it to u straight up and I got it correct

The volume of the cube expressed as a fraction will be 27x³y³ / 64.

Given that:

Volume, V = (0.75xy)³

It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of the cube expressed as a fraction is calculated as,

V = (0.75xy)³

V = (3xy/4)³

V = 27x³y³ / 64

More about the volume link is given below.

https://brainly.com/question/1578538

#SPJ1

The expression inside the integral, we get {eq}r^3 \sqrt{r^2} = r^{\frac{7}{2}} {/eq}. Evaluating the integral, we get:{eq}\int_{0}^{2\pi} \int_{0}^{6} r^3 \sqrt{r^2} \, \mathrm{d}r \, \mathrm{d}\theta = \int_{0}^{2\pi} \left[\frac{2}{9}r^{\frac{9}{2}}\right]_{0}^{6} \, \mathrm{d}\theta = \frac{2}{9}(6^{\frac{9}{2}}-0) \int_{0}^{2\pi} \mathrm{d}\theta = \boxed{432\pi} {/eq}

To change to polar coordinates, we need to express {eq}x {/eq} and {eq}y {/eq} in terms of {eq}r {/eq} and {eq}\theta {/eq}. Using the conversion formulas, we have {eq}x = r\cos{\theta} {/eq} and {eq}y = r\sin{\theta} {/eq}. The limits of integration also change to reflect the new coordinate system. In polar coordinates, the disk {eq}x^2 + y^2\leq 36 {/eq} becomes {eq}0\leq r\leq 6 {/eq} and {eq}0\leq \theta\leq 2\pi {/eq}. Substituting these values, we get:

{eq}\iint_{D} (x^2 + y^2)^\frac{3}{2} \, \mathrm{d}x \ \mathrm{d}y = \int_{0}^{2\pi} \int_{0}^{6} r^3 \sqrt{r^2} \, \mathrm{d}r \, \mathrm{d}\theta {/eq}

Know more about integral here:

https://brainly.com/question/18125359

#SPJ11

Answer:

\(\large \boxed{ (p+6)(p-6) }\)

Step-by-step explanation:

\(p^2 - 36\)

Rewrite 36 as 6 squared.

\(p^2 - 6^2\)

Apply difference of two squares formula:

\(a^2-b^2 =(a+b)(a-b)\)

\(a=p\\b=6\)

\(p^2 - 6^2=(p+6)(p-6)\)

Answer:

since is its a possibility of 7 or 11 we add the individual probabilities

so the answer is 1/6+ 1/18=3/18+1/18=4/18=2/9

2/9.

I hope now you'll understand

Answer:

71

Step-by-step explanation:

i used my calculator :D

Answer:

Depends. See text.

Step-by-step explanation:

Surface area or volume?

Ther are two options.

Case 1: we know nothing about the green angles I've marked in green. Data is insufficient to determine the perimeter of the trapezoid base, and then to calculate the surface area.

Case 2:Unlikely, since the right angles are marked everywhere else when not obvious: the base of the prism is a right trapezoid, ie two of the angles measures 90°. In that case we can easily find the length of the missing side with pythagorean theorem: \(l=\sqrt{1+3^2}= \sqrt{10}\). Perimeter becomes \(2p=6+7+3+\sqrt{10}=16+\sqrt{10}\). Base area is \(A_b=\frac12(6+7)\times 3 = \frac{39}2\) And the total surface becomes \(S= 2A_b+2pH = 39+(16+\sqrt{10})20 = 39+320+20\sqrt{10}=359+20\sqrt{10}\)

Or is it the volume you want? Way simpler, we calculate the area of the prism (see above) and multiply it by the height of the solid:

\(V = A_bH = \frac{39}2\times 20 = 390\)

Answers:

======================================================

Explanation:

Use the graph to see that the left and right endpoints of the original segment are (2,4) and (6,6) in that order.

Then for each point, we multiply each coordinate by the scale factor 2. This will move the points to the proper location such that the segment is now twice as long as compared to the original.

The left endpoint (2,4) moves to (4,8) after we double the coordinates.

The right endpoint (6,6) moves to (12,12) after we double the coordinates.

The final segment has the left and right endpoints of (4,8) and (12,12) in that order.

Side note: The original and final segments are parallel to one another. This is because both segments share the same slope.

The value of the card in 2002 ​is $12.00. Hence, relationship between x and y is not proportional to each other in this case.

An equation is an expression that shows the relationship between two or more numbers and variables.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The number of years between 1996 to 2002 would be:

= 2002 - 1996

= 6 years

The relationship that is relating the value of the card y in dollars and the number of years x the player has been in retirement can be expressed as an equation in the form of the following;

y = 5.54 + 1.06x

where x = 6 years

y = 5.54 + 1.06(6)

y = 5.54 + 6.36

y = $12.00

The value of the card in 2002 ​is $12.00.

The relationship between x and y is not proportional to each other in this case.

Learn more about equations here;

https://brainly.com/question/10413253

#SPJ1

Answer:

3.15

Step-by-step explanation:

This graph is proportional. divide the y by x (k=y/x) (constant of proportionality. 6.3/3=3.15 18.9/6=3.15 28.35/9=3.15 15.75/6=3.15 3.15/1=3.15

W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

To show that W=Rn, we need to show that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W.

Let v be any vector in Rn. Since the n non-zero orthogonal vectors span W, we can write v as a linear combination of them:

v = c1v1 + c2v2 + ... + cnvn

where c1, c2, ..., cn are scalars, and v1, v2, ..., vn are the n non-zero orthogonal vectors that span W.

To show that v is in W, we need to show that v is orthogonal to all vectors in W except itself. Since the n non-zero orthogonal vectors are linearly independent, any linear combination of them that is orthogonal to v must be the zero vector.

Therefore, if w is any vector in W that is not equal to v, we have:

=  = c1 + c2 + ... + cn = 0

since v is orthogonal to all the non-zero orthogonal vectors. This means that v is orthogonal to all vectors in W except itself.

Therefore, since v is in W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

Know more about Non-zero orthogonal vectors here:

https://brainly.com/question/30264840

#SPJ11

Answer:

1/7

Step-by-step explanation:

negative reciprocal

Answer:

x=1

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

8 - 7x = 1

- 8       - 8

-7x = -7

/-7    /-7

x = 1

Answer:

Below in bold.

Step-by-step explanation:

Vertex form.

y = a(x - h)^2 + k

The point (h, k) is the vertex so from the graph:

y = a(x - 1)^2 - 8

From the x -interesect we see that x = 6 when y = 0 so

0 = a(6 - 1)^2 - 8

25a - 8 = 0

a = 8/25

So the vertex form is

y = (8/25)(x - 1)^2 - 8.

Factored form:

y = (8/25)(x + 4)(x - 6)  

- as -4 and 6 are the zeros of the equation.

Standard form:

From the factored form we have

y = (8/25)(x^2 - 2x - 24)

y = 8/25 x^2 - 16/25 x - 192/25

or (in decimal form):

y = 0.32x^2 - 0.64x - 7.68.

The relationship between p(n) and n is given by p(n) = 0.0005n

An equation is an expression used to show the relationship between two or more numbers and variables.

Let p represent the weight in pounds and n represent the weight in tons.

1 pound = 0.0005 ton, hence:

p(n) = 0.0005n

The relationship between p(n) and n is given by p(n) = 0.0005n

Find out more on Equation at: https://brainly.com/question/13763238

The correct answer to the equation result = (h/3) * (y(1) + 4*sum(y(2:2:n)) + 2*sum(y(3:2:n-1)) + y(n+1));

Here's an example MATLAB code that implements the composite trapezoidal rule and the composite Simpson's rule for approximating definite integrals:

% Function to evaluate the relevant function f(x)

function y = evaluateFunction(x)

   % Define the function f(x) here

   y = log(x);  % Example: ln(x)

end

% Composite trapezoidal rule

function result = compositeTrapezoidalRule(a, b, n)

   h = (b - a) / n;

   x = linspace(a, b, n+1);

   y = evaluateFunction(x);

   result = (h/2) * (y(1) + 2*sum(y(2:n)) + y(n+1));

end

% Composite Simpson's rule

function result = compositeSimpsonsRule(a, b, n)

   h = (b - a) / n;

   x = linspace(a, b, n+1);

   y = evaluateFunction(x);

   result = (h/3) * (y(1) + 4*sum(y(2:2:n)) + 2*sum(y(3:2:n-1)) + y(n+1));

end

% Main program

a = 1;  % Lower limit of integration

b = 2;  % Upper limit of integration

n = 100;  % Number of subintervals

% Approximate the integral using the composite trapezoidal rule

approximation_trapezoidal = compositeTrapezoidalRule(a, b, n);

% Approximate the integral using the composite Simpson's rule

approximation_simpsons = compositeSimpsonsRule(a, b, n);

% Display the results

disp("Approximation using the composite trapezoidal rule:");

disp(approximation_trapezoidal);

disp("Approximation using the composite Simpson's rule:");

disp(approximation_simpsons);

To use this code, you need to define the function you want to integrate within the evaluateFunction function. In this example, the function evaluateFunction is defined to compute the natural logarithm of x.

You can change the values of a, b, and n to approximate different integrals. The n value determines the number of subintervals and can be adjusted to control the accuracy of the approximation.

To investigate the behavior of the errors, you can compare the approximations with the exact values of the integrals if known. You can also experiment with different values of n to observe how the errors decrease as the number of subintervals increases.

The choice of which technique is more accurate for a given cost depends on the specific function being integrated and the desired level of accuracy. Generally, the composite Simpson's rule provides a more accurate approximation than the composite trapezoidal rule for the same number of function evaluations, but it may require more computational resources.

Learn more about statistics here:

https://brainly.com/question/31527835

#SPJ11

(b) To solve the equation csc²z = cotz +3, we can use the reciprocal and Pythagorean identities to rewrite everything in terms of sin and cos:

csc²z = cotz + 3

1/sin²z = cosz/sinz + 3

1 = cosz + 3sin²z

Rearranging and using the identity sin²z + cos²z = 1, we get:

cosz = 1 - 3sin²z

Substituting this into the original equation, we get:

1/sin²z = (1 - 3sin²z)/sinz

Multiplying both sides by sin²z and simplifying, we get:

1 = sinz - 3sin³z

This is a cubic equation in sinz, which can be difficult to solve exactly. One possible method is to use the rational root theorem to find integer roots, and then use polynomial division to factor the equation. Another method is to make a substitution, such as u = sinz, and then solve the resulting quadratic equation for u.

Example 23: To simplify the expression tan n(2 cos⁻¹x), we can use the double angle formula for cosine:

cos(2θ) = cos²θ - sin²θ

Letting θ = cos⁻¹x, we get:

cos(2 cos⁻¹x) = cos²(cos⁻¹x) - sin²(cos⁻¹x)

= x² - (1 - x²)

= 2x² - 1

Therefore, the expression becomes:

tan n(2 cos⁻¹x) = tan n(cos⁻¹x + cos⁻¹x)

= tan n(cos⁻¹x) + tan n(cos⁻¹x)

= (sin n(cos⁻¹x) / cos n(cos⁻¹x)) + (sin n(cos⁻¹x) / cos n(cos⁻¹x))

= 2(sin n(cos⁻¹x) / cos n(cos⁻¹x))

= 2 tan n(cos⁻¹x)

Using the identity sin²θ + cos²θ = 1, we can write:

tan²θ + 1 = sec²θ

Therefore,

tan n(cos⁻¹x) = √(tan²n(cos⁻¹x))

= √(sec²n(cos⁻¹x) - 1)

= √(1/(cos²n(cos⁻¹x)) - 1)

= √(1/(x²)^n - 1)

Putting this back into the previous expression, we get:

tan n(2 cos⁻¹x) = 2√((1/x^2)^n - 1)

Example 24: To simplify the expression cos x sin² x so that it only involves first powers of trigonometric functions, we can use the identity:

sin²x = (1 - cos 2x)/2

Substituting this into the expression, we get:

cos x sin² x = cos x (1 - cos 2x)/2

Expanding and simplifying, we get:

1/2(cos x - cos³x)

Learn more about equation here:

https://brainly.com/question/29538993

#SPJ11

Answer: Fritz Perk

Have a great day.

Answer:

\((\frac{1}{14} ,-\frac{7}{6})\)

Step-by-step explanation:

You can use the midpoint formula: \(\frac{ChangeInX}{2} ,\frac{ChangeInY}{2}\)

So, the Change In X is: \(\frac{4}{7} -\frac{3}{7} = \frac{1}{7}\)

And the Change in Y is: \(-\frac{5}{3} - \frac{2}{3} = -\frac{7}{3}\)

Once you divide both of the changes by 2, you get

X: \(\frac{1}{14}\)

Y: \(-\frac{7}{6}\)

So the midpoint is: \((\frac{1}{14} ,-\frac{7}{6})\)