Prove or disprove the identity. if you find the identity is true, state the first line of the proof. if you find the identity is false, write the correct equation by replacing the right side. sec2 x(1 – sin2 x) = csc2 x cos x

Answer:

147.75

Step-by-step explanation:

2lw+2lh+2wh

2 (5.5)(3)+2 (5.5)(6.75)+2(3)(6.75)

=147.75

Final answer:

To find the surface area of a rectangular prism with dimensions 5.5 cm by 3 cm by 6.75 cm, we calculate the area of each pair of faces and sum them up to get a total surface area of 147.75 square centimeters.

Explanation:

To find the exact value of the surface area of a rectangular prism, we use the formula for surface area, which is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism. Given the dimensions, l = 5.5 cm, w = 3 cm, and h = 6.75 cm, we can calculate the surface area as follows:

Calculate the area of the two length by width sides: 2(5.5 cm  imes 3 cm) = 33 cm²

Calculate the area of the two length by height sides: 2(5.5 cm  imes 6.75 cm) = 74.25 cm²

Calculate the area of the two width by height sides: 2(3 cm  imes 6.75 cm) = 40.5 cm²

Add these areas together to get the total surface area: 33 cm² + 74.25 cm² + 40.5 cm² = 147.75 cm²

Hence, the exact value of the surface area of the rectangular prism is 147.75 square centimeters.

[tex]

2h\div0.5h=4 \\

\frac{3}{4}\cdot4=\frac{12}{4}=\boxed{3}

[/tex]

For the first 8 hours he makes $12.00 per hour.

$12.00 * 8 = $96.00

Now you have $128.00 = 16.00h + $96.00

Subtract 96 from each side:

32 = 16h

Divide both sides by 16:

h = 2

He worked 2 hours of overtime.

a.

[tex]z=-\dfrac{5\sqrt3}2+\dfrac52i=5\left(-\dfrac{\sqrt3}2+\dfrac12i\right)=5e^{i5\pi/6}[/tex]

[tex]w=1+\sqrt3\,i=2\left(\dfrac12+\dfrac{\sqrt3}2i\right)=2e^{i\pi/3}[/tex]

b. Not exactly sure how DeMoivre's theorem is relevant, since it has to do with taking powers of complex numbers... At any rate, multiplying [tex]z[/tex] and [tex]w[/tex] is as simple as multiplying the moduli and adding the arguments:

[tex]zw=5\cdot2e^{i(5\pi/6+\pi/3)}=10e^{i7\pi/6}[/tex]

c. Similar to (b), except now you divide the moduli and subtract the arguments:

[tex]\dfrac zw=\dfrac52e^{i(5\pi/6-\pi/3)}=\dfrac52e^{i\pi/2}[/tex]

Answer:

14.7

Step-by-step explanation:

a^2+b^2=c^2

15^2+b^2=21^2

225+b^2=441

subtract 441-225=216

square root of 216 = 14.6969384567

= 14.7

Answer:

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

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

x² + 15² = 21²

x² + 225 = 441 ( subtract 225 from both sides )

x² = 216 ( take the square root of both sides )

x = [tex]\sqrt{216}[/tex] = [tex]\sqrt{36(6)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{6}[/tex] = 6[tex]\sqrt{6}[/tex]

V = (π/6)d^3

Using π = 22/7 and d = 14 ft, the volume is

 V = (22/7)/6*(14 ft)^3 = 4,312/3 ft^3

Answer:

[tex]g(x)=3x+2[/tex]

Step-by-step explanation:

we have

[tex]f(x)=2x[/tex] ----> linear equation

[tex]gof(x)=6x+2[/tex] ---> linear equation

therefore

g(x)-----> will be a linear equation

so

Let

[tex]g(x)=ax+b[/tex]

so

[tex]gof(x)=a(2x)+b[/tex] ----> equation A

[tex]gof(x)=6x+2[/tex] ----> equation B

equate equation A and equation B

[tex]a(2x)+b=6x+2[/tex]

[tex]2ax=6x ----> a=3[/tex]

[tex]b=2[/tex]

Hence

[tex]g(x)=3x+2[/tex]

Answer:

21 in

Step-by-step explanation:

The law of cosines is helpful for this. The angle opposite the shorter diagonal is the supplement of the angle shown, so is 60°.

If we designate the known sides as "a" and "b", the short diagonal as "c" and the smaller angle as C, then the law of cosines tells us ...

c^2 = a^2 + b^2 -2ab·cos(C)

For the given dimensions, we have ...

c = √(15^2 +24^2 -2·15·24·cos(60°)) = √441 = 21 . . . inches

Answer:3100 with 9%

Step-by-step explanation:

Answer:

The answer is $3,100 at 9%; $4,900 at 11%

Step-by-step explanation:

You can solve this problem with a system of equations, that is, a system that can contain 2 or more equations. In this case, arms 2 linear equations with two variables: x and y. So first you define what your variables are:

Now you can define the system of equations. On the one hand you know that in the account that has 11% interest Mr. Brownwood deposited $1800 more than in the other account. In an equation and according to the previously defined variables this means: y=x+1800 Equation (A)

On the other hand, you know Mr. Brownwood earned $ 818 in interest. This means that the sum between the interest generated in the account deposited with 9% interest plus the interest generated in the account deposited with 11% interest is $ 818. And to calculate the amount of money generated by interest you multiply the percentage of interest by the amount deposited.  Remember that to convert from percentage to decimal you must divide the number by 100. Then 9% is 0.09 and 11% is 0.11. In summary, considering this, you get the equation: 0.09*x+0.11*y=818 Equation (B)

Now you have both equations with the two variables to solve the system. There are several ways to solve the system. One of the most used ways is substitution, which consists in isolating one of the variables from one of the equations and replacing it in the other equation.

In this case you isolate the variable "y" from equation A, and you get:  y=1800+x

Now replace it in equation (B): 0.09*x+0.11*(1800+x)=818

First you apply distributive property, which consists of distributing the multiplication by the terms within the parenthesis:

0.09*x+0.11*1800+0.11*x=818

0.09*x+198+0.11*x=818

Now, we leave the variable x on one side of the equality, in this case the left, and the numbers without the variable on the other side, in this case the right. To pass the numbers from one side of the equality to the other, you must keep in mind that you must use the opposite operation, that is, if the number 198 is adding on one side of the equality, the other side is subtracted:

0.09*x+0.11*x=818-198

Now you perform the corresponding operations. Then you isolate the variable and, and as in the previous case, you pass the number that accompanies the variable on the other side of equality with the opposite operation. In this case it is multiplying and its opposite operation is the division:

0.2*x=620

[tex]x=\frac{620}{0.2}[/tex]

x=3100

Now you replace this value in either of the two equations, A or B, and solve that equation to get the value of y. So: y=4900

Remembering that x was amount of money invested in the account with 9% interest and y was amount of money invested in the account with 11% interest, you can say that $3100 was the amount invested at 9% and $4900 was the amount invested at 11%

Angle p and Angle q are both inscribed angles. This means that their angle is half of the inscribed arc.

measure of angle p = 1/2 60 degrees

angle p = 30 degrees

measure of angle q = 1/2 100 degrees

angle q = 50 degrees

Answer:

30

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

To divide by a fraction, multiply by the reciprocal:

(3/4) / (1/8)

(3/4) * (8/1)

Answer B.

To find the quotient 3/4 divided by 1/8

B) multiply 3/4 by 8!

I hope this helps you! ☺

Answer:

  a = 2(vt -d)/t^2

Step-by-step explanation:

Add the term containing "a":

  d + a(t^2/2) = vt

Subtract d:

  a(t^2/2) = vt -d

Multiply by the inverse of the coefficient of "a":

  a = 2(vt -d)/t^2

Answer:

41.09%

Step-by-step explanation:

step 1

Find the capital gain

$9,100-$6,450=$2,650

step 2

Express his capital gain as a percent of the original purchase price

we know that

$6,450 ( original purchase price) -----> represent 100%

so by proportion

100%/6,450=x/2,650

x=2,650*100/6,450

x=41.09%

Answer:

∠BAD=20°20'

∠ADB=34°90'

Step-by-step explanation:

AB is tangent to the circle k(O), then AB⊥BO. If the measure of arc BD is 110°20', then central angle ∠BOD=110°20'.

Consider isosceles triangle BOD (BO=OD=radius of the circle). Angles adjacent to the base BD are equal, so ∠DBO=∠BDO. The sum of all triangle's angles is 180°, thus

∠BOD+∠BDO+∠DBO=180°

∠BDO+∠DBO=180°-110°20'=69°80'

∠BDO=∠DBO=34°90'

So ∠ADB=34°90'

Angles BOD and BOA are supplementary (add up to 180°), so

∠BOA=180°-110°20'=69°80'

In right triangle ABO,

∠ABO+∠BOA+∠OAB=180°

90°+69°80'+∠OAB=180°

∠OAB=180°-90°-69°80'

∠OAB=20°20'

So, ∠BAD=20°20'

Answer:

The measure of ∠BAD and ∠ADB is 20°20' and 34°90' respectively.

Step-by-step explanation:

Given that AB is tangent to the circle k(O) at B, and AD is a secant, which goes through center O. Point O is between A and D∈k(O).

measure of arc BD is 110°20'.

we have to find the measure of ∠BAD and ∠ADB

∠4=110°22'

In ΔOBD, by angle sum property of triangle

∠1+∠2+∠4=180°

∠1+∠2+110°20'=180°

∠1+∠2=69°80'

Since OB=OD(both radii of same circle) therefore ∠1=∠2

[tex]2\angle 2=69^{\circ}80'[/tex]

[tex]\angle 2=\frac{69^{\circ}80'}{2}=34^{\circ}90'[/tex]

m∠ADB=34°90'

As OB is radius of circle and AB is tangent therefore by theorem which states that radius is perpendicular on the tangent line gives

[tex]\angle 6=90^{\circ}[/tex]

By exterior angle property

∠5=∠1+∠2=69°80'

By angle sum property in ΔABO

∠3+∠6+∠5=180°

∠3+90°+69°80'=180°

∠3=20°20'

[tex]\bf (x-4)+(3x)+100=180\implies x-4+3x+100=180 \\\\\\ 4x+96=180\implies 4x=84\implies x=\cfrac{84}{4}\implies x=21[/tex]

Answer:

A. 20.

Step-by-step explanation:

The denominators 49 and 100  are the squares of 1/2 of the lengths of the minor and major axis.  The standard form is x^2/a^2 + y^2/b^2 = 1  so

a = 2 * √49 and b = 2 * √100.

The length of the major axis is therefore    2* √100

= 2 * 10

= 20 (answer).

Answer:  A. 20

Step-by-step explanation:

For the general equation of ellipse :-

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

If a > b , then the length of major axis = 2a

If b> a , then the length of major axis = 2b

The given equation : [tex]\dfrac{(x-3)^2}{49}+\dfrac{(y+6)^2}{100}=1[/tex]

Which can be written as :

[tex]\dfrac{(x-3)^2}{7^2}+\dfrac{(y+6)^2}{10^2}=1[/tex]

Here 10 >7 , then the length of major axis =2(10)=20 units

True, we have the exactly same values in both domains.

Answer:

this is true!

Step-by-step explanation:

it is true because both have the exactly same values in both domains.

hope this helps :)

Answer:

The true properties are:

A.) The circumcenter of a right triangle falls on the side opposite the right angle

B.) The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides

D.) The circumcenter is equidistant from each vertex of a triangle - The circumcenter of a triangle is the point which is equidistant from the three vertices of the triangle.

The false property is :

C.) The circumcenter of a triangle is always inside it - The circumcenter is not always inside the triangle. Its a point where all three lines intersect and its not necessary that it lies within the triangle.

Final answer:

The circumcenter is defined as the point where the perpendicular bisectors of a triangle's sides intersect and is equidistant from each vertex, which applies to all types of triangles. However, it lies on the hypotenuse for right triangles and can be outside the triangle for obtuse ones.

Explanation:

The properties of the circumcenter of a triangle are a critical concept in geometry. Here's how each option relates to this concept:

B.) The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides. This is a defining property of the circumcenter and is always true regardless of the type of the triangle.

D.) The circumcenter is equidistant from each vertex of a triangle. By definition, the circumcenter is the point from where you can draw a circle (circumcircle) that encompasses all three vertices of the triangle at equal distances.

Now for the other options that are not always true:

A.) The circumcenter of a right triangle falls on the side opposite the right angle. This is true specifically for right triangles, but it's not a general property of the circumcenter for all types of triangles.

C.) The circumcenter of a triangle is always inside it. This is not true. For obtuse triangles, the circumcenter lies outside the triangle, while for acute triangles it is inside, and for right triangles, it is on the triangle.

Answer:

D

Step-by-step explanation:

just took it

70 over sin40 degrees

Answer:

The length of the kite string in terms of trigonometric ratios, if we call it L, is [tex]L=\frac{70}{sin(40\°)}ft[/tex]

Step-by-step explanation:

As we have to use the trigonometric ratios, and knowing that in a right triangle the relation

[tex]hypotenuse*sin(angle)=opposite leg[/tex]

is valid. We call the hypotenuse as L, and we know the other two data (angle and opposite leg), so we have that

[tex]L*sin(40\°)=70ft\Leftrightarrow L=\frac{70}{sin(40\°)}ft[/tex]

Then,

[tex]L=\frac{70}{sin(40\°)}ft[/tex]

is the answer that we are looking for to solve the problem.

The answer is:

The second option,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Discarding each given option in order to find the correct one, we have:

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}[/tex]

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

The statement is true, we can prove it by using the following properties of exponents:

[tex](a^{b})^{c}=a^{bc}[/tex]

[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]

We are given the expression:

[tex](\sqrt[m]{x^{a} } )^{b}[/tex]

So, applying the properties, we have:

[tex](\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }[/tex]

Hence,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}[/tex]

[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }[/tex]

Hence, the answer is, the statement that is true is the second statement:

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Have a nice day!

Answer:

D)

Step-by-step explanation:

The exponential functions are in the form of

[tex]f(x)= ka^x[/tex]

Hence we can see here that the variable x is in the exponential in such functions. Therefore the option D is the correct as in this the x is the exponent.

Therefore the option D) is our exponential functions

Answer:

  see below for a graph

Step-by-step explanation:

You know the line crosses the x-axis at x=6, so one way to write the equation is by translating the line with slope -1/2 to a point 6 units to the right of the origin.

  y = -1/2(x -6)

ANSWER

False

EXPLANATION

The tangent function has no amplitude because it is not bounded.

The given tangent function is

[tex]f(t) = 5 \tan(2t) [/tex]

This is of the form

f(t)=a tan(bt)

The period is given by

[tex]T = \frac{\pi}{ |b| } [/tex]

[tex]T = \frac{\pi}{ |2| } = \frac{\pi}{2} [/tex]

The first statement is true but the second is false.

Hence the whole statement is false.

Answer:F

Step-by-step explanation:

Answer:it’s B

Step-by-step explanation:

Answer:

D) [tex]x^5 + 3x^4 - 2x^3 - 3x^2 + 2[/tex]

Step-by-step explanation:

A polynomial in its standard form is when the terms are arranged in descending order of exponent. The highest exponent goes first and smallest goes to the end of the polynomial.

The only one of the polynomials in the options that meets the requirements is D. Because the term with exponent 5 is at the beginning, then the term with exponent 4, and so on until the independent term.

The answer is: D) [tex]x^5 + 3x^4 - 2x^3 - 3x^2 + 2[/tex]

Answer:

Step-by-step explanation:

Left Frame

Formula

Area of Hexagon = 3*sqrt(3)*a^2 / 2

Area of a Square = a^2

In both cases a is a side length

Givens

A = 384*sqrt(3)

Solution

384*sqrt(3) = 3*sqrt(3)*a^2 / 2     Divide by sqrt(3) on both sides.

384 = 3 * a^2 / 2                           Multiply by 2

768 = 3 * a^2                                Divide by 3

256 = a^2                                     Take the square root of both sides

a = 16

Each side of the square will be = a

The area of the square = a^2

a^2 = 16^2 = 256

Center Frame

I don't know how to expand the question so that I'm doing some sort of step-by-step explanation. The question just means what does a equal when t = 0

The answer is 15.

Right Frame

The tangents meet the circumference of the circle at a 90o angle when the radius is connected by the point of  contact. Call the central angle (LON) = x

The two tangents and the two radii form a kite which is a quadrilateral.

All quadrilaterals have 4 angles that add up to 360.

x + 90 + 90 + 60 = 360           Combine the like terms on the left

x + 240 = 360                           Subtract 240 from both sides

x = 360 - 240

x = 120

The length of the arc is given by (Central angle / 360) * Circumference

x is the central angle so the central angle = 120

Length = (120 / 360) * 96

Length = 1/3 * 96

Length = 32

The solution involves using the distance formula to calculate the lengths of the sides of triangles ABC and ABD, and the Pythagorean theorem to identify the type of triangles they are by their side lengths.

To determine the characteristics of triangle ABC with vertices A(1, 7), B(-2, 2), and C(4, 2), we use the distance formula which is relevant because the length of the side of the triangle labeled a is the difference in the x-coordinates of points A and B. The same applies for side b, being the difference in the y-coordinates of points B and C. The length of side c is derived from the Pythagorean theorem, understanding that c represents the longest side of a right triangle, which is the hypotenuse.

Considering triangle ABD with an additional point D(1, 2), we first need to determine the lengths of the sides by using the formula for distance between two points in a coordinate plane for sides AB, BD, and AD. This will help to ascertain the type of triangle ABD is, based on the lengths of its sides. The length of side AD can be directly obtained since points A and D have the same x-coordinate.

The longest side of triangle ABC, which we determine by comparing the calculated lengths of AB, BC, and AC, will help us state whether the triangle is isosceles, scalene, or equilateral. For triangle ABD, once we have the lengths of AB, BD, and AD, we can determine its type similarly. This understanding stems from the standard geometric principles and the properties of triangles in a Euclidean space.

Answer:

6 per minute

Because you divide by 8 minutes

to find out how many stamps monica originally had, you’d have to do the equation given, “reversed”

equation given: 35 + 20 - 5 - 10

but because we are trying to find how many she originally had left, you’d have to do opposite operations (reverse) in the equation given.

35 - 20 + 5 + 10 = 30

so, this means that monica had 30 stamps originally

Answer:

The location of point K is (1 , 2)

The location of point L is (7 , 0)

Step-by-step explanation:

* Lets revise how to find the location of a point between two points

- If point (x , y) is between two points (x1 , y1) , (x2 , y2) at a ratio

 m1 from (x1 , y1) and m2 from (x2 , y2)

∴ x = [x1(m2) + x2(m1)]/(m1 + m2)

∴ y = [y1(m2) + y2(m1)]/(m1 + m2)

* Now lets solve the problem

- Point J is (-5 , 4) and point M is (10 , -1)

∵ Point K is 2/5 of JM

∴ m1 = 2 ⇒ ratio from K to J

∴ m2 = 5 - 2 = 3 ⇒ ratio from K to M

∴ x = [(-5)(3) + (10)(2)]/(2 + 3) = [-15 + 20]/5 = 5/5 = 1

∴ y = [(4)(3) + (-1)(2)]/(2 + 3) = [12 + -2]/5 = 10/5 = 2

* The location of point K is (1 , 2)

∵ Point L is 4/5 of JM

∴ m1 = 4 ⇒ ratio from K to J

∴ m2 = 5 - 4 = 1 ⇒ ratio from K to M

∴ x = [(-5)(1) + (10)(4)]/(2 + 3) = [-5 + 40]/5 = 35/5 = 7

∴ y = [(4)(1) + (-1)(4)]/(2 + 3) = [4 + -4]/5 = 0/5 = 0

* The location of point L is (7 , 0)

Answer:

$25.11

Step-by-step explanation:

You have to divide 75.33 by the total number of shirts, 3, to see what one costs.

75.33/3=25.11

Answer:

each shirt will cost $25.11

Step-by-step explanation:

if each of the three friends gets a shirt and the total for all of them is $75.33, each shirt costs $25.11

75.33/3=25.11

please mark brainliest