Find the surface area
Round to the nearest tenth

Answer:

  2. 139π/90 radians ≈ 4.852

  3. -(9√5 +8√7)/77

  4. 2+√3

Step-by-step explanation:

You want exact answers involving various trig identities and angle sum formulas.

There are π radians in 180°, the number of radians in 278° is ...

  278°(π/180°) = (278/180)π

  278° = (139/90)π radians ≈ 4.852 radians

The cosine of the sum of angles is ...

  cos(x +y) = cos(x)cos(y) -sin(x)sin(y)

The relationship between sine and cosine is ...

  cos(x) = ±√(1 -sin(x)²)

  sin(x) = ±√(1 -cos(x)²)

The signs will depend on the quadrant of the angle.

To use the angle sum relation, we need the sine of the angle whose cosine is given, and vice versa.

  sin(arccos(-2/7)) = -√(1 -(-2/7)²) = -(√45)/7 = (-3/7)√5 . . . . in QIII

  cos(arcsin(-3/11)) = √(1 -(-3/11)²) = (√112)/11 = (4/11)√7 . . . . in QIV

The cosine of the sum of the angles is then ...

  cos(arccos(-2/7) +arcsin(-3/11)) = (-2/7)(4√7/11) -(-3√5)/7·(-3/11)

  = -8√7/77 -9√5/77

  cos(x +y) = -(9√5 +8√7)/77

The formula for the tangent of the sum of angles is ...

  tan(x +y) = (tan(x) +tan(y))/(1 -tan(x)tan(y))

We know that tan(π/4) = 1 and tan(π/6) = 1/√3, so the tangent of the sum of the angles is ...

  tan(π/4 +π/6) = (1 +1/√3)/(1 -(1·1/√3)) = (√3 +1)/(√3 -1) = (√3 +1)²/2

  tan(π/4 +π/6) = 2 +√3

__

Additional comment

A suitable calculator can be very handy computing and/or checking your results.

2) 278° to Radians = 4.85202

3) the exact value of cos (x+ y) is -0.0914

4) the exact value of the expression is 3.73

The formula ofr conversion from degree to radian is

2) 278° × π/180 = 4.852rad

3) in the above given expressions, Sin(x) is negative.

Using Pythagorean rule, we can state:

sin(x ) = √(1 - cos^2(x)) =

√(1 - (-2/7)²)

= -3√(3)/7

Also,

given that cos( y) is positive, we c  n also use the Pythagorean idetity

cos  (y) = √(1 - sin ²(y) )

= √(1 - (-3/1 1)²)

= 8√(2)/11

substituting into cos (x + y)


cos(x+y) = cos(  x)cos (y ) - sin (x) sin(y)

= (-2/7)( 8 √(2)/11) - (-3√(3)/7) ( -3/11)

= -1 6 √(2) /77 + 9√( 3)/ 77

= -0.09141506142

The exact value is approximately -0.0914

3)

Using the formula for tangent of sum of angles we say

tan( ( π/4) + (π/6) )   = (tan ( π / 4) + tan (π/6))/(1 - tan ( π/4) tan( π/6))

Sutstituting ....

tan ((  π/4) + ( π/6) )  = (1 + √ 3/3)/( 1 - √ 3 /3 )

tan( (π/ 4) + (π /6 )) =   (1 + √3/   3) (1 + √3/3 )]/ [(1 - √3/ 3)(1 + √3/3)]

Simplifying

  tan ( (π /4) + ( π/6) ) = ( 2 + √3 )/  ( 2 - √ 3)

This is the exact value of tan((π/4) + (π/6)) or 3.73

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The answers are:

[tex]m \angle1+ m\angle2 + m\angle3=180^o[/tex]  is the sum of interior angles in a triangle.

[tex]m \angle1+ m\angle5 = m\angle AYX[/tex] is Definition of parallel lines.

[tex]m \angle AYX+m\angle 4=180^o[/tex] Definition of a straight angle

[tex]m\angle5=m\angle2[/tex] is Substitution

[tex]m \angle1+ m\angle5 + m\angle4=m \angle AYX+m\angle 4[/tex] Substitution

An angle in geometry is the measurement of the amount of rotation that occurs between two lines, rays, or line segments that have a shared endpoint, or vertex. Angles are expressed in terms of degrees, radians, or other angular measuring units.

A protractor, a tool with a semicircular or circular scale and degree markings, can be used to measure angles. Angles may also be labelled using symbols, such as ∠ABC or ∠PQR, in which the letter in the middle of the symbol designates the vertex of the angle.

An auxiliary line that is parallel to XZ given is the triangle formed by XYZ and AY.

[tex]m\angle 1+m\angle 2+m\angle3=180^o[/tex] Definition of the sum of interior angles in a triangle

[tex]m\angle1=m\angle AYX[/tex] Corresponding angles are congruent (alternate interior angles)

[tex]m \angle 2 = m \angle 4[/tex] Corresponding angles are congruent (alternate interior angles)

[tex]m \angle AYX + m \angle 4 = 180^o[/tex] Definition of a straight angle

[tex]m \angle 1 + m \angle 5 = m \angle AYX[/tex] Definition of parallel lines

[tex]m \angle 5 = m \angle 2[/tex] Substitution

[tex]m \angle 1 + m \angle 2 + m \angle 3 = m \angle 1 + m \angle 5 + m \angle 4[/tex] Substitution

[tex]m \angle 1 + m \angle 5 + m \angle 4 = m \angle AYX + m \angle 4[/tex] Substitution

[tex]m \angle 1 + m \angle 2 + m \angle 3 = m \angle AYX + m \angle 4[/tex] Transitive property of equality

[tex]m \angle 1 + m \angle 2 + m \angle 3 = 180^o[/tex] Substitution

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Answer: The primary rectangle contains a length of 2a units (since it is labeled as "2a" within the diagram), so its zone is 2a x a = 2a^2 square units.

The moment rectangle contains a length of 3a units (since it is labeled as "3a" within the diagram), so its range is 3a x a = 3a^2 square units.

The third rectangle contains a length of 4a units (since it is labeled as "4a" within the graph), so its range is 4a x a = 4a^2 square units.

To discover the overall region of the expansive rectangle, able to include the zones of these three rectangles:

Add up to zone = 2a^2 + 3a^2 + 4a^2

Disentangling this expression, we are able combine the like terms (2a^2, 3a^2, and 4a^2) to urge:

Add up to range = (2 + 3 + 4) a^2

Step-by-step explanation:

Answer:

26π

Step-by-step explanation:

radius=13

double radius to find diameter

diameter=26

equation for circumference= π×d

circumference= 26π

The length of FG chord is 5 units.

What bout chord?

A chord is a line segment that joins two points on the circumference of a circle. More specifically, a chord is a straight line that intersects a circle at two points, and the segment of the line between these two points is called a chord.

The length of a chord can be calculated using the Pythagorean theorem, given the radius of the circle and the distance between the two points on the circumference. The length of a chord is always less than or equal to the diameter of the circle.

Chords have various applications in geometry, trigonometry, and calculus. For example, in trigonometry, the chord function is defined as the ratio of the length of a chord to the radius of the circle. In calculus, chords are used in the definition of the derivative, which is the slope of the tangent line to a curve at a given point.

According to the given information:

2(x + 2 )=  ( 5 x - 5 )

2x + 4 = 5x -5

9 = 3x

3 = x

The length of FG is = x+2 = 3+2 = 5 units

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The length of FG chord is 5 units.

What bout chord?

A chord is a line segment that joins two points on the circumference of a circle. More specifically, a chord is a straight line that intersects a circle at two points, and the segment of the line between these two points is called a chord.

The length of a chord can be calculated using the Pythagorean theorem, given the radius of the circle and the distance between the two points on the circumference. The length of a chord is always less than or equal to the diameter of the circle.

Chords have various applications in geometry, trigonometry, and calculus. For example, in trigonometry, the chord function is defined as the ratio of the length of a chord to the radius of the circle. In calculus, chords are used in the definition of the derivative, which is the slope of the tangent line to a curve at a given point.

According to the given information:

2(x + 2 )=  ( 5 x - 5 )

2x + 4 = 5x -5

9 = 3x

3 = x

The length of FG is = x+2 = 3+2 = 5 units

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Therefore , the solution of the given problem of unitary method comes out to be Stacy's Bake Shop sells cupcakes for less than The Best Cake Shop does according to the idea of unit pricing.

Use the tried-and-true fundamental methodology, the real variables, and any useful information you learn from the general and specific questions to complete the assignment. Customers may be given another chance to taste the products in expression response. If these improvements don't happen, we'll lose out on significant advancements in programming comprehension.

Here,

Due to the idea of unit pricing, Stacy's Bake Shop sells cupcakes for less money than The Best Cake Shop.

In order to compare products with varying quantities or sizes, unit pricing, also known as price per unit, is used.

In this instance, Stacy's Bake Shop charges $21 for a dozen cupcakes, hence the price per cupcake is calculated as

=>  $21 /12, or $1.75 per cupcake.

On the other hand, The Best Cake Shop charges $12 for a half-dozen cupcakes; this indicates that each cupcake costs $2, or $12 divided by six.

As a result, Stacy's Bake Shop charges $1.75 less each cupcake than The Best Cake Shop, which charges $2.

As a result, Stacy's Bake Shop sells cupcakes for less than The Best Cake Shop does according to the idea of unit pricing.

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The ratio between the number of people who do not enjoy reading and the number of people who do not enjoy playing videogames is given as follows:

3 to 1.

The ratio between two amounts a and b is given as follows:

a to b.

The amounts for this problem are given as follows:

Hence the ratio is of:

9/3 = 3/1 = 3 to 1.

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The question that is a statistical question is "How many miles did your family drive last week?"

A statistical question is a question that requires collecting and analyzing data to answer.

It involves investigating a specific variable or variables and determining patterns, trends, or relationships within the data.

The question "How many miles did your family drive last week?" is statistical, as it involves collecting and analyzing data related to a specific variable (miles driven) over a certain period of time (last week).

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The blanks when completed are

In a scale drawing, the scale factor represents the ratio of the size of an object in the drawing to the size of the corresponding object in real life.

In the given scale drawing, we have

Longest side in B = 12

So, the scale factor is

scale factor = size of object in drawing / size of corresponding object

This gives

scale factor = 12 / 4

scale factor = 3

This means that

Every side length in A grew by a factor of 3

Using the scale ratio formula, we have

A length in B/A corresponding length in A = 3

Lastly, the size of the angles remain unchanged

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The value of k in the given graph is 4

Explain the term graph

A graph is a visual representation of data that displays the relationship between two or more variables. It consists of a set of points or vertices connected by lines or curves that represent the data points. Graphs are used to analyze and interpret data and to communicate information effectively in various fields, including mathematics, science, and business.

According to the given information

We are given that g(x) = f(x) + k, where f(x) and g(x) are two parabolas that open up and pass through the point (-3, -3) and (-3, 1), respectively.

Since both parabolas pass through the point (-3, -3), we know that:

f(-3) = -3

g(-3) = -3 + k = 1

Solving for k, we get:

k = 1 - (-3) = 4

Therefore, the value of k is 4.

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The number that needs to be added to complete the square is 169/4

To complete the square for the quadratic equation x² + 13x - 32 = 0, we need to add (13/2)² = 169/4 to both sides.

This is because the coefficient of x in the quadratic term is 13, so half of that is 6.5, and the square of that is 42.25, which simplifies to 169/4.

The equation will then become:

x² + 13x - 32 + 169/4 = 0 + 169/4

So the number that needs to be added to complete the square is 169/4, or 42.25.

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Answer: To find the area of a triangle, we can use the formula:

Area = (base x height) / 2

However, in this problem, we don't have the height of the triangle directly. Instead, we have the lengths of three sides of the triangle.

To find the height, we can use Heron's formula, which allows us to calculate the area of a triangle when we know the lengths of all three sides:

Area = √(s(s-a)(s-b)(s-c))

where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter (half of the perimeter) of the triangle:

s = (a + b + c) / 2

Once we have the area of the triangle, we can use the given price per square foot to calculate the cost of the lot.

So, to apply this to the problem at hand, we can first calculate the semi-perimeter of the triangle:

s = (94 + 188 + 168) / 2 = 250

Next, we can use Heron's formula to find the area of the triangle:

Area = √(250(250-94)(250-188)(250-168)) ≈ 7329.53 square feet

Finally, we can calculate the cost of the lot by multiplying the area by the price per square foot:

Cost = 7329.53 x $3 = $21,988.59

Therefore, the approximate cost of the triangular lot is $21,988.59.

Step-by-step explanation:

The equation where x represents the matrix would be A. [tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

To find the matrix equation representing the given system of equations, we can write the system as AX = B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants.

[tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

The system of equations is:

x + y + z = 260

x + y - z = 60

2x + y + 2z = 305

We can write this system as a matrix equation:

A = [tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right][/tex]

X = [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

So the correct matrix equation is:

AX = B

[tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

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Answer:

Circumference/Diameter = π

If the diameter is 2, then the circumference is 2π.

If the diameter is 6, then the circumference is 6π.

Answer:

691m^2

Step-by-step explanation:

This one is simpler than it looks. If you imagine the shape as a rectangle and two triangles, then move the triangle on the left over to the one on the right, the shape becomes a normal rectangle. Simply solve like your everyday quadrilateral.

area = base × height

a = 21m × 33m

a = 691m^2

Answer:

linear

Step-by-step explanation:

function declines at a constant rate of 1/2x with a y-intercept of 20 giving the equation y= 1/2x + 20

Answer: 5

Step-by-step explanation:

the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color.

How to solve the question?

To find the least number of rows, we need to determine the greatest common divisor (GCD) of 56 and 120, since each row must have the same number of blocks. We can use the Euclidean algorithm to find the GCD:

120 = 2 x 56 + 8

56 = 7 x 8 + 0

Therefore, the GCD of 56 and 120 is 8. This means that each row must have 8 blocks, and there will be a total of (56+120) = 176 blocks to be arranged.

Since each row can have either only yellow or only black blocks, we need to determine which color will have the greater number of rows. To do this, we can divide the total number of blocks by the number of blocks in each row:

Yellow blocks:

Number of rows = 56 ÷ 8 = 7 rows

Black blocks:

Number of rows = 120 ÷ 8 = 15 rows

Since there are more black blocks, we will use 15 rows of black blocks. Each row will have 8 blocks, so there will be a total of (15 x 8) = 120 black blocks.

We can then use the remaining 56 yellow blocks to create rows of only yellow blocks. Each row will have 8 blocks, so there will be a total of (56 ÷ 8) = 7 yellow rows.

Therefore, the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color

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Martina is learning different kinds of Latin dance she went to 6 salsa lessons and 12 rumba lessons each lessons cost 4$ let t equal the total number of lesson, the total cost of the lessons is $72.

The problem gives us two pieces of information:

1. Martina attended 6 salsa lessons and 12 rumba lessons, which means she attended a total of 18 lessons in total.

2. Each lesson costs $4.

To find an equation for the total number of lessons (t), we simply add the number of salsa lessons and rumba lessons:

t = 6 + 12

t = 18

So the total number of lessons Martina attended is 18.

To find an equation for the total cost of the lessons (c), we can multiply the total number of lessons by the cost per lesson:

c = t x 4

c = 18 x 4

c = 72

So the total cost of the lessons Martina attended is $72.

Thus, the equation for the total number of lessons is t = 6 + 12 = 18 and the equation for the total cost of the lessons is c = t x 4 = 18 x 4 = 72.

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Answer:

4.) 32 answer

Step-by-step explanation:

2×2 is 4

4× 8 is 32

The logarithmic form of the equation (1/7)³ = 1/343 is given as follows:

[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]

A logarithm is a mathematical function that represents the power to which a given base must be raised in order to obtain a given number. Logarithms are often used to simplify calculations involving very large or very small numbers.

In this problem, we raise 1/7 to the third power to obtain the number 1/343, hence the logarithm of base 3 of the number 1/343 is of 1/7, and then the expression is given as follows:

[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]

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The variable d represents the number of days he spends on vacation, and the variable p represents the total number of postcards he buys Cooper will have bought a total of 18 postcards after 2 days of vacation.

If p = 9d represents the total number of postcards Cooper buys in relation to the number of days he spends on vacation, we can substitute d = 2 into the equation to find the total number of postcards he buys after 2 days of vacation:

p = 9d

p = 9(2)  [Substitute d = 2]

p = 18

Therefore, Cooper will have bought a total of 18 postcards after 2 days of vacation.

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the correct answers are E(-4, 5) and F(3, 2). According to given probabilities  condition

How to solve the question?

To find the coordinates of Checkpoints E and F, we need to first understand what is meant by "located at CD's location in a 180° rotation of the course."

A 180° rotation means that we flip the course upside down, with the line segment connecting Checkpoints C and D acting as the axis of rotation. This means that Checkpoints E and F will be on the same line as CD, with E being the reflection of C and F being the reflection of D across the line CD.

To find the coordinates of E, we reflect C across the line CD. To do this, we first find the slope of the line CD:

slope = (2 - 5) / (-3 - (-4)) = -3

The midpoint of CD is:

midpoint = ((-3 + (-4))/2 , (2 + 5)/2) = (-3.5, 3.5)

The line perpendicular to CD passing through the midpoint has slope -1/(-3) = 1/3. Using point-slope form, we can find the equation of this line:

y - 3.5 = (1/3)(x + 3.5)

Simplifying, we get:

y = (1/3)x + 4

To reflect C across CD, we can find the intersection point of this line with the line passing through C and CD. This line has slope -3 and passes through (-4, 5). Using point-slope form, we can find its equation:

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

Simplifying, we get:

y = -3x - 7

Setting these two equations equal to each other, we get:

(1/3)x + 4 = -3x - 7

Solving for x, we get:

x = -4

Substituting this value back into either equation, we get:

y = 5

Therefore, the coordinates of Checkpoint E are (-4, 5).

To find the coordinates of F, we reflect D across CD. We can use a similar method as above to find the line passing through D and CD:

slope = (2 - 5) / (-3 - (-4)) = -3

y - 2 = (-3)(x + 3)

Simplifying, we get:

y = -3x - 7

To reflect D, we find the intersection point of this line with the line perpendicular to CD passing through the midpoint:

y - 3.5 = (1/3)(x - (-3.5))

Simplifying, we get:

y = (1/3)x + 4

Setting these two equations equal to each other, we get:

(1/3)x + 4 = -3x - 7

Solving for x, we get:

x = 3

Substituting this value back into either equation, we get:

y = 2

Therefore, the coordinates of Checkpoint F are (3, 2).

So the correct answers are E(-4, 5) and F(3, 2).

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Answer:

127.5

Step-by-step explanation:

multiply 15 and 17 divide by 2 and boom

Therefore , the solution of the given problem of angles comes out to be KL has a measurement of 19.49.

The largest and smallest walls of a skew are found at the intersection of the pathways connecting its ends. Two pathways could meet at a crossroads. Another result of two entities interacting is an angle. More than anything else, they resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their endpoints to produce a two-dimensional curve.

Here,

It looks to be a right-angled triangle with the sides identified as KL, KM, and LM based on the photograph provided. The measurements are as follows:

=> KL = 8.58

=> KM = 9.36

=> LM = 10.13

=> KM + LM = KL

Since KM and LM are the two sides that make up KL, we may sum them to find the measurement of KL.

=> KM + LM = 9.36 + 10.13 = 19.49

KL thus has a measurement of 19.49.

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Answer: x ≈ 5.085

Step-by-step explanation:

     We will utilize logarithms to help us solve.

Given:

     [tex]\displaystyle 4^{x-3}=18[/tex]

The logarithm of both sides of the equation:

     [tex]\displaystyle log(4^{x-3})=log(18)[/tex]

Logarithm power property:

     (x - 3)log(4) = log(18)

Divide both sides of the equation by log(4):

      x - 3 = [tex]\frac{log(18)}{log(4)}[/tex]

Add 3 to both sides of the equation:

      x =  [tex]\frac{log(18)}{log(4)}[/tex] + 3

Compute:

     x ≈ 5.085

Answer: $3.00

Step-by-step explanation:

To figure this out, we can use the following formula:

[tex]\textsf{Cost per pound x number of pounds we want to buy}[/tex]

In this case, we want to buy 2.5 pounds of apples, so we can multiply 2.5 by $1.20 to get the total cost:

[tex] \textsf{2.5 x 1.20 = 3} [/tex]

So, 2.5 pounds of apples will cost $3.00

The function (5) is 10 given that f(x) = x + 5  if x ≥ 0

To solve for f(5), we have to look at the function rule that says f(x) = x + 5 if x ≥ 0. Following this rule we say f(x) = 5 + 5 = 10. The number 10 is greater than 0 which make it valid.

All other rule does not apply to finding f(5).

The above answer is in response to the full question below

if  f(x) = { 2x−3 if x ≤ -4

            {   x²  If -4 < x < 0

             {  x + 5  if x ≥ 0

What is f(5)?

A. 25

B. 7

C. -4

D. 10

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y is a function of x.

A mathematical relationship between an input (x) and an output (y) where each input has exactly one output is known as a function. There are no multiple possibilities of y for a single value of x in the preceding equation, which expresses y as a combination of x², x, and a constant term. As a result, the equation meets the criteria for a function.

Yes, y = 2x² - 4x + 10 is a function.

A function is a mathematical rule that assigns to each input (x-value) exactly one output (y-value). In the given equation, for any value of x, we can calculate the corresponding value of y using the given equation. Therefore, y is a function of x.

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The value of tanQ is 4/3

What is trigonometric ratio?

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

The values of the functions are expressed as follows;

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

The opposite in the triangle is 12 and the adjascent is 9 while th hypotenuse is 15.

therefore , since tan(tetha) = opp/adj

then, tanQ = 12/9

simplifying the value to the nearest term,

tanQ = 4/3

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answer:

17%

I hope this helps