Which can be proven? Select all that apply.
A. ∠ C E D ≅ ∠ A H J
B. A B ≅C B
C. C B ≅D B
D. ∠ D A G ≅ ∠ J C F

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

for such more question on common difference

https://brainly.com/question/25731911

#SPJ8

Using angle relationships, the missing measures are:

m<3 = 138 degrees.

m<5 = 42 degrees.

m<8 = 138 degrees.

Using angle relationships, each of the measure of the angles can be calculated as follows:

Given that, m<1 = 138 degrees.

m<3 = m<1 [vertical angles are congruent]

Substitute:

m<3 = 138 degrees.

m<5 + m<3 = 180

Substitute:

m<5 + 138 = 180

m<5 = 180 - 138

m<5 = 42 degrees.

m<8 = m<3 [alternate interior angles are congruent]

m<8 = 138 degrees.

Learn more about missing angles measure on:

https://brainly.com/question/29115116

#SPJ1

\(\mathrm{Domain\:of\:}\:x^2+2x-15\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\)

\(\mathrm{Range\:of\:}x^2+2x-15:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:-16\:\\ \:\mathrm{Interval\:Notation:}&\:[-16,\:\infty \:)\end{bmatrix}\)

\(\mathrm{Axis\:interception\:points\:of}\:x^2+2x-15:\quad \mathrm{X\:Intercepts}:\:\left(3,\:0\right),\:\left(-5,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:-15\right)\)

\(\mathrm{Vertex\:of}\:x^2+2x-15:\quad \mathrm{Minimum}\space\left(-1,\:-16\right)\)

Answer:

0.27

Step-by-step explanation:

The standard deviation of a uniform distribution is:

σ² = (b − a)² / 12

σ² = (32.51 − 31.58)² / 12

σ² = 0.0721

σ = 0.268

Rounded to the hundredths place, the standard deviation is 0.27.

To solve this question, we use concepts of the uniform probability distribution.

Using this, we get that the standard deviation in volumes of quart-size Hellmann's mayonnaise jars is of 0.2685 fluid ounces.

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The standard deviation is:

\(S = \sqrt{\frac{(b-a)^2}{12}}\)

The actual volumes of quart-size jars of Hellmann's mayonnaise are uniformly distributed from 31.58 to 32.51 fluid ounces.

This means that \(a = 31.58, b = 32.51\)

Find the standard deviation in volumes of quart-size Hellmann's mayonnaise jars (in fluid ounces).

\(S = \sqrt{\frac{(32.51 - 31.58)^2}{12}} = 0.2685\)

Thus, the standard deviation is of 0.2685 fluid ounces.

A similar example is given at https://brainly.com/question/15855314

The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).

For such more question on equation

https://brainly.com/question/29174899

#SPJ8

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

y/5 - 7 = - 1

y = ?

Step 02:

We must apply the algebraic rules.

y/5 - 7 = - 1

y/5 = - 1 + 7

y/5 = 6

y = 6 * 5

y = 30

The answer is:

y = 30

The equation of line FG is given as follows:

y = -0.5x - 5.5.

The circle has a center of (1, -1), hence the equation is given as follows:

(x - 1)² + (y + 1)² = r².

Point (-1, -5) is on the circumference of the circle, hence the radius is obtained as follows:

(-1 - 1)² + (-5 + 1)² = r²

r² = 40.

Hence:

(x - 1)² + (y + 1)² = 40.

Applying implicit differentiation, the derivative is given as follows:

2(x - 1) + 2(y + 1)m = 0

2x - 2 +2m(y + 1) = 0

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

At x = -1 and y = -5, hence the slope is given as follows:

m = -2/4

m = -0.5.

Hence the equation is given as follows:

y + 5 = -0.5(x + 1).

y = -0.5x - 5.5.

More can be learned about the equation of a tangent line at https://brainly.com/question/7252502

#SPJ1

what is your clear question? it lacks some details

Answer:

14

Step-by-step explanation:

i got it right and you can tell that they are almost the same size.

The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

Learn more about trigonometric ratio here: brainly.com/question/28016662

#SPJ1

Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

Answer:

No   g(x) = x/6     for (60, 10) to be a possible solution

by this function 60 people would have to donate 1/6th of a garment each to achieve 10 full garments

Step-by-step explanation:

g(x)   number of items

   x   number of people  

the data point (60, 10) make sense as a possilbe solution     NO

g(x) = number of items       x = 60   g(x) = 10

g(60) = x/6 = 10              

         = 60/10            

by this function 60 people would have to donate 1/6th of a garment each to achieve 10 full garments

Answer: 0.00923521

Step-by-step explanation:

Given : The probability U.S households play video or computer games=69%=0.69

here, the probability of each U.S household play video or computer games is fixed as 0.69

Then, the probability of each U.S household not play video or computer games= 1-0.69=0.31

For independent events the probability of their intersection is product of probability of each event.

Now, the probability that none play video/computer games will be :-

\((0.31)^4=0.00923521\)

Answer:

(k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2, or p = 4k^2 - 24k + 180

Step-by-step explanation:

A rectangle has four sides, two sides both have equal width, while the other two have equal length. The perimiter is the total sum of these sides. We can use the following equation to represent the perimiter using the width and length:

p = 2w + 2l

We know that the width equals (k+3)(k+3), so 2w would equal 2(k+3)(k+3). In the form of a quadratic equation, this would equal 2k^2+12k+18.

We also know that the length equals (k-9)(k-9), so 2l would equal 2(k-9)(k-9). As a quadratic equation, this would equal 2k^2-36k+162.

Plugging these values into our equation we get:

p = (k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2.

Or in the form of a quadratic equation:

p = 2k^2 + 12k + 18 + 2k^2 - 36k + 162

=

p = 4k^2 - 24k + 180

Hope this helps!

The perimeter of the rectangle can be calculated using the formula 2(length + width). Substituting the given expressions for length and width, we get 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to the expression 4k^2-24k+180.

The perimeter of a rectangle is calculated by adding the lengths of all its sides. With the width given as (k+3)(k+3) centimeters, and the length as (k-9)(k−9) centimeters, we can substitute these into the formula for the perimeter of a rectangle, which is 2(length + width).

Therefore, the expression representing the perimeter of the rectangle is 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to 2[(k^2+6k+9)+(k^2-18k+81)], which further simplifies to 2[2k^2-12k+90], and ultimately simplifies to 4k^2-24k+180.

https://brainly.com/question/31695951

#SPJ2

The inverse function of f(n) is:

g(n) = -(4/7)*n - 8/7

Two functions are inverses if the composition is equal to the identity, so if g(n) is the inverse of f(n), we must have that:

f( g(n) ) = n

Replacing the actual function we will get:

-2 - (7/3)*g(n) = n

Now we can solve this for the inverse function g(n), then we will get:

-2 - (7/3)*g(n) = n

(-7/4)*g(n) = n + 2

g(n)  = (-4/7)*(n + 2)

g(n) = -(4/7)*n - 8/7.

That is the inverse function.

Learn more about inverses at:

https://brainly.com/question/3831584

#SPJ1

Answer:

We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).

Step-by-step explanation:

f(x) = x² + 2x - 15

The x-coordinate of the vertex is computed as follows:

To find the y-coordinate, you need to replace the x-coordinate into the formula, as follows:

Then, the vertex is at (-1, -16)

If  u = - 3i + 2i,  v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.

To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:

3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j

Next, we can perform the scalar multiplication of u and the vector 6i + 14j:

5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)

Expanding the product, we get:

5(-18i² + 36ij + 42ij - 28j²)

Since i² = j² = -1, we can simplify this expression as:

5(18 + 70) = 440

Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.

The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.

To learn more about vectors click on,

https://brainly.com/question/9201864

#SPJ1

Answer: 314.16

Step-by-step explanation: To find the area of a circle you have to square the radius then multiply by pi. 10 squared is 100 then multiplied by pi is 314.16 (rounded to the nearest hundredth).

Answer: 24 inches

Step-by-step explanation:

First, remember that 1 ft is equal to 12 in

Then, if 1 ft = 12 in

1 = 12in/1ft

this means that we can write a constant:

C = 12in/1 in

and C = 1, then we can write the width 2ft as:

2ft = 2ft*C = 2ft*12in/1ft = 24in

The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.

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

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

From the graph, the x coordinate 2, have a y coordinate of 120. Hence:

The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

no

yes

no

no

Step-by-step explanation:

this should be true

a+b>c

a+c>b

b+c>a

Given:

The function is:

\(y=\sec^{-1}(x)\)

To find:

The range of the given function.

Solution:

We have,

\(y=\sec^{-1}(x)\)

The range of secant inverse function is:

\(Range=\{y|0\leq y\leq \pi , y\neq \dfrac{\pi}{2}\}\)

The range of the given function in interval notation is:

\(Range=\left[0,\dfrac{\pi}{2}\right)\text{ and }\left( \dfrac{\pi}{2}, \pi\right ]\)

Therefore, the correct option is C.

Answer:

The quadratic formula allows us to solve any quadratic equation that's in the form ax^2 + bx + c = 0.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

For more such questions on parking cost

https://brainly.com/question/18091509

#SPJ8

The graph of the linear equation  y=x+2 is plotted.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

The given equation is:

y = x+2

Put value of 'x' and find 'y'

for x = 0, y = 2 : (0,2)

for x = 1, y = 3: (1,3)

for x = 2, y = 4 : (2, 4)

Thus, the graph of the linear equation  y=x+2 is plotted.

know more about drawing the graph

https://brainly.com/question/12980786

#SPJ1

Therefore, the math expression for the time taken is:

time = 186 m ÷ (735 km/h × 1000 m/km ÷ 3600 s/h) = 186 m ÷ 205 m/s = 0.9073 s

Speed is a measure of how fast an object is moving relative to a reference point. It is defined as the distance traveled by an object in a given amount of time. The standard unit of measurement for speed is meters per second (m/s) in the metric system, but it can also be measured in miles per hour (mph), kilometers per hour (km/h), or other units depending on the context.

Given by the question.

We can use the formula:

distance = speed × time

To find the time taken to cover a distance of 186 m at a speed of 735 km/h, we first need to convert the speed to meters per second (m/s).

1 km = 1000 m

1 h = 3600 s

So,735 km/h = (735 × 1000) m/ (3600 s) = 205 m/s

Now, we can plug in the values into the formula:

186 m = 205 m/s × time

Solving for time, we get:

time = 186 m ÷ 205 m/s = 0.9073 s

To learn more about distance:

https://brainly.com/question/15172156

#SPJ1