In the right AABC with m/C=90°, mZA=75°, and AB = 12 cm. Find the area
of A ABC.
A =
ABC
cm²

Answer:

perimeter is 36 and area I think is 72

Step-by-step explanation:

Yes, this is correct. An isometry is a transformation that preserves the sample size and shape of an object, meaning that the preimage and image are congruent.

An isometry is a transformation that preserves the size and shape of an object. This means that the preimage and image are congruent, meaning that they have the same size and shape. In order to determine if a transformation is an isometry, one must first identify the preimage and image. Once this has been done, the lengths of the corresponding sides must be compared in order to determine if they are congruent. If the lengths match, then the transformation is an isometry. Additionally, the angles of the preimage and image should also be compared to ensure that they are the same. If all the sides and angles match, then the transformation is an isometry.

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The value of σ1 that is required to cause shear failure along the joint that is inclined to the major principal plane by 45°, 55° and 65° are 6.51 MPa, 8.28 MPa and 10.44 MPa, respectively.

To calculate the value of  σ1, use the Mohr-Coulomb failure criterion

τf = c + σn tan φ

where:

τf = shear stress required to cause failure

c = cohesion = 5 MPa

σn = normal stress on the joint

φ = friction angle = 35°

When the joint is inclined to the major principal plane by 45°, the major principal stress (σ1) is equal to the maximum principal stress.

The intermediate principal stress (σ2) is equal to the minor principal stress (σ3) because the joint is inclined at 45° to the major principal plane.

Therefore:

σ1 = σn + σ3

= σn + 2 MPa

The angle between the joint and the plane of σ1 is 45°.

τf = 5 MPa + σn tan 35° = σ1 sin 45° tan 35°

Substitute σ1

5 MPa + σn tan 35° = (σn + 2 MPa) sin 45° tan 35°

By solving for σn

σn ≈ 4.51 MPa

Therefore, the value of σ1 required to cause shear failure along the joint that is inclined to the major principal plane by 45° is:

σ1 ≈ 6.51 MPa

Follow the steps above to calculate for 55°, and 65°.

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We have found two quadratic functions with x-intercepts (-5,0) and (5,0): f(x) =\(x^2 - 25\), which opens upward, and g(x) = \(-x^2 + 25\), which opens downward.

For the quadratic function that opens upward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

f(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens upward, then a must be positive. Expanding the equation, we get:

f(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open upward, we need the coefficient of x^2 to be positive, so we can set a = 1:

f(x) = x^2 - 25

For the quadratic function that opens downward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

g(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens downward, then a must be negative. Expanding the equation, we get:

g(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open downward, we need the coefficient of x^2 to be negative, so we can set a = -1:

g(x) = -x^2 + 25

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Answer:

-1

Step-by-step explanation:

She walked down 2 flights, then up 3 flights. This would cause her to be 1 floor above her floor. So, she would have to walk down 1 flight (hence the negative in the -1) and she would be on her floor.

Answer:

-1

Step-by-step explanation:

Answer:

y -3 = -4(x+2)

Step-by-step explanation:

The point slope form of a line is

(y-y1) = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y -3 = -4(x- -2)

y -3 = -4(x+2)

Answer:

81

Step-by-step explanation:

93-12=81

Step-by-step explanation:

"to solve for h" just means to transform the equation, so that instead of V we get h alone on one side of the equation.

V = pi×r²×h

h = V / (pi×r²)

that's it.

for the slope question :

the slope is the factor of x (2/3 and 3/2) and indicates how steep the line is. and it is expressed as y/x ratio defining how many units y changes, when x changes a certain amount of units.

the bigger the number, the steeper the line.

so, the 4th answer option is correct. g(x) is steeper than f(x).

the lines are not parallel, because they do not have the same slope.

they are not perpendicular, because perpendicular slopes turn the y/x ratio upside down AND flip the sign.

e.g. the perpendicular slope of 2/3 would be -3/2.

Answer:  3 necklaces and bracelet sets can be made from the  28 1/3 inches of wire.

Step-by-step explanation:

step 1

LET  I set of necklace and bracelet be represented as ( A bracelet and a necklace)

 if Tominka uses 6 1/9 inches of wire to make a necklace and 3 1/3 of wire to make a bracelet  for a set

Then Total Length of wire that can be used for a set = 6 1/9 inches+ 3 1/3 inches = 9 (1+ 3)/9

= 9 4/9 inches.

Step 2

IF  a set (One necklace and bracelet) can use = 9 4/9 inches

and Total wire used = 28 1/3inches

Then Number of  necklaces and bracelet sets that can be made  from the 28 1/3 inches wire = 28 1/3inches /9 4/9 inches

=85/3 / 85/ 9  = 85/3  x 9/ 85  = ( 85 cancels 85 )

9/3 = 3

 3 necklaces and bracelet sets can be made from the  28 1/3 inches of wire.

The weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.

Building Price per square ft ($) Number of sq. ft Building 1 75 and 125,000, Building 2 85 and 37,000, Building 3 90 and 77,500, Building 4 45 and 35,000, Building 5 50 and 40,000. Now, the formula to calculate weighted average price per square foot is,

Weighted Average Price per square foot = [ (Price per sq. ft of Building 1 * Number of sq. ft of Building 1) + (Price per sq. ft of Building 2 * Number of sq. ft of Building 2) + (Price per sq. ft of Building 3 * Number of sq. ft of Building 3) + (Price per sq. ft of Building 4 * Number of sq. ft of Building 4) + (Price per sq. ft of Building 5 * Number of sq. ft of Building 5) ] / Total sq. ft of all buildings.

Applying the values in the formula,

Weighted Average Price per square foot = [(75 * 125000) + (85 * 37000) + (90 * 77500) + (45 * 35000) + (50 * 40000)] / (125000 + 37000 + 77500 + 35000 + 40000)= [9375000 + 3145000 + 6975000 + 1575000 + 2000000] / 297500= 23092500 / 297500= 77.72

Therefore, the weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.

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The value of the triple integral is -16.

Triple integral is a mathematical concept used in calculus to calculate the volume of three-dimensional objects. It extends the concept of a single integral to functions of three variables and integrates over a region in three-dimensional space.

The triple integral of a function f(x, y, z) over a region E in three-dimensional space is denoted by:

∭E f(x, y, z) dV

We can set up the triple integral as follows:

∫∫∫ 16y dV

Where the limits of integration are:

0 ≤ x ≤ 2

0 ≤ y ≤ (2- \(x^2\)z)/(2y)

0 ≤ z ≤ 2/\(x^{2y\)

Note that the upper bound of integration for y is not a constant, but depends on both x and z.

Integrating with respect to y first, we get:

∫∫∫ 16y dV = ∫0^2 ∫\(0^(2-x^2z)/(2x)\)∫\(0^(2/x^2y) 16y dz dy dx\)

= ∫\(0^2\) ∫\(0^(2-x^2z)/(2x) 32/x dx dz\)

= ∫\(0^2\) [16(\(2-x^2z)/x^2\)] dz

= ∫\(0^2 (32/x^2 - 16z)\) dz

= 32∫\(0^2 x^-2 dx - 16\)∫\(0^2\)z dz

= 16 - 16(2)

= -16

Therefore, the value of the triple integral is -16.

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Answer:

-3/2

Step-by-step explanation:

Count the rise = -3

Count the run= 2

Rise/run= -3/2

Answer:

-7/-4 or 1.75

Step-by-step explanation:

Another formula for the slope of a line is (y2-y1)÷(x2-x1)

So all we need is to find the points (x1, y1) and (x2, y2)

Point 1: (1, -3)

Point 2: (-3, 4)

Sub this into the equation:

(-3-4) ÷ (-3-1) = -7 ÷ -4 = 1.75

(a) Limits of integration are needed to evaluate the definite integral.(b) The graph of y = ar³ + bx² + cx + d has no inflection points.(c) The approximate percentage change in y = (2x + 3)^4 when 'a' increases from 1 to 1.01 is 800%.



(a) To evaluate the definite integral ∫[(VE) (√T-1)³] dr, we need to know the limits of integration for 'r'. Without the limits, we cannot calculate the definite integral. Please provide the limits so that I can assist you further.

(b) To show that the graph of y = ar³ + bx² + cx + d has exactly one inflection point, we need to examine the second derivative of y. Taking the derivative of y with respect to x, we have y'' = 6ar + 2b. Since a is greater than 0, the coefficient of r is positive. Thus, the second derivative is always positive, which means there is no inflection point in the graph of y = ar³ + bx² + cx + d.

(c) The given function is y = (2x + 3)^4. To estimate the percentage change in y when 'a' increases from 1 to 1.01, we need to find the derivative of y with respect to 'a'. Differentiating y with respect to 'a', we get dy/da = 4(2x + 3)^4.



To estimate the percentage change, we substitute x = 1 into the derivative expression, giving us dy/da = 4(2 + 3)^4 = 4(5)^4. Then, we calculate the percentage change as (dy/da)(Δa/a) * 100, where Δa = 1.01 - 1 and a = 1. Plugging in the values, we get [(4(5)^4)(0.01/1)] * 100 = 800%.

Therefore, the approximate percentage change in y when 'a' increases from 1 to 1.01 is 800%.

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The limit of the given expression is 0, which is option (A).

To find the limit of the given expression, we can use L'Hôpital's rule, which states that if we have an indeterminate form of the type 0/0 or infinity/infinity, then we can take the derivative of the numerator and denominator separately and evaluate the limit again.

Let's apply L'Hôpital's rule to the given expression:

lim x→[infinity] ln(bx+1)/ln(ax^2+3) = lim x→[infinity] (d/dx ln(bx+1))/(d/dx ln(ax^2+3))

Taking the derivative of the numerator and denominator separately, we get:

lim x→[infinity] b/(bx+1) / lim x→[infinity] 2ax/(ax^2+3)

As x approaches infinity, the terms bx and ax^2 become dominant, and we can ignore the constant terms 1 and 3. Therefore, we can simplify the above expression as:

lim x→[infinity] b/bx / lim x→[infinity] 2ax/ax^2

= lim x→[infinity] 1/x / lim x→[infinity] 2/a

= 0/2a

= 0

Hence, the limit of the given expression is 0, which is option (A).

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Answer:

20 square feet

Step-by-step explanation:

The length of a rectangular deck is five times it's width if the decks perimeter is 24 feet what is the decks area

Step 1

We find the Length and Width of the deck

Perimeter of a rectangle = 2L + 2W

The length of a rectangular deck is five times it's width

W = Width

L = Length = 5W

P = 24 feet

Perimeter = 2(5W) + 2W

24 = 10W + 2W

24 = 12 W

W = 24/12

W = 2 feet

Solving for L

L = 5W

L = 5 × 2 feet

L = 10 feet

Step 2

We find the area of the deck

Area of the deck(Rectangle) = Length × Width

= 10 feet × 2 feet

= 20 square feet

Answer:

34 students

Step-by-step explanation:

Turn 40% to decimal = 0.4

Then multiply it to 57.

57 * 0.4 = 22.8

Round it.

22.8 = 23

Now subtract it to 57

57 - 23 = 34

Answer:

Step-by-step explanation:

The dimension of W is 3 , the subspace W is defined as {(a,b,c): a, b, and c are real numbers}.

Since there are three free variables, a, b, and c, the dimension of W is 3. This means that any three linearly independent vectors in W can form a basis for W.

To show that W is a subspace of R³, we need to show that it satisfies three conditions: (1) the zero vector is in W, (2) W is closed under addition, and (3) W is closed under scalar multiplication.

(1) The zero vector is (0,0,0), which is in W since it satisfies the condition that a, b, and c are real numbers.

(2) Suppose (a₁, b₁, c₁) and (a₂, b₂, c₂) are in W. Then (a₁+a₂, b₁+b₂, c₁+c₂) is also in W since a₁+a₂, b₁+b₂, and c₁+c₂ are real numbers.

(3) Suppose (a,b,c) is in W and k is a scalar. Then (ka, kb, kc) is also in W since ka, kb, and kc are real numbers.

Therefore, W is a subspace of R³ and has dimension 3.

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Answer:

Step-by-step explanation:

12 frdb

Answer:

Step-by-step explanation:

So abc = 789.0

Answer:

Jo's age = x = 8 years

Step-by-step explanation:

Let

Jo's age = x

Jo's mother, Anne's age = 4x

In four years time, Anne will be three times as old as Jo.

Jo's age =3( x + 4)

Jo's mother, Anne's age = 4x + 4

How old is Jo?

Equate Jo's age and his mother's age

3(x + 4) = 4x + 4

3x + 12 = 4x + 4

3x - 4x = 4 - 12

-x = - 8

Divide both sides by -1

x = 8

Therefore,

Jo's age = x = 8 years

We can see here that with the information given, one can prove that this quadrilateral is a parallelogram. Thus, it is yes>

A polygon with four sides and four vertices (corners) is called a quadrilateral. Its internal angles add up to 360 degrees.

Squares, rectangles, parallelograms, trapezoids, and rhombuses are all examples of quadrilaterals.

We can see that looking at the quadrilateral, we can deduce that it is parallelogram. This is because the opposites sides are equal. Also, their opposite angles are equal.

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Answer:

x < - 10

Step-by-step explanation:

Given

- 4(- 4 + x) > 56 ← distribute left side

16 - 4x > 56 ( subtract 16 from both sides )

- 4x > 40

Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity.

x < - 10

Answer:

6/3=2/1

Step-by-step explanation:

6/3 is the same as 2/1 because if we divide the common denominator, 3, on both sides, your answer will be 2/1.

Answer:

x>5

Step-by-step explanation:

The dotted line means it does not include 5, and the colored in area means that's what it includes. So I'm pretty sure it's what I wrote ^^ but if not it's x<5.

Hope this helps!

Can I be marked brainliest?

:)

The linear equation that relates the time with the number of calls is:

Y = (2min)*X

We know that Carlos is a receptionist at a law firm. We know that he spends 2 minutes routing each phone as it comes in.

So if we define Y as the number of minutes Carlos spends routing calls, and X as the number of calls that come in, the linear equation resulting will be:

Y = (2min)*X

By evaluating that linear equation in the correspondent value of X, we will get the time it took to connect those calls.

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Answer:

194 cents is the correct answer

Step-by-step explanation:

6.99 dollars is 41.94

Answer:

B: -1.94

Step-by-step explanation:

First, you would want to multiply 6 and 6.99

You should get 41.94.

Finally, subtract 41.94 with 40.00. (41.94-40.00).

You should get -1.94. The reason why we add a negative sign is because the total cost of the 6 bikes is more then what she payed with.

The divergence theorem states that the surface integral of the divergence of a vector field over a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by the surface

we are given the vector field F = (11x, 2y, \(z^{2}\)) and the surface S defined by the equation \(x^2 + y^2 + z^2\)= 1, which represents a unit sphere.

To evaluate the surface integral ∬S F · ds using the divergence theorem, we first need to calculate the divergence of the vector field F. The divergence of F, denoted as ∇ · F, is given by the sum of the partial derivatives of the components of F with respect to their corresponding variables. Therefore, ∇ · F = ∂(11x)/∂x + ∂(2y)/∂y + ∂(z^2)/∂z = 11 + 2 + 2z.

Applying the divergence theorem, the surface integral ∬S F · ds is equal to the triple integral ∭V (∇ · F) dV, where V represents the volume enclosed by the surface S.

Since the surface S is a unit sphere centered at the origin, the triple integral ∭V (∇ · F) dV can be evaluated by integrating over the volume of the sphere.

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