Let B be an invertible matrix such that B^(-1) (see photo)
Find the solution of the equation Bx = (see photo)
Bx = 1
2
3
B^-1 = -1 0 1
2 2 0
1 0 1

The division expression that represents the weight of the steel structure divided by the total weight of the bridge's materials is 400 tons ÷ (1,000 tons + 400 tons + 200 tons) = 25%.

The total weight of the bridge's materials is the sum of the weight of concrete, steel structure, glass, and granite, which is:

1,000 tons + 400 tons + 200 tons = 1,600 tons

Simplifying the expression by dividing both numerator and denominator by 400 tons gives:

Weight of steel structure / Total weight of bridge's materials = [tex]\frac{1}{4}[/tex]

Weight of steel structure / Total weight of bridge's materials

[tex]= \frac{400 tons}{1,000 tons + 400 tons + 200 tons}[/tex]

[tex]= \frac{400 tons}{1,600 tons}[/tex] = 0.25

Therefore, the weight of the steel structure is one-fourth (or 25%) of the total weight of the bridge's materials.

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The complete question is:

Write a division expression that represents the weight of the steel structure divided by the total weight of the bridge's materials. Concrete weighs 1,000 tons, Steel structure weighs 400 tons and glass and granite weighs 200 tons.

The volume of the fully inflated balloon is [tex]\frac{19652}{3}[/tex]π inch³ and volume of half inflated balloon is  [tex]\frac{19652\pi }{6}[/tex].

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

Diameter of a fully inflated balloon = 34 inch

Radius is half the diameter.

Radius of fully inflated balloon = 34 / 2 = 17 inches

Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³, where r is the radius.

(a) Volume of fully inflated balloon = [tex]\frac{4}{3}[/tex] π (17)³

                                                    = [tex]\frac{19652}{3}[/tex]π inch³

(b) Volume of the half inflated balloon = Half of the fully inflated volume

                                                          = ([tex]\frac{19652}{3}[/tex]π / 2) inch³

                                                          = [tex]\frac{19652\pi }{6}[/tex] inch³

(c) Volume of half inflated balloon = [tex]\frac{19652\pi }{6}[/tex]

[tex]\frac{4}{3}[/tex] π r³ = [tex]\frac{19652\pi }{6}[/tex]

[tex]\frac{4}{3}[/tex] r³ = [tex]\frac{19652}{6}[/tex]

r³ = [tex]\frac{19652}{8}[/tex]

r = 13.49 inch

Hence the volume and radius are found.

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The correct answer is option c. translation of 1 unit left and 3 units down.

The transformation represented by S + [\begin{array}{ccc}-1&-1&-1\\-3&-3&-3\end{array}\right] is a translation of 1 unit left and 3 units down. This can be seen by examining the values in the matrix. The -1 in the first row represents a translation of 1 unit left, while the -3 in the second row represents a translation of 3 units down. Therefore, the correct answer is option c. translation of 1 unit left and 3 units down.

To summarize, the transformation represented by the given matrix is a translation of 1 unit left and 3 units down. This is indicated by the values of -1 and -3 in the matrix.

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The result of sin (A - B) is 21/221.

To evaluate sin (A - B), we can use the formula:

sin (A - B) = sin A * cos B - cos A * sin B.

We are given that sin A = 12/13 and cos B = 8/17. We need to find cos A and sin B to use the formula.

Since A is in Quadrant II, cos A is negative. We can use the Pythagorean identity, sin²A + cos²A = 1, to find cos A:

cos²A = 1 - sin²A
cos²A = 1 - (12/13)²
cos²A = 1 - 144/169
cos²A = 25/169
cosA = -5/13

Similarly, since B is in Quadrant IV, sin B is negative. We can use the Pythagorean identity to find sin B:

sin²B = 1 - cos²B
sin²B = 1 - (8/17)²
sin²B = 1 - 64/289
sin²B = 225/289
sinB = -15/17

Now we can plug in the values into the formula:

sin (A-B) = (12/13)*(8/17) - (-5/13)*(-15/17)
sin (A-B) = 96/221 - 75/221
sin (A-B) = 21/221

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The value of z when t=2 is 24

The value of z varies inversely with t, which means that the product of z and t is a constant. We can write this relationship as:

zt = k

Where k is the constant. We are given that z=6 when t=8, so we can plug these values into the equation to find k:

6*8 = k

k = 48

Now we can use this value of k to find the value of z when t=2. Plugging in these values gives us:

z*2 = 48

Solving for z gives us:

z = 48/2

z = 24

Therefore, the value of z when t=2 is 24.

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Answer: Roshan: 250/5 = 50 Rs.

Isha: 250 - 50 = 200 Rs.

Step-by-step explanation:

Using algebra, we can conclude that, if Jamie only works 10 hours during the week, he will not be able to meet his goal of earning at least $279, because the total pay he will earn, which is $232.50, is less than the amount he wants to earn.

The method to use to solve this problem would be algebra. We will use variables to represent the number of hours that Jamie works during the week and on the weekend, and we used equations to express the relationship between the total pay Jamie earns and the number of hours he works.

Let's first find out how many hours Jamie works during the week and on the weekend.

Let's say Jamie works x hours during the week. Then, he works 2x hours on the weekend.

The total amount of money Jamie earns is given by:

Total pay = Pay for week hours + Pay for weekend hours

Pay for week hours = $7.75 per hour * x hours

Pay for weekend hours = $7.75 per hour * 2x hours = $15.50 per hour * x hours

Total pay = $7.75x + $15.50x = $23.25x

Now let's substitute x = 10, since Jamie wants to work 10 hours during the week, to see if he can meet his goal of earning at least $279:

Total pay = $23.25 * 10 = $232.50

Since $232.50 is less than $279, Jamie will not meet his goal by working 10 hours during the week alone. He will need to work more hours during the week and/or on the weekend to reach his goal.

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Step-by-step explanation:

1 hour = 60 minutes

1/3 × 60 minutes = 20 minutes texting a friend.

1/4 × 60 minutes = 15 minutes brushing and pyjamas.

the remaining time for reading we can get in 2 ways :

1. 60 - 20 - 15 = 25 minutes reading

2. via the fractions

1/1 is the whole hour

1/1 - 1/3 - 1/4

to make this calculation, we need to bring all fractions to the same denominator.

the smallest number (LCM - least common multiple) that can be divided by 1, 3 and 4 is 12

1/1 × 12/12 = 12/12

1/3 × 4/4 = 4/12

1/4 × 3/3 = 3/12

so,

12/12 - 4/12 - 3/12 = 5/12

5/12 × 60 minutes = 5× 60/12 = 5×5 = 25 minutes reading.

To find the factor of these two rational expressions, we need to factor each expression separately and then compare them to find any common factors.

First, let's factor the expression 22x + 11 x2 – 3x – 10:
(22x + 11 x2) + (-3x - 10)
11x(2 + x) - (3x + 10)
(11x - 10)(x + 2)

Next, let's factor the expression 1 – 2c 20c2 + 10c:
(1 - 2c) + (20c2 + 10c)
(1 - 2c) + 10c(2c + 1)
(1 - 2c)(10c + 1)

Now, we can compare the factors of each expression to see if there are any common factors. In this case, there are no common factors between the two expressions.

Therefore, the factor for these two rational expressions is 1.

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The distance between the stop signs is 0.375 miles or roughly 0.6 kilometers.

distance between stop signs = 3 miles / 8

= 0.375 miles

While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."

Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

The scalar quantity known as distance measures "how much ground an object has traversed" while moving.

From the question:

We can use the following calculation to calculate the separation between the stop signs:

distance between stop signs = total distance/number of intervals

There are 8 spaces between the stop signs and a total distance of 3 miles in this instance. As a result, we can determine the separation between the stop signs as:

distance between stop signs = 3 miles / 8

= 0.375 miles

As a result, there are 0.375 miles (or 0.6 kilometers) between each stop sign.

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Answer:

Step-by-step explanation:

Both angles are equal so,

1+16x =17x-3

16x-17x= -3-1

-x = -4

x = 4

Answer:

.7x 63 = 90  (.7 is the same as 70%.  If they took off 30%, they left on 70%)

90 ÷ 3 = 30

Jennifer originally paid $30.00 a shirt.

Check

30 x .3 = 9  This is the amount of the discount per shirt.

30 - 9 = 21  Discounted cost per shirt.

21 x 3 = 63 The cost of three shirts.  

This checks.

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

300

Answer:150 m

Step-by-step explanation:

2cm/25 m = 2 cm: 2500 cm= 1cm:1250 1250x12=15000 convert back to meters 150 m

The final answer of Using Descartes's Rule of Signs, we can determine that there are either 2 or 0 positive real zeros and 0 negative real zeros of [tex]f(x)=8x^4-7x^3-4x^2-2x+7[/tex]

To determine the possible numbers of positive and negative real zeros of f(x)=8x^(4)-7x^(3)-4x^(2)-2x+7 using Descartes's Rule of Signs, we must first count the number of sign changes in the polynomial.

For positive real zeros, we look at the original polynomial: f(x)=8x^(4)-7x^(3)-4x^(2)-2x+7.

There are two sign changes: from 8x^(4) to -7x^(3) and from -2x to +7.

Therefore, there are either 2 or 0 positive real zeros.

For negative real zeros, we look at the polynomial with x replaced by -x: f(-x)=8(-x)^(4)-7(-x)^(3)-4(-x)^(2)-2(-x)+7.

Simplifying, we get [tex]f(-x)=8x^4+7x^3-4x^2+2x+7[/tex]. There are no sign changes in this polynomial, so there are 0 negative real zeros.

In conclusion, Using Descartes's Rule of Signs, we can determine that there are either 2 or 0 positive real zeros and 0 negative real zeros of [tex]f(x)=8x^4-7x^3-4x^2-2x+7[/tex]

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Answer:

angle 1 will be 32

angle 2 will be 2

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The expanded form of the expression [tex](0.1x^4 - \frac{1}{2}x^3)^3[/tex] is,

[tex]0.001x^{12} - 0.015x^{11}- 0.15x^{10}-0.125x^9[/tex]

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

We know, (a - b)³ = a³ - 3a²b + 3ab² - b³.

Given, [tex](0.1x^4 - \frac{1}{2}x^3)^3[/tex].

Here, [tex]a = 0.1x^4[/tex] and [tex]b = \frac{1}{2}x^3[/tex].

Therefore, [tex](0.1x^4 - \frac{1}{2}x^3)^3[/tex].

[tex]= (0.1x^4)^3 - (\frac{1}{2}x^3)^3 - 3.(0.1x^4)^2.\frac{1}{2}x^3 + 3.(0.1x^4).(\frac{1}{2}x^3)^2[/tex].

[tex]= 0.001x^{12} - 0.125x^9 - 0.015x^{11} - 0.15x^{10}[/tex].

[tex]= 0.001x^{12} - 0.015x^{11}- 0.15x^{10}-0.125x^9[/tex].

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The solutions are x = 3√2 and x = -3√2.

There are several methods that can be used to solve a quadratic equation. The most commonly used methods are:

1. Factoring
2. Completing the square
3. Quadratic formula
4. Graphing

Now, let's solve each equation using one of the methods listed above.

a. 2x^2 - 7x + 3 = 0

We can use the factoring method to solve this equation. First, we need to find two numbers that multiply to give us 3 and add to give us -7. The numbers are -3 and -1. So, we can factor the equation as follows:

(2x - 1)(x - 3) = 0

Now, we can set each factor equal to zero and solve for x:

2x - 1 = 0 => x = 1/2

x - 3 = 0 => x = 3

So, the solutions are x = 1/2 and x = 3.

b. x^2 + 10x + 1 = 0

We can use the quadratic formula to solve this equation. The quadratic formula is:

x = (-b ± √(b^2 - 4ac))/(2a)

Plugging in the values of a, b, and c, we get:

x = (-(10) ± √((10)^2 - 4(1)(1)))/(2(1))

Simplifying, we get:

x = (-10 ± √96)/2

So, the solutions are x = (-10 + √96)/2 and x = (-10 - √96)/2.

c. x² – 18=0

We can use the square root method to solve this equation. First, we need to isolate the x^2 term on one side of the equation:

x^2 = 18

Now, we can take the square root of both sides:

x = ±√18

Simplifying, we get:

x = ±3√2

the solutions are x = 3√2 and x = -3√2.

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Answer:

75 dollars.

Step-by-step explanation:

Each person costs 25 dollars and p=3 we just put this into a equation.

25 × 3 = 75

C = 75

y = -2x + 14

To reflect the equation y = 4 across the y-axis, we need to change the sign of the x-term. Since there is no x-term in the original equation, we can simply add a negative x-term to get the reflected equation: y = -x + 4.

Next, to translate the equation to the right 3 units, we need to subtract 3 from the x-term. This gives us the translated equation: y = -(x - 3) + 4.

Finally, to vertically stretch the equation by a factor of 2, we need to multiply the entire equation by 2. This gives us the final transformed equation: y = 2(-x + 3) + 8.

In summary, the equation y = 4 reflected across the y-axis, translated to the right 3 units, and vertically stretched by a factor of 2 is y = -2x + 14.

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Answer:

∠BCA 57 degrees

Step-by-step explanation:

∠ABC + (5x + 12) = 180

=> ∠ABC = 180 - (5x + 12)

∠BAC + (9x + 1) = 180

=> ∠BAC = 180 - (9x + 1)

∠BCA + (10x - 37) = 180

=> ∠BCA = 180 - (10x - 37)

∠ABC + ∠BAC + ∠BCA = 180

Substitute to find x

[180 - (5x + 12)] + [180 - (9x + 1)] + [180 - (10x - 37)] = 180

180 + 180 + 180 - 5x - 9x - 10x - 12 - 1 + 37 = 180

564 - 24x = 180

24x = 564 - 180

24x = 384

x = 384/24 = 16

Substitue x = 16

∠BCA = 180 - (10x - 37)

∠BCA = 180 - 10(16) + 37 = 57

Answer:

m∠BCA = 57°

Step-by-step explanation:

To find the measure of angle BCA we must first find the value of x.

The diagram gives expressions for the exterior angles of the triangle.

The exterior angles of a triangle sum to 360°. Therefore, to calculate the value of x, equate the sum of the exterior angles to 360° and solve for x.

⇒ (9x + 1)° + (5x + 12)° + (10x - 37)° = 360°

⇒ 9x + 1 + 5x + 12 + 10x - 37 = 360

⇒ 9x + 5x + 10x + 1 + 12 - 37 = 360

⇒ 24x - 24 = 360

⇒ 24x - 24 + 24 = 360 + 24

⇒ 24x = 384

⇒ 24x ÷ 24 = 384 ÷ 24

⇒ x = 16

Each interior and exterior angle of a triangle form a linear pair.

As the sum of angles of a linear pair is always equal to 180°, to find the measure of angle BCA, equate the sum of ∠BCA and its exterior angle to 180°:

⇒ (10x - 37)° + m∠BCA = 180°

Substitute the found value of x and solve for the angle:

⇒ (10(16) - 37)° + m∠BCA = 180°

⇒ (160 - 37)° + m∠BCA = 180°

⇒ 123° + m∠BCA = 180°

⇒ 123° + m∠BCA - 123° = 180° - 123°

⇒ m∠BCA = 57°

Therefore, the measure of angle BCA is 57°.

Water turning to blood will be the first plague that will be present.

Both humans as well as mammals can contract the plague. The protozoan parasite is the bacterium that causes it. The most common ways for humans to contract the plague are through handling a plague-infected animal or by getting bitten by a rodent bug that is carrying the disease.

The 10 plagues in the correct order are:

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a) To perform a regression analysis based on the results of Table 1, we need to write down a linear regression model that captures the possibility of interaction between factors A and B. The model can be written as follows: Y = B0 + B1*A + B2*B + B3*A*B. Where Y is the dependent variable, A and B are the independent variables, B0 is the intercept, B1 and B2 are the coefficients of A and B respectively, and B3 is the coefficient of the interaction term A*B.

b) To estimate the coefficient B2, we need to use the regression analysis results from Table 1. The estimate of B2 can be obtained by looking at the coefficient of the independent variable B in the table. If the table does not provide the estimate of B2, we can use the following formula to calculate it: B2 = (SSB - SSB/A)/(dfB - dfB/A)

Where SSB is the sum of squares for factor B, SSB/A is the sum of squares for factor B after adjusting for factor A, dfB is the degrees of freedom for factor B, and dfB/A is the degrees of freedom for factor B after adjusting for factor A.

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The circumference of the circle with a diameter of 28 cm will be 87.92 cm.

It is the close curve of an equidistant point drawn from the hub. The radius of a rotation is the distance between the center and the rim.

Let r be the radius of the circle. The circumference of the circle will be given as,

C = 2πr units

The diameter of the circle is 28 cm. Then the radius is calculated as,

r = d / 2

r = 28 / 2

r = 14 cm

Then the circumference of the circle is given as,

C = 2 · π · 14

C = 28 × 3.14

C = 87.92 cm

The circumference of the circle with a diameter of 28 cm will be 87.92 cm.

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Starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.

Algebraic expression can be defined as combination of variables and constants.

To find the future amount of the investment after 40 years, we can use the formula for compound interest:

Future Amount = Present Value x (1 + Interest Rate/Compounding Frequency)^(Compounding Frequency x Time)

In this case, the present value (PV) is $500, the interest rate (r) is 15%,

the compounding frequency (n) is 1 (since the interest is compounded every 2 years).

The time (t) is 40 years.

Plugging in the values, we get:

Future Amount = [tex]500 \times (1 + 0.15/1)^{(1 \times 40/2)}[/tex]

Future Amount = [tex]500 \times (1.15)^{20}[/tex]

Future Amount = [tex]500 \times 13.591409[/tex]

Future Amount = $6,795.70 (rounded to the nearest cent)

Therefore, starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.

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The values are given as follows:

The value of AC can be obtained applying the Pythagorean Theorem, as follows:

(AC)² = 20² + 15²

AC = sqrt(20² + 15²)

AC = 25.

Then there are two similar triangles, with dimensions given as follows:

Then the value of x is obtained as follows:

15/20 = x/(25 - x)

3/4 = x/(25 - x)

4x = 3(25 - x)

7x = 75

x = 10.7.

Then the altitude BD is obtained with the geometric mean theorem as follows:

BD² = 10.7 x (25 - 10.7)

BD² = 153

BD = sqrt(153)

BD = 12.4.

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The value of the numerical expression will be 36. Then the correct option is 36.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The numerical expression is given below.

[tex]\rightarrow \dfrac{\left ( 27 \right)^{2/3} \times \sqrt{16}}{5^0}[/tex]

Simplify the expression, then we have

⇒ (∛(27)² × √16) / 5⁰

⇒ (3)² × 4

⇒ 9 × 4

⇒ 36

The value of the numerical expression will be 36. Then the correct option is 36.

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The complete question is given below.

Compute the expression [tex]\dfrac{\left ( 27 \right)^{2/3} \times \sqrt{16}}{5^0}[/tex]

a) 36

b) 35

c) 34

d) 1

Answer: 7704

Step-by-step explanation:

( see image !)

The volume of the left-hand cylinder is less than the volume of the right-hand cylinder.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

The volume of the cylinder is given by:

V = π r² h

where r = radius

         h = height

Consider the left-hand side cylinder.

radius = h

height = g

Then the volume is V1 =  π h²g

Now consider the right-hand side cylinder

radius = g

height = h

Then the volume is V2 =  π g²h

It is given that g > h

Taking V1/V2 = π h²g/π g²h = h/g = k

where k is a constant.

Now V1 = k V2

This means that V2 will be k times V1.

So right-hand side cylinder has the largest volume among the two.

Therefore the volume of the left-hand cylinder is less than the volume of the right-hand cylinder.

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