Bridges in mathematics grade book page 124 answers

Answer:

A?

Step-by-step explanation:

The given quadrilaterals, 1 and 2,  are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.

3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.

4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.

3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:

Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:

AB = √((7 - 0)² + (1 - 0)²) = √50

BC = √((5 - 7)² + (6 - 1)²) = √29

CD = √((-2 - 5)² + (5 - 6)²) =√50

DA = √((0 - (-2))² + (0 - 5)²) = √29

We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.

Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:

Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:

Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5

Slope of RS = (4 - 3) / (4 - (-1)) = 1/5

Slope of QR = (4 - 1) / (4 - 3) = 3

Slope of SP = (3 - 0) / (-1 - (-2)) = 3

The lengths of opposite sides can be calculated using the distance formula:

PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26

RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3

QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10

SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10

We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.

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Using the Least Cost Method, 200 cases should be shipped to Toronto from Hamilton and 100 cases from Hamilton to London with the remaining 140 cases shipped from Waterloo to London to complete the orders.

The Least Cost Method is a method of solving transportation problems. The allocation starts by allocating with the cell or column with the minimum cost.

The lower-cost cells are first chosen over the higher-cost cells to obtain the least cost of transportation.

                        Toronto        London

Demand           200 cases   240 cases

Hamilton = 300 cases

Waterloo = 200 cases

                        Toronto        London

Hamilton           $0.50           $0.60

Waterloo           $0.70           $0.65

                        Toronto                              London

Hamilton           $100 (200 x $0.50)        $144 (240 x $0.60)

Waterloo           $140 (200 x $0.70)        $156 (240 x $0.65)

The number of cases that should be shipped from each warehouse to minimize transportation costs is as follows:

                        Toronto             London

Hamilton         200 cases         100 cases (at a total cost of $60)

Waterloo         0 case               140 cases (at a total cost of $91)

Total               200 cases        240 cases

Total transportation

costs       $100 (200 x $0.50)  $151 (100 x $0.60 + 140 x $0.65)

Thus, using the Least Cost Method, 200 cases should be shipped to Toronto from Hamilton and 100 cases from Hamilton to London with the remaining 140 cases shipped from Waterloo to London to complete the orders with the total transportation cost incurred for the two orders from Toronto and London as $251.

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Answer:

9599

Step-by-step explanation:

use technology.

Answer:

9595

Step-by-step explanation:

x = 331 x 29

= 9595

331

x 29

----------

9595

Step-by-step explanation:

7/ 12 is equivalent to - 7/-12

1) 3:00 to 4:00

2) 103

The required solution is 4:00 to 5:00 and  87  customers.

It is required to fill in the blanks.

The arithmetic refers to working with numbers by doing addition, subtraction, multiplication, and division. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given:

According to question , Initially, there were 75 customers.

From 1:00 to 2:00, a total of 30 more people entered, meaning there were

 75 + 30 - 12

= 93 people.

From 2:00 to 3:00, a total of 14 more people entered, meaning there were

93 + 14 - 8  

= 99 people.

From 3:00 to 4:00, a total of 18 people entered, meaning there were

 99 + 18 - 30

= 87 people.

4:00 to 5:00   :  If the store does not accept any more customers except those who are already inside then, all 87 must leave between 4:00 to 5:00 in order to left from the store by 5:00.

Therefore, the required solution is 4:00 to 5:00 and  87  customers.

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The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Answer:

250 hours

Step-by-step explanation:

The first charge is 10 hours, the second charge is 10(0.96) hours, and so on -- the total of these two is 10+10(0.96)  and we need to keep adding our battery usage up until there is no more battery. The third one is 10(0.96)*(0.96), or 10(0.96)².

This can be seen as a geometric series, with 10 as the first tern, or a, and 0.96 as the common ratio, or r. The sum of this is

\(a\frac{1-r^{n}}{1-r}\), with n being the number of terms. Since 0.96 to the power of n never actually reaches 0 no matter how high n goes if the number is not infinite, we can say n is infinity. As r^n is really close to 0 when n equals infinity (so close that, for our purposes in this equation, we can just assume it's 0), our equation is then

\(10\frac{1}{0.04} =10*25=250\)

Note that the probability that a student chosen at random will play an instrument besides the guitar is 29/45.

To derive the probability, that a  chosen at random will play an instrument other than guitar , we have to first find the sum total of all students who can play an instrument that is not a guitar.

From the table, we can se that this is:

3 + 10 + 5 = 18 on the 7th grade

while the 8th grade we have 3 + 6 + 2 = 11

18 + 11 = 29

So that total students in the middle school is

12 + 3  + 10 +5 + 4 + 3 + 6 + 2 =   45

hence the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form is 29/45

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The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

thanks for the points

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                                   error

Answer:

x ≈ 75.2

Step-by-step explanation:

using the tangent ratio in the right triangle

tan62° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{40}\) ( multiply both sides by 40 )

40 × tan62° = x , then

x ≈ 75.2 ( to the nearest tenth )

Answer:

i'm not sure if it is the right answer or not

Step-by-step explanation:

Let's assume AC is a straight line and B is one the line, between A and C

AC-AB=BC

52-4x-8=6x+4

10x=40

x=4

--> BC=6x+4=6.4+4=28

ANSWER:

The function given in the question is given below as

To figure out the graph of

First of all, we will have to substitute the value of x=4x in f(x)

Therefore,

Using the graphing tool, we will have the graph of the function be

Hence,

The final answer is OPTION B

Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.

The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:

Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.

Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.

Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.

Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.

Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.

Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.

Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.

Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.

Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.

It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.

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The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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Answer:

\( m =\frac{y_2 -y_1}{x_2 -x_1}\)

Where x for this case represent the time and y the height waist off ground.

We have one point that can be extracted from the graph on this case:

\( x_1 = 1, y_1= 3\)

Bout for the other point we have:

\( x_2 = 5.3 , y_2 = 9.6\)

Is important to notice that 9.6 is an estimation since we don't have the scale to identify the real value. so then if we replace we got:

\( m =\frac{9.6-3}{5.3-1}= 1.535\)

And for this case we can conclude that this slope is positive and around 1.5 and 1.6. And that means if we increase the time in one unit then the height off waist off ground would increae about 1.5 to 1.6 ft

Step-by-step explanation:

In order to calculate the slope we need to use the following formula:

\( m =\frac{y_2 -y_1}{x_2 -x_1}\)

Where x for this case represent the time and y the height waist off ground.

We have one point that can be extracted from the graph on this case:

\( x_1 = 1, y_1= 3\)

Bout for the other point we have:

\( x_2 = 5.3 , y_2 = 9.6\)

Is important to notice that 9.6 is an estimation since we don't have the scale to identify the real value. so then if we replace we got:

\( m =\frac{9.6-3}{5.3-1}= 1.535\)

And for this case we can conclude that this slope is positive and around 1.5 and 1.6. And that means if we increase the time in one unit then the height off waist off ground would increae about 1.5 to 1.6 ft

Answer: 120 degrees.

Step-by-step explanation: A 90-degree angle would be a right angle. The segments would be perpendicular. In a 180-degree angle, the line would be flat. This angle is between these two angle measures. It appears quite close to a 120-degree angle such as the one shown below:

Because of this, I would estimate that the angle is around 120 degrees. It may be 130 degrees or 110 degrees but it appears to be approximately 120 degrees.

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

  {-15, -5}

Step-by-step explanation:

The constant on the left needs to be the square of half the x-coefficient:

  (20/2)^2 = 100

To get it to that value, we can add 18 to both sides of the equation:

  x^2 +20x +100 = 25 . . . add 18 to both sides of the equation

  (x +10)^2 = 25 . . . . . . .  . write the left side as a square

  x +10 = ±√25 = ±5 . . . . . take the square root

  x = -10 ±5 = {-15, -5}

The solutions are x = -15 and x = -5.

_____

The attached graph shows the solutions to ...

  x^2 +20x +82 -7 = 0 . . . . . the result of subtracting 7 from both sides

Answer:

sqdancefan

Genius

40.3K answers

503.3M people helped

Answer:

 {-15, -5}

Step-by-step explanation:

The constant on the left needs to be the square of half the x-coefficient:

 (20/2)^2 = 100

To get it to that value, we can add 18 to both sides of the equation:

 x^2 +20x +100 = 25 . . . add 18 to both sides of the equation

Step-by-step explanation:

Answer:

Step-by-step explanation:

Graph A

Answer:

Step-by-step explanation:

Let the required distance is x and the height of the tower is t.

Use similar triangle ratios to find the value of t:

Use Pythagorean to find the value of x:

Answer:

42 ft  (nearest foot)

Step-by-step explanation:

The problem has been modeled as 2 similar right triangles.  The smaller right triangle has a base of 3 ft and a height of 10 ft.  The larger right triangle has a base of 12 ft.

Pythagoras Theorem:  \(a^2+b^2=c^2\)

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Use Pythagoras Theorem to calculate the hypotenuse of the smaller triangle.

Given:

Substitute the given values into the formula and solve for the hypotenuse (c):

\(\implies \sf 3^2+10^2=c^2\)

\(\implies \sf c^2=109\)

\(\implies \sf c=\sqrt{109}\:\:ft\)

Similar Triangle Theorem

If two triangles are similar, the ratio of their corresponding sides is equal.

\(\implies \sf hypotenuse_{large}:base_{large}=hypotenuse_{small}:base_{small}\)

\(\implies \sf c:12=\sqrt{109}:3\)

\(\implies \sf \dfrac{c}{12}=\dfrac{\sqrt{109}}{3}\)

\(\implies \sf c=\dfrac{12\sqrt{109}}{3}\)

\(\implies \sf c=42\:ft\:\:(nearest\:foot)\)

Therefore, the length of the guy wire (hypotenuse of the largest right triangle) to the nearest foot it 42 feet.

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The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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Answer:

true

Step-by-step explanation:

true

Answer:

Probability that it is a red card: 50%

Probability that it is a black card: 50%

Step-by-step explanation:

You have an even probability of getting a red card or a black card. This is true because there are an even number of red cards and black cards. (25 or 26 of each, depending on if you include jokers.) Therefore, there is an even probability of getting a red card or a black card. It has to be 50%, because that is the only number in which two options can have equal numbers.

Hope this helps! :D

Answer: She would've used 82 gallons

The dimension of V when the derivative is 0 is 1 since the l polynomial reduces to a 1-dimensional space.

The dimension of a linear space in which all polynomials with degrees less than 2 is 0 is 1. To estimate the dimension, we must take into account the basic elements of the space.

Let V be the collection of polynomials with a degree less than 2. Then the basic elements of V are 1, x

Let f(x)be a polynomial in V. Then f(x) can be written as f(x)= a0 + a1 x for some constants  

We know that the derivative of f(x) is f'(x) =\(a_1$$\)

Therefore, when the derivative f'(x) is 0, it means that a1 = 0. In this case, the polynomial f(x) reduces to f(x) = a0, which is a constant.

So, the dimension of V when the derivative is 0 is 1, since the l polynomial reduces to a 1-dimensional space.

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