Write a biconditional for the following conditional. Then state the truth value of the statement
If two lines intersect at right angles, then they are perpendicular.

The surface area of the figure is calculated as 150.72 [tex]mi^2[/tex] and when rounded off to the nearest hundredth, it comes out as 151 [tex]mi^2[/tex].

A solid object's surface area can be stated as a measurement of the overall space that the object's surface takes up. As an alternate, surface area can also be described as the area of the entire outer part, or which is said as the uppermost layer of any kind of 3D object.

Square units are used in the calculation. The total area of all the outside surfaces makes up the surface area of a three-dimensional object, which is also expressed in square units.

As an example, we can take that in order to find the exact surface area of a cuboid, we have to add the areas of all 6 faces.

In this figure, we can see that it can be stated as a cylinder.

So, as we know the formula of the surface area of a cylinder can be written as:

2[tex]\pi[/tex]rh + 2[tex]\pi r^2[/tex]

Here r = 8/2

=4 mi

h = 2 mi

Thus, putting the values, we have,

Surface area = [2 x 3.14 x 4 x 2] + [2 x 3.14 x 4 x 4]

= 50.24 + 100.48

= 150.72  [tex]mi^2[/tex]

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The statement which is true about the system of three linear equations is that: B. the system can be either inconsistent and independent or consistent and dependent.

A system of three linear equations can be defined as a type of algebraic equation of the first order that has three (3) variables with each of its term having an exponent of one (1).

In Mathematics, a system of three linear equations is considered as a consistent system when it has at least one solution. However, a system of three linear equations is considered as an inconsistent system when it has no real solution.

Additionally, a system of three linear equations is considered as an independent system when it possesses exactly one solution while it is a dependent system if it has an infinite number of solutions.

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Answer:

0.375

Explanation:

The probability of red and purple can be calculated as the frequency for rean and purple over the total frequency

Red has a frequency of 4

Orange has a frequency of 1

Yellow has a frequency of 1

Green has a frequency of 7

Blue has a frequency of 1

Purple has a frequency of 2

The total frequency is

4 + 1 + 1 + 7 + 1 + 2 = 16

And the frequency for red and purple is

4 + 2 = 6

Then, the probability is equal to

P = 6/16 = 0.375

So, the answer for question 3 is 0.375

Answer:

10% profit

Step-by-step explanation:

since the item was sold for more than it cost, this is a profit

percent profit = [tex]\frac{P}{C}[/tex] × 100%

profit P = SP - CP = Rs 220 - Rs 200 = Rs 20 , then

% profit = [tex]\frac{20}{200}[/tex] × 100% = 0.1 × 100% = 10%

The 12-pack contains bottles of 16 ounces each.

The total content of sports drinks is 12 × 16 = 192 ounces.

The unit price per ounce is the ratio of the total price to the total contents:

The unit price per ounce is $0.06

The rate is positive because she is withdrawing funds from her account. So, Option C is the correct option.

The momentum of a variable is represented by the rate of change, which is used to mathematically describe the percentage change in value over a defined period of time.

Jessica's savings account balance is plotted against the number of months.

Rate of withdrawal from her account is given as:

Amount in Savings account/Number of months

= 1000/10

= 100 dollars/month

Therefore, Jessica is withdrawing 100 dollars per month from her savings account.

As a result, the rate is positive because she is taking money out from her account. Option C is thus the right option.

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A: 10%

B: 6950*10%=695

Answer:

I don't know why you asking me??

Answer:-1,1

Step-by-step explanation:

-1,1

if x=3 we get

The balance Ranjan will receive from the cashier is ₹ 0

Based on the information given, we have that;

Now, expand the bracket for the payment, we have;

(2a+b )²

(2a +b) (2a + b)

Multiply through

4a² + 2ab + 2ab + b²

Add like terms

4a² + 4ab + b²

Now, let's add the amount for the items bought

a² –ab -b²  + 2a² +8ab-2b² + a² –3ab + 4b²

add like terms

4a² +  4ab + b²

Now, subtract the amounts

4a² + 4ab + b² - 4a² +  4ab + b²

₹ 0

Hence, the balance is ₹ 0

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Answer:

1/3 or 2/6

Step-by-step explanation:

you just plug the coordinates into a calculator and look at the rise over run.

The average rate of change of the function is found as 1.

For the given question;

The function is given by the equation;

g(x) = -x² - 9x + 27

The interval of the function lies as;

-9 ≤ x ≤ -1.

Let,

a = -1 ans b = -9

Then,

g(a) = g(-1), Put x = -1 in the function.

g(-1) = -(-1)² - 9(-1) + 27

g(-1) = 35

Now, g(b) = g(-9), Put x = -9 in the function.

g(-9) = -(-9)² - 9(-9) + 27

g(-9) = 27

Thus, the average rate of change of the function is-

Average rate of change = [g(a) - g(b)]/[a - b]

= [35 - 27]/[-1 + 9]

= 8/8

= 1

Thus, the average rate of change of the function is found as 1.

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Answer:

  -8/3

Step-by-step explanation:

You want the slope of the line shown in the graph.

Whether counting grid squares on the graph, or using the slope formula, it is convenient to choose two points on the grid where the line crosses the intersection of grid lines.

It appears, the line passes through grid points (1, 4) and (4, -4). Using the slope formula, we find the slope of the line to be ...

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -4)/(4 -1) = -8/3

The slope of the line is -8/3.

The slope is the ratio of "rise" to "run" for the line. From the two points we see where the line crosses grid intersections, we have a "rise" of -1 from y=4 to y=-4, and a "run" of 3 from x=1 to x=4.

  rise/run = -8/3 = slope of the line

Answer:

"If the time taken by the person to get to work is T minutes, the equality that models this situation is   | t - 50 | = 10 the minimum time taken by the person to get to work is 40 min, the maximum time taken is 60 min.

Step-by-step explanation:

The difference between the time and 50 minutes is 10 minutes.

This can be expressed as:

The minimum and maximum time can be found by solving the equation above:

The blanks to be filled in as:

The inequality equation is 3c + 2.25b <=15 which represents the possible values of cupcakes and brownies that can be purchased by Aisha with the given amount of money.

Cost of each cupcake = $3

Cost of each brownie = $2.25

Total money available with Aisha to spend on cupcakes and brownies = $15

Let c represent the number of cupcakes purchased by Aisha and b represent the number of brownies purchased by Aisha

Formulating the inequality equation we get the following:

Cost of each cupcake*Number of cupcakes purchased + Cost of each brownie*Number of brownies purchased <= Total money available with Aisha

3c + 2.25b <=15

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Solution:

Given the points below;

To find the equation of the line that passes through the points, we will apply the formula below

Where

Substitute the values of the coordinates into the formula above

Hence, the equation of the line is

The graph is shown below with the points indicated using a graphing tool

To answer this question, we can proceed as follows:

1. We have that the after-tax total was $1,253.07.

2. We have that the tax rate in the area is 7.1%.

3. Then to find the pre-tax subtotal, we can proceed as follows:

Therefore, we have:

4. Finally, we need to add the like terms as follows:

And using technology, we can divide both sides by 1.071:

Therefore, the pre-tax subtotal is $1,170.

The fraction of Jena's income does she plan to spend each month on these two items together is 1/2

Amount of Jena's income spent on savings = 1/3 × $3800

= 1266.666666666666

Approximately,

= $1,266.67

Amount of Jena's income spent on groceries = 1/6 × $3800

= 633.3333333333333

Approximately,

= $633.33

Amount spent on the two items = $1,266.67 + $633.33

= $1900

Fraction of Jena's income spent on the two items = 1/3 + 1/6

= (2+1) / 6

= 3/6

= 1/2

So therefore, Jena spent 1/2 of her income on savings and groceries.

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We need to transform a number that is written in scientific notation to the standard notation. For that we have to move the dot to the right, because the exponent of the power is positive, every time we do that we will subtract one from the exponent. When there is no more dot we will add zeros. This is done below:

The correct answer is 207,000.

The ordered pair that represents the image of the point after the transformation is (3, 5)

The ordered pair of the point is given as

D = (0, 2)

The above point is an ordered pair on a coordinate plane

The sequence of transformations of the points is given as

(x, y) → (x+10, y − 8) and (x, y) → (x − 7, y + 15).

When the above transformations are applied on the point, we have:

So, we have the following equation

(x, y) → (x + 10 - 7, y − 8 + 15)

Evaluate the sum and the difference

So, we have the following equation

(x, y) → (x + 3, y + 7)

Recall that

D = (0, -2)

So, we have

D' = (0 + 3, -2 + 7)

Evaluate

D' = (3, 5)

Hence, the image of point D is (3, 5)

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An exponential function is defined as a function of the form:

where a, b and c are constants.

We notice that the function given has this form, therefore the function given is an exponential function.

Answer:

Angle a

Step-by-step explanation:

the sum of the interior angles of a triangle is 180.  If one angle is 60 and another angle is 90, then the third angle has to be 30.

60 + 90 + 30 = 180

90>60>30

A transformative sequence is a particular arrangement of transforming events. This suggests that a series of transformations may manage more than one transition, and that the order in which they occur is crucial. A and B are similar in this case.

When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.

Formally, two sets of points are said to be congruent if, and only if, an isometry, which is a collection of rigid motions including translation, rotation, and reflection, can transform them into one another.

This shows that resizing an object will not allow it to be properly aligned with another object, only by moving and reflecting it. Therefore, two independent plane figures on a piece of paper are congruent if we can cut them out and then precisely line them up. The paper might be distributed.

Each box is the same size in terms of length and width. The only change is where the figure is located.

Transformations can be divided into four categories: translation, rotation, reflection, and dilation.

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Congruent refers to things that are exactly the same size and shape.

Hence, A and B are congruent.

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The expression equivalent to -40(4) +2³ is -152 by the concept of BODMAS Rule.

It is generally understood that two things are equivalent if they are the same. Similar to this, analogous mathematical expressions are those that are the same even if they appear to be different. However, when the values are plugged into the expression, both expressions provide the same outcome.

BODMAS is formally known as Brackets (Numbers inside the Bracket always comes first)

Priority for brackets is Orders in a bar (the power)

Division

Multiplication

Addition

Subtraction

To solve the above expression, follow the above order

-40(4) +2³ = -160+8 = -152

Therefore, the expression equivalent to -40(4) +2³ is -152.

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The BEST explanation of the effect of the Diaspora on Jewish people is d) They developed new rituals to accommodate the loss of the Temple.

Some of the new rituals developed by the Diaspora Jews included:

The Diaspora did not affect the Jewish people by dividing their homeland, making the destroyed Temple of Jerusalem the center of their religiosity, or making Rabbis insignificant.

Thus, the Diaspora affected the Jewish people in Option D.

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a) Their homeland was divided into Israel and Judah.

b) The Temple of Jerusalem became the center of religious activity.

c) Rabbis no longer served as significant religious leaders.

d) They developed new rituals to accommodate the loss of the Temple.

Answer:

[tex]\frac{4}{x2}[/tex]

Step-by-step explanation:

h (x) = log (N) = [tex]\frac{4}{x -2} {2}[/tex]

g (x) = (x - 1)

g (x) = [tex]\frac{4}{x2}[/tex]

Answer:

C

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{EF}{BC}[/tex] = [tex]\frac{11}{66}[/tex] = [tex]\frac{1}{6}[/tex]

Using long division:

So:

Answer:

A