Given: Lines p and q are parallel and r is a transversal.

Prove: ∠2 ≅ ∠7
Parallel lines p and q are cut by transversal r. On line p where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 1, 2, 4, 3. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 5, 6, 8, 7.

A 2-column table with 4 rows. Column 1 is labeled statements with the entries p is parallel to q and r is a transversal, A, B, angle 2 is congruent to angle 7. Column 2 is labeled reasons with the entries given, vertical angles are congruent, correlated angle theorem, transitive property.

Which statements could complete the proof?

A:



B:

Step-by-step explanation:

if I understand the question, write an equation for n in terms of i for number of Id cards an d for number driver license.

n = 15i + 20d

The value of n for a total minutes processing id card applications and driver's license applications would be 35 minutes.

Used the concept of addition that states,

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that,

For her job, Natasha spent a total of n minutes processing id card applications and driver's license applications.

And, it takes Natasha 15 minutes to process an id card application and 20 minutes to process a driver's license application.

Now by the given condition, we get;

n = 15 minutes + 20 minutes

n = 35 minutes

Therefore, the value n is 35 minutes.

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The completed table is given below,

the percentage of girls in the class is 47.62%,

the percentage of boys in the class is (100-47.62)% = 52.38%,

the percentage of students that love Math is 36.5%,

the percentage of students that love Reading is 22%, and

the percentage of students that love Science is 41.27%

To make comparison and statistical analysis easier, numerical data is systematically and logically represented in tabulations as rows and columns. Grouping relevant data together makes comparison easier and aids in statistical analysis and interpretation.

To put it another way, tabulation is the process of organizing data and presenting it in a tabular format. Depending on the type of categorization, it might be double, complicated, or simple.

The below table yields that

The total number of students is 315

The fraction of girls in the class is 150/315 = 0.4762

So, the percentage of girls in the class is 47.62%

Hence the percentage of boys in the class is (100-47.62)% = 52.38%

The fraction of students that love Math is 115/315 = 0.365

So, the percentage of students that love Math is 36.5%

The fraction of students that love Reading is 70/315 = 0.22

So, the percentage of students that love Reading is 22%

The fraction of students that love Science is 130/315 = 0.4127

So, the percentage of students that love Science is 41.27%

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Answer:

1 55

2 455

3554

Step-by-step explanation:

nfn

Answer:

2

[tex]3 \times 3[/tex]

The range of the relation is {0, 2, 4}

The range of the relation are the y values

From the table, we have:

y values = 0, 2, 4, 2, 0

Remove the repetition

y values = 0, 2, 4

Hence, the range of the relation is {0, 2, 4}

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Step-by-step explanation:

here is your answer. where are you from

The cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

For example, if you say 678, we must also know the whole number, but if you say 80%, it becomes evident. The percentage is the same as the amount of that value but ranges from 1 to 100.

Let's say

Cost of article = c

Given,

Marked 40% above the cost price and sold with 15% discount including 10% VAT at Rs. 26,894

1.4c - 0.15×(1.4c) = 26894

c = Rs 22600

So,

Marked price = 1.40c = Rs 31640

Profit percentage = ( 26894 - 22600)22600 = 19%.

Hence cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.

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Answer:

7

Step-by-step explanation:

You were correct in setting the equation equal to 0 because the problem is asking for when the rock hits the ground and in this problem, you may  assume that the ground is y=0, unless the problem says otherwise.

Ok so where you went wrong is that when you factored out and got

(x-7)(x+2), which is correct, you forgot to set these equal to zero (because your actual equation is set to zero). So you should have

x-7 = 0

and

x+2 = 0

and this gives the actual answers +7 and -2. And since time cant be negative its 7 seconds.

This was a silly mistake and happens a lot more often than you think, so I wouldn't worry too much but make sure you practice more, better to lose points on harder questions than easy ones.

Good luck with your exam !

Answer:

7 seconds

Step-by-step explanation:

Given function:

[tex]y=-2x^2+10x+28[/tex]

where:

To find the time when the rock hits the ground, set the equation to zero and solve for x.

First, simplify by factoring out the common term  -2:

[tex]\implies -2(x^2-5x-14)=0[/tex]

Divide both sides by -2:

[tex]\implies x^2-5x-14=0[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=1 \cdot -14=-14[/tex]

[tex]\implies b=-5[/tex]

Therefore, the two numbers that multiply to -14 and sum to -5 are: -7 and 2

Rewrite b as the sum of these two numbers:

[tex]\implies x^2-7x+2x-14=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies x(x-7)+2(x-7)=0[/tex]

Factor out the common term (x - 7):

[tex]\implies (x+2)(x-7)=0[/tex]

Therefore:

[tex]\implies x+2=0 \implies x=-2[/tex]

[tex]\implies x-7=0 \implies x=7[/tex]

As time cannot be negative, the rock hits the ground in 7 seconds.

The correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given expression:-

2.3p – 10.1 = 6.5p – 4 – 0.01p

The same expression will be calculated as:-

Multiply the given expression by 100 we will get our answer.

E = 100 (s 2.3p – 10.1 = 6.5p – 4 – 0.01p )

E = 230p – 1010 = 650p – 400 – p

Therefore  the correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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The value of x will be 158. The value of x is obtained by simplifying the equation.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Identity used;

(x+a)(x-a) = x² - a²

Given expression;

3(x-7)(x+7) - (x-1)(3x+2) = 13

Solving the equation step by step;

[tex]\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158[/tex]

Hence, the value of x will be 158.

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Answer:

cost of car = 34500

selling price = 29700

amount of loss = 34500 - 29700 = 4800

loss percentage = (loss amount ÷ cost price ) * 100

= 13.913 ≈ 14% loss

Answer:

1m=100cm

1m squared=100cm×100cm

1msquared= 10000cm squared

She has to multiply 10000 to convert square centimetres to square meters. Hence option D is correct.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

We know that 1 meter is equal to 100 cm now for a 1-meter square the centimetres will be calculated as,

1m=100cm

1m squared=100cm×100cm

1msquared= 10000cm squared

Hence option D is correct.

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Answer:

[tex]\fbox {x = 3}[/tex]

Step-by-step explanation:

Decimal form of the lower and higher limits :

Hence, the best one which lies in the middle of the limits would be 0.3.

Now, equate the middle part :

Answer:

3. undefined (vertical line)

4. 1

7. -4

8. 3

11. undefined (vertical line)

12. -1/3

Step-by-step explanation:

You can use the slope formula to calculate the slope which is (y2-y1)/(x2-x1)

3. (-4 - (-2)) /  (6-6)  denominator is 0 here so the slope is undefined (vertical line)

4. (7 - 1) / (-2 - (-4)) = 6 / 6 = 1

7. (1 - (-7)) / (2 - 4) = 8 / -2 = -4

8. (-1 - 5) / (0 -2 ) = -6 / -2 = 3

11. (3 - 0) / (-6 - (-6)) = 3 / 0 = undefined (vertical line

12. (2 - 3) / (-5 - (-2) = 1 / -3 = -1/3

Answer:

x=2

Step-by-step explanation:

combine like terms to get 15x=30. divide by 15 on both sides to get x=2

Answer:

x=2

Step-by-step explanation:

1. Simplify the expression

4x+9x+2x=30

Simplify the arithmetic:

15x=30

2. Isolate the x

15x=30

Divide both sides by 15:

[tex]\frac{15x}{15}=\frac{30}{15}[/tex]

Simplify the fraction:

[tex]x=\frac{30}{15}[/tex]

Find the greatest common factor of the numerator and denominator:

[tex]x=\frac{2\cdot 15}{1\cdot 15}[/tex]

Factor out and cancel the greatest common factor:

[tex]x=2[/tex]

Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

Terms and topics

Answer:

1317 is the additive inverse of x = -1317.

Step-by-step explanation:

Additive inverse of a number which when added to the original number gives zero as the result.

Additive inverse of x = -1317

-1317 + 1317 = 0

1317 is the additive inverse of x = -1317.

Verification of -(-x) = x

L. H. S

-(-x) = -{-(-1317)}

= - 1317

R. H. S

x = -1317

Thus, L.H.S. = R.H.S

-(-x) = x

Verified

Answer:

lklklkj

Step-by-step explanation:

67890-

If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)

Binary operators are operators that involves two functions, there are four binary operators: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division. First, we determine the domains of the functions f(x) and g(x):

f(x):

Domain - [-3, 3]

g(x):

Domain - (- ∞, + ∞)

If we divide f(x) by g(x), then we must take g(x) = 0 into account, since it leads to indetermination. In this case, x = 1/3. Then, the domain of the resulting function:

(f/g)(x):

Domain - [-3, 1/3) ∪ (1/3, 3]

If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)

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Answer:

all 50 states

Step-by-step explanation:

Answer:

[tex]log\boxed{7}[/tex]

Step-by-step explanation:

Answer:

The height of the balloon at 09 18 =  788.4 meters.

Step-by-step explanation:

As the hot air balloon is descending.

and the height of the balloon n minutes after it starts to descend is [tex]h_{n}[/tex]

meters.

The height of the balloon (n +1) minutes after it starts to descend, [tex]h_{n+1}[/tex]meters, is given by

[tex]h_{n+1}[/tex]= [tex]k *h_{n}+20\\[/tex] where K is a constant

Here the balloon starts to descend from a height of 1200 meters at 09 15

So [tex]h_{n}[/tex]=1200 meters

At 09 16 the height of the balloon is 1040 meters.

So  [tex]h_{n+1}[/tex]= 1040 meters

the height of the balloon at 09 18 = [tex]h_{n+3}[/tex] meters

now  [tex]h_{n+1}[/tex]= [tex]k *h_{n}+20\\[/tex]

k = [tex]\frac{h_{n+1 }-20 }{h_{n} }[/tex]

k= (1040 - 20) ÷ 1200

k = 0.85

Now [tex]h_{n+2}[/tex] = (0.85 × 1040) +20 =904 meters

Similarly  [tex]h_{n+3}[/tex] = (0.85 × 904) +20 = 788.4 meters.

Therefore the height of the balloon at 09 18 =  788.4 meters.

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Answer:

i think the answer is C. 1/2

The equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52  milligram remains

The missing information in the question is:

[tex]f(t)=m(0.5)^{\frac th}[/tex]

When the mass is 50 mg, it means that:

m = 50

So, we have:

[tex]f(t)=50(0.5)^{\frac th}[/tex]

When 10 years remain in the life of the substance, it means that:

t = 10

So, we have:

[tex]f(t)=50(0.5)^{\frac {10}h}[/tex]

The half life is 5.3. So, we have

[tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex]

Evaluate the equation

f(t) = 13.52

Hence, the required equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52  milligram remains

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Answer:c

Step-by-step explanation:

Answer:

let the original price be X

now new price = original price + increment

increment = 5 % of X = X/20

new price = 194.25

now, 194.25 = X + X / 20 = 21X / 20

X = 194.25 * 20 / 21

X = 185

original price = 185

After transferring $450 from the savings account to the checking account, the updated balance in :

All of that is based on the notion that Sarah's savings and checking accounts are distinct from one another.

Assume that, Sarah's savings account balance was 'x' and checking account balance was 'y'.

She transferred $450 from the savings to the checking account.

∴Updated savings account balance= x-450 units

∴Updated checking account balance= y+ 450 units.

Therefore, it can be concluded that the current value of Sarah's savings account would be the amount >$450, and the updated value of her checking account would be the balance <$450 if she transferred $450 from her savings account to her checking account.

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Answer:

The answer would be 6x^2 + 5x - 4 = 0

Answer:

20.4 years (nearest tenth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 15000=6000\left(1+\frac{0.045}{12}\right)^{12t}[/tex]

[tex]\implies \sf \dfrac{15000}{6000}=\left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf 2.5=\left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf \ln (2.5)=\ln \left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf \ln (2.5)=12t \ln \left(1.00375\right)[/tex]

[tex]\implies \sf t=\dfrac{\ln (2.5)}{12 \ln (1.00375)}[/tex]

[tex]\implies \sf t=20.40017123[/tex]

Therefore, it would take 20.4 years (nearest tenth) for the investment to reach $15,000.

By definition of the subtraction of squares, the binomial 49 · x² - 36 have the following two factors: 7 · x + 6, 7 · x - 6 (Correct choices: C, D)

A subtraction of squares is a binomial which satisfies the following property:

a² - b² = (a - b) · (a + b)     (1)

If we know that a² = 49 · x² and b² = 36, then we have the following factors:

49 · x² - 36 = (7 · x - 6) · (7 · x + 6)

By definition of the subtraction of squares, the binomial 49 · x² - 36 have the following two factors: 7 · x + 6, 7 · x - 6 (Correct choices: C, D)

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Answer:

[tex] \frac{18}{12} = \frac{24}{x - 2} [/tex]