Calculate the area of triangle OPQ.

The congruence property that shows that  if ΔABC ≅ ΔDEF, then  ΔDEF ≅ ΔABC is; A: Reflexive Property

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

Now, since we are told that ΔABC is congruent to ΔDEF, then it means that by the reflexive property of congruence we can equally say that ΔDEF are congruent to angles of ΔABC

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Answer:

The answer is C. U=3x and V=2y^3

Step-by-step explanation:

3x*3x=9x^2

2y^3*-2y^3=-4y^6

Other variables cancel each other out

I think factorizing everything you can first will make the simplification ... well, simpler.

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \div \dfrac{x(x+7)}{(x+7)(x+9)}[/tex]

The factors of [tex]x+7[/tex] in the second rational expression cancel:

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \div \dfrac{x}{x+9}[/tex]

Now, use the property

[tex]\dfrac ab \div \dfrac cd = \dfrac ab \times \dfrac dc[/tex]

(this is the property of multiplication having to do with multiplicative inverse, or "inverting the divisor" as the question calls it) to write

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \times \dfrac{x+9}x[/tex]

and we see some more cancellation, namely of the factors of [tex]x[/tex] and [tex]x+9[/tex].

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \boxed{\dfrac{x-3}{x+4}}[/tex]

The least distance from point P to line l is approximately equal to 3.536 units.

There are several ways to calculate the least distance, in this case we decided to use the approach based on vectors and projections. First, we generate two auxiliary vectors:

Vector parallel to the line l

[tex]\overrightarrow {AB} = (5, 1) - (2, 4)[/tex]

[tex]\overrightarrow{AB} = (3, - 3)[/tex]

A vector from one point on the line l to the point P

[tex]\overrightarrow{AP} = (1, 1) - (2, 4)[/tex]

[tex]\overrightarrow {AP} = (- 1, - 3)[/tex]

Now we proceed to find the vector distance by using the following vectorial formula:

[tex]\vec d = \frac{\overrightarrow{AP} \,\bullet\, \overrightarrow {AB}}{\overrightarrow {AB} \,\bullet \,\overrightarrow {AB}} \cdot \overrightarrow{AB} - \overrightarrow {AP}[/tex]

[tex]\vec d = \frac{(-1)\cdot (3) + (- 3) \cdot (- 3)}{3^{2}+ (-3)^{2}} \cdot (3, - 3) - (-1, - 3)[/tex]

[tex]\vec d = - \frac{1}{6}\cdot (3, - 3) - (- 1, - 3)[/tex]

[tex]\vec d = \left(-\frac{1}{2}, \frac{1}{2} \right) + (1, 3)[/tex]

[tex]\vec d = \left(\frac{1}{2}, \frac{7}{2} \right)[/tex]

The magnitude of the vector distance is determined by Pythagorean theorem:

[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{7}{2} \right)^{2}}[/tex]

d ≈ 3.536

The least distance from point P to line l is approximately equal to 3.536 units.

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Answer:

not a function because it doesn't pass the vertical line test

Step-by-step explanation:

even though they have different y coordinates they still don't pass the test

The only option that represents the correct repeating decimal is; Option C; 0.35 + 0.0035 + 0.000035

We want to find the option that is equal to the repeating decimal 0.353535.

Option A; 35 + 0.35 + 0.0035

When we add the above, we arrive at 35.3535 which is not equal to 0.353535. Thus, option A is incorrect.

Option B; 0.0035+ 0.000035 + 0.00000035

When we add the above, we arrive at 0.00353535 which is not equal to 0.353535. Thus, option B is incorrect.

Option C; 0.35 + 0.0035 + 0.000035

When we add the above, we arrive at 0.353535 which is not equal to 0.353535. Thus, option C is correct.

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Answer:

1.) C - 0.35+0.0035+0.000035+...

2.) The first term of the geometric series is 0.35.

3.) The common ratio of the geometric series is 0.01

4.) The simplified fractional representation of 0.353535... is 35 / 99

Step-by-step explanation:

Edge

Option 3 and 4. The two options that shows the correct representation of the inequality are:

–3(2x – 5) < 5(2 – x)

We have to open up the brackets by multiplying the sides

= -6x + 15 < 10 - 5x

Hence the  third option is certified to be correct.

Next this inequality has to be shown on a number line.

To do this we have to solve the inequality completely

From -6x + 15 < 10 - 5x

we have to take like terms

-6x+5x < 10 - 15

-x < -5

x<5

The sign of inequality has to be reversed given that the coefficient of x was negative.

Hence x>5. The number line would start from the right and it would move towards the right

From the solution here, we can see that the two correct options are

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Answer: 2.96% rounded

Step-by-step explanation: 10/30) x (9/29) x (8/28)  =  720 / 24,360 = 6/203 = 2.96%

A scenario that would best model the graph on Holly, her home, and school is:

As Holly was heading to school, she felt uneasy and had to wait for 10 mins to catch her breath.

After doing so, she then continued to school which was 6 miles from her home. When she got there, she went to the nurse's office.

She waited in school for 15 minutes and was then told to go home to rest and recuperate. She then made the journey back home in a car and arrived in 10 minutes.

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The time taken to burn off the entire pizza by walking is 568.32 minutes.

2,368 = 125 × w

2,368 = 125w

w = 2,368 / 125

w = 18.944

Total time needed to burn all calories = 30 minutes × 18.944

= 568.32 minutes

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Answer:

The product is the difference of squares is [tex]$$\left(11-b\right)\left(11+b\right)=121-{{b}^2}$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(11-b)(11+b)=(11)^{2}-(b)^{2} \\&(11-b)(11+b)=121-b^{2}\end{aligned}$$[/tex]

Answer:

Here you go with your correct answer

The  size of the sample should be obtained at 2401 in order to be 95% confident

Given that:

Margi of error, [tex]ME=0.02[/tex]

Population proportion, [tex]p=0.50[/tex]

To Find: The size of the sample that should be obtained in order to be 95% confident

Let the size of the sample be n

Using formula,

[tex]n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401[/tex]

Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident

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1 gallon (gal) = 128 fluid ounce (fl oz)

1 hour (hr) = 60 minutes (min)

Convert 1 fl oz/min to gal/hr.

[tex]\dfrac{1\,\rm fl.oz}{1\,\rm min} \times \dfrac{1\,\rm gal}{128\,\rm fl.oz} \times \dfrac{60\,\rm min}{1\,\rm hr} = \dfrac{60}{128} \dfrac{\rm gal}{\rm hr} \approx \boxed{0.47 \dfrac{\rm gal}{\rm hr}}[/tex]

The different statements and reasons to prove that −3(x + 8) = −21 are as detailed below.

Statement 1; −3(x + 8) = −21

Reason 1; Given

Statement 2; −3(x + 8)/-3 = −21/-3

Reason 2; Division property of Equality

Statement 3; x + 8 - 8 = 7 - 8

Reason 3; Subtraction Property of Equality

Statement 4; x = -1

Reason 4; Given

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The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

Lets simplify the problem,

Let assume  the "tens" digit be x

Then the "units" difference =  (x-1), according to the condition.

Hence, the number itself is N = 10x + (x-1).

Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.

From the last statement of the problem, we have this equation

[tex]N+8 = 8*(x+y),or11x + 7 = 8*(x+(x-1)).[/tex]

Simplify and find "x"

[tex]11x + 7 = 8*(2x-1)11x + 7 = 16x - 87 + 8 = 16x - 11x15 = 5xx = 15/5 = 3[/tex].

Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

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The equation of the trend line is y = 3x + 15

Start by entering the table of values in a graphing calculator.

From the graphing calculator, we have the following summary:

The equation of the trend line is represented as:

y = bx + a

Where

b = SP/SSX = 52.5/17.5 = 3

a = MY - bMX = 25.5 - (3*3.5) = 15

This gives

y = 3x + 15

Hence, the equation of the trend line is y = 3x + 15

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The number of sides the regular polygon has is: B. 8.

A polygon with an n-side have a sum of interior angles which can be determined using the formula: (n - 2)180, where n is the number of sides of the regular polygon.

Thus, to find the measure of each interior angle of the polygon, we have: interior angle of a polygon = sum of interior angles ÷ number of sides.

Given the following information about the regular polygon:

Interior angle of the regular polygon = 135 degrees.

Plug this into the given formula for finding the interior angle of a polygon:

135 = (n - 2)180/n

Multiply n by both sides of the equation

135 × n = (n - 2)180/n × n

135n = (n - 2)180

Open the bracket

135n = 180n - 360

Subtract both sides by 180n

135n - 180n = 180n - 360 - 180n

-45n = -360

Divide both sides by -45

-45n/-45 = -360/-45

n = 8

Thus, the number of sides that the regular polygon has is: B. 8 sides.

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Answer:

5 weeks

Step-by-step explanation:

We know that she works at a rate of $12 an hour, she also works 20 hours a week.

The total amount she makes per week is $240 (12 x 20). However, that is without deductions. We have to subtract $34 from the $240.

$240 - $34 = $206.

$206 is the amount she makes in a week and she wants to save $950. How many weeks does she have to save? Well, let's divide.

$950 / $206 = 4.6 weeks. However, if we have to round up to 5 weeks.

The system of equation have one solution.

x² + y² = 25

x² - 6 = 0

x² = 6

x = √6

Therefore, let's substitute the value of x in equation (i)

x² + y² = 25

(√6)² + y² = 25

y² = 25 - 6

y² = 19

hence,

y = √19

Therefore, the system of equation have one solution.

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Answer:

l = (S/pi)-r^2

Step-by-step explanation:

Just rearrange the equation.

S = pi*l + pi * r^2

S-pi*r^2 = pi*l

l = (S-pi*r^2)/pi

l = (S/pi)-r^2

Answer:

b = 24 meter

Step-by-step explanation:

Using Pythagoras theorem:

a² + b² = c²

Here given: a = 10 m, b = ?, c = 26 m

Insert values

10² + b² = 26²

b² = 26² - 10²

b² = 676 - 100

b² = 576

b = √576

b = 24

Answer:24

Step-by-step explanation: i found the answer using the pythogaras theorem,the formula used is, h squared=b squared +p squared,formula used to find missing legnths of triangles such as hypotaneous and height.in this question you have to find the height,as you can see to the opposite of hypotaneous its height/perpendicular.

so according to formula,h squared=b squared+p squared

so,26 squared=10 squared+p squared.

in order to find p

p squared=26 squared -10 squared

which gives us 576

and p squared =576

the square on the p will go on the other side and become an underroot.

take the underoot of 576

which gives us p=24.

so the legnth is 24, found using pythogares theorem.by rearranging the formula and making p the subject in the formula

The true statement about this information is that: A. It is both a relation and a function.

A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population.

In this context, we can infer and logically deduce that the true statement about this information collected by Jen is that it's both a relation and a function because it indicates a relationship between two variables.

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Answer:

It is both a relation and a function.

Step-by-step explanation:

The equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16

We have:

x = -2 and x = 2

Rewrite as:

x + 2 = 0 and x - 2 = 0

Multiply both equations

(x + 2)(x - 2) = 0

This gives

x^2 - 4 = 0 --- option (a)

Add 4 to both sides

x^2 = 4

Multiply by 4

4x^2 = 16 --- option (d)

Hence, the equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16

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Answer:

Slope=14.000/2.000=7.000

x-intercept = 300/-7 = -42.85714

 y-intercept = 300/1 = 300.00000

Step-by-step explanation:

The computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.

It should be noted that the subtraction line is simply used to subtract numbers.

In this case, the computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.

When subtracting the numbers on the number line, we will move towards the left hand side of the number line.

An illustration of the number line is given.

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24.85

Step-by-step explanation:

First find the square root of 8.2 and subtract from the square root of 7.5. Multiply 3.5 by 0.71, the answer you get divide it by the answer you get after finding the square root.