What is the smallest possible length of the hypotenuse for a non-degenerate
right triangle with integer side lengths given that it has at least 1 leg of length
84.

Answer:

122

Step-by-step explanation:

Given information, line t is parallel to line s.

angle 1 and angle 2 are alternate angles and so their measure is equal to each other:

10x + 2 = 12x - 22 transfer like terms to the same side of the equation

2 + 22 = 12x - 10x

24 = 2x divide both sides by 2

12 = x to find the measure of angle 2 replace x with the value we found

12*12 - 22 = 122

The addition of the polynomials 14x² - 8x + 3 and - 6x² + 7x - 11 is 8x² - x - 8

(14x^2 - 8x + 3) + (-6x^2 + 7x - 11)

= 14x² - 8x + 3 - 6x² + 7x - 11

= 14x² - 6x² - 8x + 7x + 3 - 11

= 8x² - x - 8

Therefore, the addition of the polynomials 14x² - 8x + 3 and - 6x² + 7x - 11 is 8x² - x - 8

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Answer:

Supplementary angles

Step-by-step explanation:

The two angles combined form a line and their measures add to 180°.

Answer: Supplementary angles

Answer: [tex]\triangle COA \cong \triangle DOB[/tex] by the rule ASA

Step-by-step explanation:

[tex]\overline{CO} \cong \overline{OD}[/tex]  (given)

[tex]\angle ACO \cong \angle ODB[/tex] (given)

[tex]\angle COA \cong \angle BOD[/tex] (vertical angles)

So, [tex]\triangle COA \cong \triangle DOB[/tex] by the rule ASA.

The relative frequency of the class interval 65-75 is .20.

The word 'relative' is used to indicate that an event is being considered in relation or in proportion to something else.

Frequency is a way to measure how often a particular event occurs. Relative frequency, on the other hand, is a way to measure how often a particular event occurs against total occurrences.

Given that: 50 participants scored between 65 and 75 on a test.

Hence,

The relative frequency of the class interval 65-75 = 75 - 65 = 20

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Answer: C

Step-by-step explanation:

12in is 1 ft

652/12 is 54r4

so atlease 55

Answer:

13.8

Step-by-step explanation:

because they're similar, we know that

zy ÷ wz has the same ratio as xy ÷ wv

12 / 15 = 11 / wv

cross multiply

12wv = 165

÷ 12     ÷12

wv = 13.75

13.75 rounded to nearest tenth is 13.8

The bat will not fit in the cube shaped box

The side length of the cube is given as:

x = 17

The diagonal of the cube is calculated as

[tex]d = x\sqrt 3[/tex]

So, we have:

[tex]d = 17\sqrt 3[/tex]

Evaluate

d = 29.4

29.4 is less than the length of the bat (30 inches)

This means that the bat will not fit in the cube shaped box

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Answer: 9

Step-by-step explanation:

The interior angle of the 8-sided polygon is

[tex]\frac{180(8-2)}{8}=135^{\circ}[/tex]

The interior angle of the 10-sided polygon is

[tex]\frac{180(10-2)}{10}=144^{\circ}[/tex]

Taking the difference, we get [tex]b=9^{\circ}[/tex]

Answer:

Step-by-step explanation:

do a squared plus b squared = c squared like

2 and 5 thingy squared by 2 + 6 squared = c squared

unsquare c and you get your answer

The value of x is 184.

What is the value of x?

Given Information

The measure of angle 2 = 92°

The measure of angle 4 = (x/2)°

From the figure, it can be seen that angle 2 and 4 make vertically opposite angles.

Vertically Opposite Angles

The pair of angles that are formed by two intersecting lines and are opposite to each other are defined as vertically opposite angles. The values of vertically opposite angles are always equal.

Here, in this case, ∠1 and ∠3 make a pair of vertically opposite angles. ∠2 and ∠4 form another pair of vertically opposite angles. Hence,

∠4 = ∠2

(x/2) = 92

x = 92 × 2

x = 184

Thus, the value of x is 184.

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Answer:

184

Step-by-step explanation:

edge

By ASA postulate it can be say that the triangle ABC and triangle MRQ are congruent

The sum of all three angles(interior) of a triangle is 180 degrees, and the exterior angle of a triangle measures the same as the sum of its two opposite interior angles.

Using Angle Sum Property, in ΔMRQ

<M + <R + <Q= 180

<M + 42 + 85 = 180

<M = 180 -42

<M= 53°

Now, In ΔMRQ and ΔABC  

<A= <R ,

<B = <M

AB = MR

Hence, By ASA criteria ΔMRQ ≅ ΔABC  

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Answer:

0.00694444444444444444444444444444

Rounded to the nearest thousandths: 0.007

Step-by-step explanation:

Use calculator.

Hope this helps!

If not, I am sorry.

Step-by-step explanation:

[tex] = 3 {x}^{2} + 10x + 3[/tex]

[tex] = 3 {x}^{2} + 9x + x + 3[/tex]

[tex] = 3x(x + 3) + 1.(x + 3)[/tex]

[tex] = (x + 3)(3x + 1)[/tex]

[tex] = (3x + 1)(x + 3)[/tex]

The answer is C.

Answer:

x = 80

Step-by-step explanation:

if ray RU bisects <QRS that means it divided the angle into two equal parts

then we can write the following equation to find the value of x:

<SRU = <QRU

50 = (x/2 + 10) subtract 10 from both sides

40 = x/2 multiply both sides with 2

80 = x

<QRS = 100 because it's the sum of <SRU and <QRU

Hence, The percentage of households in the town with one or more cars = 75.8%, a standard error to the estimate= 1.92%

Total sample households  = 500

Households in the town with one car = 172

Households in town with two or more cars  =207

Households in the town with one or more cars = 172 + 207

                                                                            = 379

The percentage of households in the town with one or more cars =

(379 / 500)*100 = 75.8%.

A standard error to the estimate  = 1.92%.

Hence, The percentage of households in the town with one or more cars = 75. , a standard error to the estimate= 1.92%

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Option B is correct. The statement that is true about the values we have been given here is that They are the only values that make both equations true.

We have been given two equations

The first equation is

4y-3x=16

We have to plug in the values (-5, 0.25) in this equation

4(0.25) -3(-5) =16

Then we have

1 + 15 = 16

Hence 16 = 16 This satisfies the equation.

In the second equation we have to follow the same step

-x-8y=3

Such that

-(-5)-8*0.25 = 3

5-2 = 3

3 = 3 This also satisfies the equation.

Therefore the correct answer option is B

a. They satisfy equation 8 but not equation A.

B. They are the only values that make both equations true.

C. They show that the equations represent the same line.

D. They satisfy equation A but not equation B.

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Answer:

The GCF is 2.

Step-by-step explanation:

In my opinion, one of the easier ways to find the greatest common factor of two numbers is to get the prime factors of both and multiply the common ones. The prime factorization of 8 is 2*2*2, and the prime factorization of 162 is 2*3*3 (you can make a factor tree for both of these numbers to verify this). The only common prime factor for both of these numbers is 2, which means the greatest common factor of 8 and 18 is 2.

The ordered pair that is not a solution of the system of inequalities is the one in option D (1, 7).

Here we have the system of inequalities:

y > x² - 4x-5

y < -x²  - 5x+6

If at least one of the inequalities is false for the given ordered pairs, then the ordered pair is not a solution for the system.

Then we only need to evaluate all the ordered pairs on the given inequalities and see when we have one that is false.

If you look at the pair D (1,  7) and we evaluate that on the second inequality, we get:

7 < (1)² - 5*1 + 6

7 < -2

This is false, then (1, 7) is not a solution of the sytem.

The correct option is D.

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Yes, it is true that Jimmy John was underfilling the lettuce bags with sample mean of 14.39 pounds and sample standard deviation of 0.539.

Given sample mean =14.39 pound, sample standard deviation=0.539 and stated weight=15 pounds.

We know that mean is the number which comes after dividing sum of numbers divided by numbers. Standard deviation shows how much dispersed data is. Firstly we observe through mean and because it is less than 15, it means Jimmy John's had underfilled in atleast one bag otherwise if he had not underfilled the mean may come greater than or equal to 15 pounds.

Now come along standard deviation, we can observe that standard deviation is also low means the points are not in such a way that one point lies at 15 and other one is 25. It also shows underfilling of lettuce bags.

Hence it is true that Jimmy John had underfilled the lettuce bags.

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The area or the common pasture will be 12 acres.

Based on the information given, the formula to use will be:

ab/ac = 2/4

b/c = 1/2 .... i

Also, ab/bd = 2/6

a/d = 1/3 .... ii

Multiply both equation

1/2 × 1/3 = 1/6

Therefore, the area will be

= 6 × 2

= 12 acres

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Answer:

70 km/hr

Step-by-step explanation:

You just have to add both of the average velocity as you are finding the combined average velocity of both vehicles

Answer:

a: (x + 3)(x + 4)

Step-by-step explanation:

assuming x^2 + 7x + 12 is the equation you are factoring

you would first multiply a * c

a is 1

b is 7

c is 12

1 * 12 = 12

then you take b and find what adds up to b but multiplies to ac

what adds up to 7 but multiplies to 12

3 and 4

so

you split the equation up like this

x^2 + 3x + 4x + 12

then you factor

x(x + 3) + 4(x + 3)

because x + 3 and x + 3 are the same we can do this

(x + 4)(x + 3)

that is your equation

so a is your answer

it doesnt matter if you have the (x + 3) or (x + 4) in the front

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{Option A, (x + 3)(x + 4)}[/tex]

-------------------------------------------------------------------------------------------------------------

In order to factor the polynomial we need to first split the middle term so it add up to 7 but multiplies to 12.  We know that 3 and 4 can do that.  We would the factor by grouping which would give us our final answer.

[tex]x^2 + 7x + 12[/tex]

[tex]x^2 + 4x + 3x + 12[/tex]

[tex]x(x + 4) + 3(x + 4)[/tex]

[tex](x + 3)(x + 4)[/tex]

Answer: [tex]\textsf{Option A, (x + 3)(x + 4)}[/tex]

Step-by-step explanation:

So a quadratic equation in factored form is generally given in the form: [tex]a(x-b)(x+c)[/tex]. Sometimes x may have a coefficient but I'll just create a simple quadratic equation. In this form it's easy to see that the solutions to the equation are b and -c, because if you input them in as x, you'll get one of the factors equal to 0, and it'll make the y-value zero, thus it's a solution. So b and c can literally be anything. But for this example I'll chose 3 and 6 to keep it simple. Inputting these as b and c you'll get: [tex]a(x-3)(x+6)[/tex]. Now the value of a will determine the stretch/compression, but to keep it really simple I'll just say that a=1. So now all you have to do is expand the two factors. When you expand them you'll get it in the form: [tex](x-b)(x+c) = x^2+cx-bx-bc[/tex] by using the foil method. So if you expand the two factors in this example you'll get: [tex]x^2+6x-3x-18[/tex] which simplifies to [tex]x^2+3x-18[/tex]. So cool now we have our equation. Now it's time to solve it, you can either factor it (since you literally just had it in factored form), or use the quadratic formula I'll show both methods

Factoring:

   When you factor an equation in the form: [tex]ax^2+bx+c[/tex]. You usually multiply the coefficients a and c. Then you'll find factors of ac that add up to b. In this example ac is really just c because a is 1...

   So given the equation: [tex]x^2+3x-18[/tex] You want to look for factors of -18 that add up to 3. And whenever you have a negative number as AC you really want to look for factors that have a distance of b which in this case is 3. For example I would say that 9 and 3 have a distance of 6. And then after that depending on whether b is negative or positive. I can choose which factor will be negative and which will be positive. If b was 6 well then 9 would have to be positive and 3 would be negative, but if b was -6 then 9 would have to be negative and 3 would have to be positive.

 So in this example look for factors that have "distance" of 3. Well 6 and 3 have a "distance" of 6 so I know those 2 will be the factors. Since 3 is positive that means 6 will be positive, and 3 will be negative. so they add up to 3 and multiply to get -18

   AC factors that add up to 3 and multiply to -18: 6 and -3

   Now write it in factored form using the two factors:

   [tex](x-3)(x+6)[/tex]

  Now set up each factor equal to 0 and solve for x:

   [tex]x-3 = 0\\x=3[/tex]

   [tex]x+6=0\\x=-6[/tex]

   This gives you the two solutions: x=3 and x=-6

Quadratic Formula:

   The quadratic formula is usually used when a equation can't be easily factored. The quadratic formula gives both zeroes in the equation: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]. Notice the plus or minus sign next to the square root? That's where the the two solutions will come from, or possibly one solution if it's at the vertex. or maybe even no real solutions if the quadratic never intersects the x-axis.

  Ok so let's identify  a, b, and c. We're given the equation: [tex]x^2+3x-18[/tex]. so a=1, b=3, and c=-18. Plugging these values into the equation you get:

   [tex]x=\frac{-(3)\pm\sqrt{(3)^2-4(1)(-18)}}{2(1)}\\[/tex]

   Simplifying it a bit gets you the equation:

   [tex]x=\frac{-3\pm\sqrt{81}}{2}[/tex]

   Simplifying the radical gives you:

   [tex]x=\frac{-3\pm9}{2}[/tex]

  Use the positive sign:

   [tex]x=\frac{-3+9}{2}\\x=\frac{6}{2}\\x=3[/tex]

   Use the negative sign:

   [tex]x=\frac{-3-9}{2}\\x=\frac{-12}{2}\\x=-6[/tex]

  This gives you the two solutions x=3, and x=-6
   

Answer:

9.57 moles

Step-by-step explanation:

There is 1.1  mole per liter....

1.1 M/ l * 8.7 L = 9.57 moles

Answer:

1 the vertex point if there are no other angles at the vertex that be confused.

2 three letters with the vertex as the center letter and the other letters representing points from each side.

3 a small number if one is given in the angle.

Answer:

Three Ways to Name an Angle:

1) By its Vertex

2) By the Three Points of the Angle (The Middle Point Must Be the Vertex)

3) By a Letter or Number Written Within the Opening of the Angle.

Step-by-step explanation:

Answer:

152 m²

Step-by-step explanation:

Area of flower garden

Assuming the flower garden is rectangular and its dimensions are measured in meters:

[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies \textsf{Area of flower garden} & = \sf 14 \times 20\\& = \sf 280\:\:m^2 \end{aligned}[/tex]

Total area of path and garden

If there is a 2 m wide path all around the garden, the dimensions of the total area will be the dimensions of the garden extended by 4 m:

[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies \textsf{Total area} & = \sf 18 \times 24\\& = \sf 432\:\:m^2 \end{aligned}[/tex]

Area of path

To calculate the area of the path, subtract the area of the garden from the total area:

[tex]\begin{aligned}\implies \textsf{Area of path} & = \sf Total\:area-Area\:of\:garden\\& = \sf 432-280\\& = \sf 152\:\:m^2 \end{aligned}[/tex]

The equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3

The expression is given as:

x^3 (x^2 + 5x + 7)

Expand the expression

x^3 * x^2 + x^3 * 5x + x^3 * 7

Evaluate the product

x^5 + 5x^4 + 7x^3

Expand the expression

x^5 + 4x^4 + x^4 + 8x^3 - x^3

Hence, the equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3

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The compound inequality represented by the graph shown in the image below is 5 < x < 9

An equation is an expression that shows the relationship between two or more variables and numbers.

The image shown represents a compound inequality. It represents:

x > 5 and x < 9

The compound inequality represented by the graph shown in the image below is 5 < x < 9

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