Find the value of each variable in the diagram given that a ∥ b.

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

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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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.

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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Answer:

If a function is continuous and one - to - one then it is either always increasing or always decreasing.

Step-by-step explanation:

An easy way to see this on a graph is to draw a horizontal line through the graph . If the line only cuts the curve once then the function is one - to - one.

Answer:

If a one-to-one function is not continuous, it is sometimes increasing or decreasing. If a one-one function is continuous, it is always increasing or always decreasing.

For example, if [tex]$f(x)=\left\{\begin{array}{lll}-x & \text { if } & |x| \geq 1 \\ x & \text { if } & |x| < 1\end{array}\right.$[/tex]

This function is one-to-one and it is not always increasing or decreasing.

Step-by-step explanation:

A statement that are one-to-one functions either always increasing or always decreasing is given.

It is required to explain the given condition.

To explain the given condition, consider a continuous and a not continuous function then explain about the one-to-one function.

If a one-to-one function is not continuous, it is sometimes increasing or decreasing.

For example, if [tex]$f(x)=\left\{\begin{array}{lll}-x & \text { if } & |x| \geq 1 \\ x & \text { if } & |x| < 1\end{array}\right.$[/tex]

This function is one-to-one and it is not always increasing or decreasing.

If a one-one function is continuous, it is always increasing or always decreasing.

For example, if f(x)=x-3. It is a continuous function and it reaches a minimum value at some values of x and it then keeps increasing.

There will be the same output value for different input values. It does not pass the horizontal line test and so it is not a one-to-one function.

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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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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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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The pair of equations that generates graphs with the same vertex is

B) y = –4x2 and y = 4x2

A vertex serves as  angular point that allows the meeting of two or more lines .

To express a quadratic equation we can use :

[tex][y = a(x - h) ^{2} + k][/tex]

where vertex is (-h , k)

If we look at first option, the the vertices are  [tex](-4 , 0) and (4 , 0)[/tex]

Then the second option, graphs' vertices are the same thing which is ,[tex](0 , 0).[/tex]

Therefore, the pair of equations that generates graphs with the same vertex is B) y = –4x2 and y = 4x2

CHECK THE COMPLETE QUESTION BELOW:

Which pair of equations generates graphs with the same vertex?

A) y = –(x + 4)2 and y = (x – 4)2

B) y = –4x2 and y = 4x2

C) y = –x2 – 4 and y = x2 + 4

D) y = (x – 4)2 and y = x2 + 4

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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

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: C

Step-by-step explanation:

12in is 1 ft

652/12 is 54r4

so atlease 55

The length of the run is at most 15 yards

The given parameters are:

Width = 5 yards

Height = x

Perimeter = Not more than 40 yards

The perimeter is calculated as:

P  = 2 *(Width + Height)

So, we have:

2 *(5 + x) ≤40

Divide by 2

5 + x ≤ 20

Subtract 5 from both sides

x ≤ 15

This implies that the length of the run is at most 15 yards

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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 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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The amount of Type A coffee that was used is 40 pounds.

From the given information;

Type A coffee costs Miguel $5.95 per pound

Type B coffee costs $4.65 per pound.

For this month, the equation can be expressed as:

A + 3A

Thus;

5.95A + 3(4.65)A = 796.00

5.95A +13.95A = 796.00

19.9A = 796.00

A = 796.00/19.9

A = 40

Therefore, we can conclude that the amount of pounds of type A coffee that was used is 40 pounds.

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The constant of proportionality in centimeters per minute is: 5.5.

To find the constant of proportionality of the table shown in the image attached below, use one pair of points, (12, 66).

Constant of proportionality, k = y/x, therefore, the proportional constant in centimeters per minute would be:

k = 66/12 = 5.5 cm per min.

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Answer:

200

Step-by-step explanation:

Solution,

Given,

n(A)=100

n(B)=120

A⊂B

n(A∩B)=20

n(A∪B)=n(A)+n(B)-n(A∩B)

n(A∪B)=100+120-20

n(A∪B)=200

n(A union B) is equal to the number of elements in set B, which is 120.

If A is a subset of B, it means that every element in set A is also an element of set B.

In this case, n(A) represents the number of elements in set A, which is 100, and n(B) represents the number of elements in set B, which is 120.

To find the value of n(A union B) (the number of elements in the union of sets A and B), we need to consider that the union of two sets includes all the elements that are in either set A or set B, or both.

Since A is a subset of B, all the elements in set A are already included in set B. Therefore, the union of sets A and B will be equal to set B itself.

Thus, n(A union B) is equal to the number of elements in set B, which is 120.

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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 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: 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:

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

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

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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]

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.

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:

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:

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.

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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