Choose a system of equations with the same solution as the following system:

4x − 2y = 6
2x + y = 5

A.−4x − 2y = 10
2x − 3y = 21

B.4x + 2y = 10
10x + y = 21

C.−4x − 5y = −1
2x − 6y = 10

D.3x + 2y = 6
9x + y = 17

Answer:

see explanation

Step-by-step explanation:

Since the sequence is geometric then the common ratio (r) is

r = [tex]\frac{18}{24}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75

To find the next term in the sequence, multiply the previous term by r

The next 3 terms are

18 × 0.75 = 13.5

13.5 × 0.75 = 10.125

10.125 × 0.75 = 7.59375

The n th term equation of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term, that is a = 24, hence

[tex]a_{n}[/tex] = 24[tex](0.75)^{n-1}[/tex]

Answer:

The correct answer is option B.  30°

Step-by-step explanation:

Points to remember

The central angle of an arc is double the value of arc subtended on the the other part of the circle

From the figure we can see a circle with center F.

It is given that, mAB = mBC = mCD, means that, central angles of all these three arcs are equal.

To find the m<AFB

Fro the figure we get,m<CED = 15°

Therefore central angle of arc CD = 30°

So m<AFB = 30°

The statement which is true about skew lines is:

                    Option: D

                D. Skew lines do not lie in the same plane

Skew lines-

In mathematics, skew lines are the lines which do not intersect and also they are never parallel.

Also, we know that if two lines are on the same plane i.e. coplanar this means either they will cross i.e. intersect or will be parallel.

This statement imply that skew lines do not lie in the same plane i.e. they are non-coplanar.

Hence, from all of the definition and the property above we get:

      D. Skew lines do not lie in the same plane

Answer:

(h,k)

Step-by-step explanation:

because of how the h is horizontal that is the x value and the k is vertical making it the y value.

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The vertex gets shifted by h units horizontally and k units vertically.

The parabola is defined by

y = a(x - h)² + k

has its vertex at (h,k).

After a shift by h units right, followed by a shift of k units vertically, the parabola is defined by

y = a(x - 2h)² + 2k

which has its vertex at (2h, 2k).

∴ (h,k).

Vertex Form of the Equation of a Parabola: The equation y=a(x−h)2+k y = a ( x − h ) 2 + k of a parabola is said to be in vertex form because the vertex can be determined by examining the equation: (h,k) is the vertex.

The equation of a parabola can be written in two basic forms: Form 1: y = a( x – h) 2 + k. Form 2: x = a( y – k) 2 + h.

A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.

Learn more about the parabola, refer

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Answer:

4845 ways

Step-by-step explanation:

To solve this problem we use the formula of combinations

[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]

Where n is the total number of students that can be chosen and you choose r from them.

So

[tex]n = 20\\r = 4[/tex]

Note that in this case the order in which the 4 students are chosen does not matter.

Then

[tex]20C4=\frac{20!}{4!(20-4)!}[/tex]

[tex]20C4=\frac{20!}{4!*16!}=4845\ ways[/tex]

Answer:

4845

Step-by-step explanation:

Total number of students : 20

Students to be picked : 4

Does order matter? : No

Use combination formula (see attached)

Answer:

No

Step-by-step explanation:

To determine if the 3 sides form a right triangle.

Use the converse theorem of Pythagoras.

If the square of the longest side is equal to the sum of the squares of the other two sides then the triangle is right,

longest side = 14 and 14 ² = 196

9² + 12² = 81 + 144 = 225

Since 196 ≠ 225 the triangle is not right

Answer:

y = 5x + 29

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 2 is in this form with slope m = 5

• Parallel lines have equal slopes, hence

y = 5x + c ← is the partial equation of the parallel line

To find c substitute (- 6, - 1) into the partial equation

- 1 = - 30 + c ⇒ c = - 1 + 30 = 29, thus

y = 5x + 29 ← in slope- intercept form

Answer:

D

Step-by-step explanation:

By definition:

rational number = fraction or decimals that are non-whole numbers

negative = well..... negative numbers have a minus (-) in front of them.

Looking at the options, only D has a fraction that has a (-).

Answer:

you cant do that but the answer would be 0

Step-by-step explanation:

because if you eat something it would be gone in our tummy

Answer:

The degree of the polynomial is 2

Step-by-step explanation:

The absolute degree is obtained with the sum of the exponents of all the variables of each term. The terms are the elements of the polynomial with numbers and letters separated by addition or subtraction.

Answer:

12,6

Step-by-step explanation:

The explicit rule for the arithmetic sequence on which the series is based is an = 12 + (n - 1)  * 6

Series are sum of sequences. The nth term of an arithmetic series is expressed as:

an = a + (n - 1)d

where

a is the first term = 12

n is the number of terms

d is the common difference = 18 - 12 = 24 - 18 = 6

Substitute

an = 12 + (n - 1)  * 6

Hence the explicit rule for the arithmetic sequence on which the series is based is an = 12 + (n - 1)  * 6

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Answer:8

Step-by-step explanation:

Solving the given equation we get  [tex]\[ -\frac{5}{4} < x < \frac{5}{2} \][/tex]

1. We start by isolating the absolute value expression by adding 7 to both sides of the inequality.

2. Then, we split the inequality into two cases based on the inner expression of the absolute value: when [tex]\( 5 - 8x \)[/tex] is non-negative and when it is negative.

3. Solving each case separately, we find the range of values for [tex]\( x \).[/tex]

4. Finally, we combine the solutions from both cases to get the final solution: [tex]\( -\frac{5}{4} < x < \frac{5}{2} \).[/tex]This means that[tex]\( x \)[/tex]lies between -5/4 and 5/2.

To solve the inequality[tex]\( |5 - 8x| - 7 < 8 \)[/tex], we'll first isolate the absolute value expression and then solve for [tex]\( x \).[/tex]

1. Add 7 to both sides:

[tex]\[ |5 - 8x| < 15 \][/tex]

2. Now, we'll split the inequality into two cases based on the inner expression of the absolute value:

Case 1: [tex]\( 5 - 8x \geq 0 \)[/tex]

[tex]\[ 5 - 8x < 15 \][/tex]

[tex]\[ -8x < 10 \][/tex]

[tex]\[ x > \frac{10}{-8} \][/tex]

[tex]\[ x > -\frac{5}{4} \][/tex]

Case 2:[tex]\( 5 - 8x < 0 \)[/tex]

[tex]\[ -(5 - 8x) < 15 \][/tex]

[tex]\[ -5 + 8x < 15 \][/tex]

[tex]\[ 8x < 20 \][/tex]

[tex]\[ x < \frac{20}{8} \][/tex]

[tex]\[ x < \frac{5}{2} \][/tex]

So, we have two sets of solutions:

Case 1: [tex]\( x > -\frac{5}{4} \)[/tex]

Case 2:[tex]\( x < \frac{5}{2} \)[/tex]

Combining these two cases, we get:

[tex]\[ -\frac{5}{4} < x < \frac{5}{2} \][/tex]

1. We start by isolating the absolute value expression by adding 7 to both sides of the inequality.

2. Then, we split the inequality into two cases based on the inner expression of the absolute value: when \( 5 - 8x \) is non-negative and when it is negative.

3. Solving each case separately, we find the range of values for \( x \).

4. Finally, we combine the solutions from both cases to get the final solution: [tex]\( -\frac{5}{4} < x < \frac{5}{2} \).[/tex] This means that [tex]\( x \)[/tex] lies between -5/4 and 5/2.

Complete question

Solve |5-8x| -7 < 8

Answer:

B) 3

Step-by-step explanation:

The parts on the right side are to figure out which one to use so since g(3) then you plug in 3 to the equations on the right to see which one is true. The one that it matches into then plug in 3 for x in the equation directly to the left of it:

3 ≥ 3 so 6 - (3) = 3

Answer:

C

Step-by-step explanation:

You are looking for when y divided by x is the same number per each row.

Choice A.. 4/2 doesn't equal 9/4 so not choice A

Choice B.. 4/3 doesn't equal 16/9 so not choice B

Choice C works because 12/4 = 15/5 = 18/ 6 ... all of these equal 3 so choice C is an answer

Choice D.. 4/1  doesn't equal 15/3 so not choice D

Choice C is the only one where you have y/x is the same per each row

Answer:

An exponent value in a would make the system inconsistent because it will either gain or lose height over time.

Any real number without an exponent value will make the system consitent.

Any infintite/repeating number will make the system both consistent and inconsistent. it is consisent because it will stay at a constant rate but also inconsistent because it is repeating and will never end.

Answer:

When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.

Answer:

The correct answer option is C. 180

Step-by-step explanation:

We are given a figure of a circle with two known angles measuring 137 degrees and 94 degrees and we are to find the value of x.

Finding x:

[tex]137 = \frac{1}{2} (\angle x + 94)[/tex]

[tex]137 = \frac{1}{2} \angle x + 47[/tex]

[tex]\frac{1}{2} \angle x = 137 - 47[/tex]

[tex]\frac{1}{2} \angle x = 90&#10;[/tex]

[tex] \angle x = 90 \times 2&# 1 0 [/tex]

x = 180

Answer:

the answer is 180

Step-by-step explanation:

Because yes!! Also I hope you have a wonderful wonderful day!! :D

Step-by-step explanation:

[tex]x {}^{2} = 7x + 4[/tex]

It can also be written as:-

[tex]x {}^{2} - 7x - 4 = 0[/tex]

Now, here a=1, b= -7 and c = -4

Now by quadratic formula,

[tex]d = b {}^{2} - 4ac[/tex]

Calculate d which is

[tex] \sqrt{65} [/tex]

Now, the roots will be:-

[tex]x = ( - b + \sqrt{d} ) \div 2a[/tex]

and hence it will become:-

[tex]x = (7 + \sqrt{65} ) \div 2[/tex]

and

[tex] x = (7 - \sqrt{65} ) \div 2[/tex]

Answer: third option.

Step-by-step explanation:

Move the [tex]7x[/tex] and [tex]4[/tex] to the left side of the equation:

[tex]x^2 = 7x+ 4[/tex]

 [tex]x^2 -7x- 4=0[/tex]

Now you need to apply  the Quadratic formula:

[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]

In this case you can identify that:

[tex]a=1\\b=-7\\c=-4[/tex]

Then you can substitute values into the Quadratic formula and get the following solutions:

[tex]x=\frac{-(-7)\±\sqrt{(-7)^2-4(1)(-4)} }{2*1}\\\\x_1=\frac{7-\sqrt{65} }{2}\\\\x_2=\frac{7+\sqrt{65} }{2}[/tex]

Answer:

14,836.5 in^3

Step-by-step explanation:

The volume of a cylinder is given by the equation (πr^2)h where r stands for radius and h stands for height

The radius of the cylinder is 15 in

The height of the cylinder is 21 in

Volume=15×15×21×π

=14836.5 in^3

Answer:

Since both equations are equal to each other given that they are both equal to y, you can say that . . .

2x = x^2  - 15

x^2 - 2x - 15 = 0

(x-5) (x+3) = 0

Zero Product Property

x = 5 ; x = -3

Solve for y:

y = 2(5) ; y = 2(3)

y = 10 ; y = 6

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Use the points where the line crosses the x and y axis.

(2,0) and (0,2)

Slope = change in Y over the change in x.

Slope = (2-0) / (0-2)

Slope = 2/-2

Slope = -1

Answer:

[tex]\frac{5}{6}\ of\ the \ test[/tex]

Step-by-step explanation:

we know that

Landon finished 1/2 of the test in 3/5 of an hour

so

by proportion

Find out how much of the test will he have done in one hour

[tex]\frac{(1/2)}{(3/5)}\frac{test}{hours} =\frac{x}{1}\frac{test}{hour}\\ \\x=(1/2)*(5/3)\\ \\x=\frac{5}{6}\ of\ the \ test[/tex]

Answer:

5/6

Step-by-step explanation:

you just do it.

Answer:

see explanation

Step-by-step explanation:

To find the y- intercept let x = 0

f(0) = 0² - 8(0) - 10 = 0 - 0 - 10 = - 10

The y- intercept is (0, - 10)

To find the x- intercepts let f(x) = 0, that is

2x² - 8x - 10 = 0 ( divide through by 2 )

x² - 4x - 5 = 0

Consider the factors of the constant term (- 5) which sum to give the coefficient of the x- term (- 4)

The factors are - 5 and + 1, since

- 5 × 1 = - 5 and - 5 + 1 = - 4, hence

(x - 5)(x + 1) = 0

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 1 = 0 ⇒ x = - 1

The x- intercepts are (- 1, 0) and (5, 0)

Final answer

The y-intercept of the function f(x) = 2x²8x-10 is at (0, -10), and the x-intercepts are (-1,0) and (5,0).

To determine the y-intercept and the other x-intercept of the quadratic function f(x) = 2x²-8x-10, we can use the standard forms and properties of quadratic equations.

The y-intercept occurs when x=0. Substituting x with 0 in the function, we get f(0) = 2(0)²- 8(0) - 10 = -10. Thus, the y-intercept is at (0, -10).

To find the other x-intercept given one of them as (-1,0), we can factor the quadratic equation, or use the quadratic formula. Factoring gives us:

(2x + 2)(x - 5) = 0

2x + 2 = 0 would give us an x-intercept at x = -1, which we already have. x - 5 = 0 gives us the other x-intercept at x = 5. So, the other x-intercept is at (5,0).

A. 1.5625 gal.

Formula  

divide the volume value by 128

I decided 200 by 128 and voila; there is the answer.

Answer:

x = 7

Step-by-step explanation:

The property of a parallelogram is the opposite sides are congruent, hence

AD = BC ← substitute values

5x + 3 = 38 ( subtract 3 from both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Answer:  C) 27%

Step-by-step explanation:

There are 3 dots (vitamins) on six and 11 dots (vitamins) total.

The probability is [tex]\dfrac{successes(vitamins\ on\ six)}{total\ possible\ outcomes(all\ vitamins)}=\dfrac{3}{11}=\large\boxed{27\%}[/tex]

Option: C is the correct answer.

                      C.  27%

The dot plot can be reoresented in tabular form as follows:

Number of vitamins          Number of days

          1                                         2

          3                                         1

          4                                         2

          5                                         1

          6                                         3    

          7                                          1

          9                                          1  

Hence, the total number of days= 2+1+2+1+3+1+1=11

Also, the number of days in which Omur's mother took 6 vitamins= 3

( Since there are 3 dots over 6)

Hence, the estimated probability that Omur's mom take exactly 6 vitamins tomorrow is:

       [tex]=\dfrac{3}{11}\times 100\\\\=27.27\%\\\\\text{which\ is\ approximately}\\\\=27\%[/tex]      

Answer:

A rectangle has rotational symmetry of order 2.

Step-by-step explanation:

The rotational symmetry involves rotation.

The rotational symmetry of order is the number of times a shape is mapped onto itself during a 360° rotation.

A rectangle has rotational symmetry of order 2.

When a rectangle is rotated on 180° or 360° it is mapped onto itself.

Answer:

2

180 & 360

Step-by-step explanation:

Step-by-step explanation:

The expected value is the sum of each probability times the value.

E = 0.25 (10) + 0.75 (-5)

E = -1.25

The stock is expected to decrease by $1.25.

Answer:

49

Step-by-step explanation:

The average rate of change is the ratio of the CHANGE IN Y COORDINATE and CHANGE IN X COORDINATE

In this table we are asked to determine the change in rate from x= 3 to x=5

at x =3 , y = 27

at x=5 , y=125

Hence

Change in y = 125-27 = 98

Change in x = 5-3 = 2

Hence Average Rate of Change = 98/2 = 49

Answer = 49