Write a system of linear inequalities so the points,(1,2) and (4,-3) are solutions of the system, but the point (-2,8) is not a solution of the system.

If the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.

Given that the sum of an integer and 7 more than the next consecutive integer is 66.

Integer is a number that is written without a fraction component. It can be positive as well as negative.

let the first integer be x.

Consecutive integer will be x+1.

Sum of integer and 7 more than the next consecutive integer is 66.

Sum according to the given information=x+x+1+7

=2x+8

2x+8=66

2x=66-8

2x=58

x=58/2

x=29

Next integer=29+1-30.

Hence if the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.

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Sine rule:

30/sin(17) = x/sin(90)

x sin(90)

30 x sin(90) / sin(17) = x

x = 102.6091086

So, x = 102.6 to the nearest tenth.

Hope this helps!

Answer:

y = - [tex]\frac{1}{6}[/tex] x - 1

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 = 6x - 2 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then

y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, - 2 ) into the partial equation

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = - [tex]\frac{1}{6}[/tex] x - 1 ← equation of perpendicular line

Answer:

a h>155 or h<190

Step-by-step explanation:

The height of the shortest student is 155 cm and the height of the tallest student is 190 cm, then the inequality shows the range is 155 ≤ h ≤ 190. Hence, option B is correct.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the provided data in the question,

The height of the shortest student is 155 cm and,

The height of the tallest student is 190 cm.

It means that the height rage is starting from 155 cm and ending at 190 cm.

The shortest height should be at least equal to 155 cm and the greater height is maximum 190 cm.

Therefore, the inequality according to this is 155 ≤ h ≤ 190.

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Since there are same number of either side, hence the solution has infinite number of solution

System of equations are equation that consist of two or more equations with unknown variables.

Given the equations

2x - y = 7

2y = 4x - 14

This can also be written as

2x - y = 7

y = 2x - 7

Substitute equation 2 into 1

2x - (2x - 7) = 7

2x-2x+7= 7

7 = 7

Since there are same number of either side, hence the solution has infinite number of solution

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hi

"does not change "  or "remain the same "

Answer:

  36 meters

Step-by-step explanation:

You are given an angle and the length of the side adjacent. You want to find the length of the side opposite, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

The height of Yuri's balcony is the sum of the heights of Kim's balcony and the height of Yuri's balcony above that. Each of those height is the side opposite a given angle in a right triangle. These can be found by solving the tangent relation for the opposite side:

  Tan = Opposite/Adjacent

  (Adjacent)(Tan) = Opposite

  height of Kim's balcony = (30 m)tan(40°)

  height above Kim's balcony = (30 m)tan(20°)

__

  height of Yuri's balcony = height of Kim's + height above Kim's

  height of Yuri's balcony = (30 m)tan(40°) +(30 m)tan(20°)

  height of Yuri's balcony = (30 m)(tan(40°) +tan(20°))

  height of Yuri's balcony ≈ (30 m)(0.8391 +0.3640) ≈ 36.092 m

The height of Yuri's balcony is about 36 meters.

Answer:

x + y +z= 10

Step-by-step explanation:

4x - y = 5  ---------(I)

 4y - z = 7 ---------(II)

4z - x = 18 ---------(III)

Add all the three equations,

  4x - y + 4y - z + 4z - x = 5 + 7 + 18

  4x - x  -y + 4y -z + 4z  = 30

              3x + 3y + 3z = 30

Divide the entire equation by 3

               [tex]\sf \dfrac{3x}{3}+\dfrac{3y}{3}+\dfrac{3z}{3} = \dfrac{30}{3}[/tex]

                 x + y + z = 10

Using the Pythagorean theorem, the length of line segment FJ is: 42 ft.

To find the length of line segment FJ, we need to apply the Pythagorean theorem to find the length of the segment from F to the point, say point O, on FJ where a right triangle FOG will be gotten.

Thus, we have:

FO = √(GF² - GO²)

FO = √(30² - 24²)

FO = 18 ft.

FJ = FO + GH

Plug in the values

FJ = 18 + 24

FJ = 42 ft.

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Answer:

x > - 3

Step-by-step explanation:

6(x + 2) > x - 3 ← distribute parenthesis on left side

6x + 12 > x - 3 ( subtract x from both sides )

5x + 12 > - 3 ( subtract 12 from both sides )

5x > - 15 ( divide both sides by 5 )

x > - 3

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏

✏[tex]\bigstar\textsf{Solution \quad Steps:-}[/tex] ✏

use the distributive property

[tex]\sf{\longmapsto 6x+12 < x-3}[/tex]

subtract both sides by x and 12

[tex]\sf{\longmapsto{5x < -15}[/tex]

divide both sides by 5

[tex]\sf{\longmapsto x < -3}}[/tex]

`hope it's helpful to u ~

Answer:

answer is (c)

May it help you

Option C. The inequality can then be written as  x² - 2y ≥ 5000 and 2x + 5y <1000

How to write the inequality

Stock = x² - 2y

Purchase = 2x + 5y

Stock is said to be at least 5000 dollars. We can write this as

x² - 2y ≥ 5000

Then the purchase is said to be below 1000. This is written as 2x + 5y <1000

The inequality can then be written as  x² - 2y ≥ 5000 and 2x + 5y <1000

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26.8% of examinees will score between 600 and 700.

This question is based on z score concept.

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

[tex]z={x-\mu \over \sigma }[/tex]

where:

μ is the mean

σ is the standard deviation of the population

Given:

μ = 560

σ = 90

For

600≤ X≤700

for x = 700

Z score =x - μ/σ

=(700 - 560)/90

      = 1.55556

P-value from Z-Table:

P(560<x<700) = P(x<700) - 0.5 = 0.44009

for x = 600

Z score =x - μ/σ

=(600 - 560)/90

      = 0.44444

P-value from Z-Table:

P(560<x<600) = P(x<600) - 0.5 = 0.17164

∴ P(600<x<700) = P(560<x<700) - P(560<x<600)

                           = 0.44009 - 0.17164

                          =0.26845

∴26.8% percentage of examinees will score between 600 and 700.

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Answer: Choice B is correct.

Answer:

1)  4x + 5y = 20         4x + 5y = 20  

  -2x + 3y = 12  -->  2(-2x + 3y) = 2(12)

2) 4x + 5y = 20  

  -4x + 6y = 24

3) 4x + 5y = 20  

   -4x + 6y = 24

   0x + 11y = 44

4) 11y = 44

5) y = 4

6) 4x + 5y = 20  

   4x + 5(4) = 20  

7) 4x + 20 = 20

8) 4x = 0

9) x = 0

10) The solution is the point (0, 4)

Answer:

Cos² x

Step-by-step explanation:

    [tex]\sf Cos^2 \ x *Csc^2 \ x-Cos^2 \ x *Cot^2 \ x = Cos^2 \ x (Csc^2 \ x - Cot^2 \ x)[/tex]

                                                        [tex]\sf = Cos^2 \ x \left(\dfrac{1}{Sin^2 \ x} - \dfrac{Cos^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x \left(\dfrac{1-Cos^2 \ x}{Sin^2 \ x}\right)\\\\\boxed{\bf Indentity: \ 1 - Cos^2 \ x = Sin^2 \ x}\\\\\\= Cos^2 \ x \left(\dfrac{Sin^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x[/tex]

If f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 then the inverse of function f(x) is p(-21)=-1,p(-9)=0,p(3)=1,p(15)=2 which is option d.

Given that f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 and we are required to find the inverse if the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have corresponding value of y.

The given function is as under:

f(-1)=-21,

f(0)=-9,

f(1)=3

f(2)=15

In the inverse of the function the value of x becomes the value of y and the value of y becomes the value of x. So the inverse of the function is as under:

p(-21)=-1,

p(-9)=0,

p(3)=1,

p(15)=2

Hence if f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 then the inverse of function f(x) is p(-21)=-1,p(-9)=0,p(3)=1,p(15)=2 which is option d.

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The answer is k = 7.

As the graph has been shifted down 7 units, the translation can be represented as :

g(x) = f(x) - 7

(0.5)x - k = (0.5)x - 7

k = 7

The difference of the expression is as follows:

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5) = - 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4) = x - 19

The difference of the expression can be found when we combine the like terms.

Therefore,

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5)

6y⁴ + 3y² - 7  - 12y⁴ + y² - 5

6y⁴ - 12y⁴ + 3y² + y² - 7 - 5

- 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4)

3x - 15 - 2x - 4

3x - 2x - 15 - 4

x - 19

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The solution to the system of equations is (8, -4)

The system of equations is given as;

y = -1/4x - 2

y = 3/8x - 7

See attachment for the graph of the equations

From the attached graph, we have the point of intersection to be

(x, y) = (8, -4)

Hence, the solution to the system of equations is (8, -4)

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Based on the calculations, the magnitude of m∠EFH is equal to 112°.

In Geometry, the sum of two (2) non-adjacent interior angles in a triangle is equal to its exterior angle. Thus, we have:

(3x - 3) + 76 = 8x + 8

3x + 73 = 8x + 8

73 - 8 = 8x - 3x

65 = 5x

x = 65/5

x = 13.

From triangle GFH, we have:

m∠EFH = ∠F = 8x + 8

m∠EFH = 8 (13) + 8

m∠EFH = 104 + 8

m∠EFH = 112°.

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Answer:

Step-by-step explanation:

for the first one, it is x=2

for the second one, it is x=9

Answer:

The answer is 75 and here's why.

Let's figure out the amount of remaining votes to prove this.

250 total votes   -    150 votes for candidate a = 100 votes.

               minus ↑ sign

Candidate B received 25% of the votes, so let's find 25% of 100

100 * 0.25 = 25 votes

Candidate B only got 25 votes (that's kinda sad, poor guy)

100 - 25 votes = the # of votes candidate C got

Candidate C got 75 votes!

Answer and Step-by-step explanation:

We are given a triangle, a quadrilateral inside a triangle. and exterior angles of the triangle at linear bisectors.

We can figure out the interior angles of the shape to find a by using the linear bisector theorem, in which a line separated by another line will have two angles that will add to 180 degrees.

For the bisected line with the angle of 60 degrees, the other angle will have to equal 120. We know this by taking 60 from 180.

The perpendicularly bisected line will always have 90 degrees for the angles, so the interior angle will be 90 degrees.

For the bisected line with the angle of 80 degrees, the other angle will have to equal 100. We know this by taking 80 from 180.

Now, we have angles to determine a.

Quadrilaterals consist of 4 interior angles, which, when added together, equals 360 degrees.

360 - 90 - 100 - 120 = a

260 - 90 - 120 = a

140 - 90 = 50 = a

So, angle a is equal to 50 degrees.

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Answer:

6x^3 -2x^2-11x + 4

Step-by-step explanation:

(3x - 4)(2x^2 + 2x - 1)

(3x - 4)(2x^2 + 2x - 1)

[(3x)(2x^2 + 2x - 1)]  +  [-4(2x^2 + 2x - 1)]

6x^3 + 6x^2 - 3x           -8x^2 - 8x + 4

6x^3 + [6x^2-8x^2] [- 3x- 8x] + 4

6x^3 -2x^2-11x + 4

Answer:

[tex]6x^3-2x^2-11x+4[/tex]

Step-by-step explanation:

Given expression:

[tex](3x-4)(2x^2+2x-1)[/tex]

Distribute the parentheses:

[tex]\implies 3x(2x^2+2x-1)-4(2x^2+2x-1)[/tex]

[tex]\implies 3x \cdot 2x^2+3x \cdot 2x +3x \cdot -1 -4 \cdot 2x^2-4 \cdot 2x-4 \cdot -1[/tex]

[tex]\implies 6x^3+6x^2 -3x -8x^2-8x+4[/tex]

Collect like terms:

[tex]\implies 6x^3+6x^2-8x^2 -3x -8x+4[/tex]

Combine like terms:

[tex]\implies 6x^3-2x^2-11x+4[/tex]

The graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.

Here we have:

[tex]f(x) = x^3\\\\g(x) = (x - 2)^3 + 6[/tex]

You can notice that if we take f(x), and we shift it 2 units to the right, we have:

g(x) = f(x - 2)

Then if we apply a shift upwards of 6 units, then we have:

g(x) = f(x - 2) + 3

Replacing f(x) by the cubic parent function, we have:

[tex]g(x) = (x - 2)^3 + 6[/tex]

So we conclude that the graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.

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Let [tex]P[/tex] be the number of plain cakes sold, and [tex]D[/tex] the number of decorated cakes sold.

Each plain cake sells for $7, so [tex]P[/tex] cakes sells for [tex]\$7P[/tex].

Similarly, each decorated cakes goes for $11, so [tex]D[/tex] cakes are worth [tex]\$11D[/tex].

The baker sells all but 3 cakes, so

[tex]P + D = 117[/tex]

After the sale, the baker earns a total of $991, so

[tex]7P + 11D = 991[/tex]

Now just solve the system of equations for [tex]P[/tex] and [tex]D[/tex]. This is easily done by substitution or elimination.

(The selected answer is actually the correct one.)

Answer:

where is the table?

Step-by-step explanation: