Find the value of x

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GIVING 20 points!!!

Answer:

perimeter is 36 cm

Step-by-step explanation:

Answer:

(a): x is 3 and ky is -1

(b): k is -2

Step-by-step explanation:

Let: 3x + ky = 8 be equation (a)

x - 2 ky = 5 be equation (b)

Then multiply equation (a) by 2:

→ 6x + 2ky = 16, let it be equation (c)

Then equation (c) + equation (b):

[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]

Then ky :

[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]

[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]

Simultaneous equations are used to represent a system of related equations.

The value of k when [tex]y = \frac 12[/tex] is -2

Given that:

[tex]3x + ky = 8[/tex]

[tex]x - 2ky = 5[/tex]

[tex]y = \frac 12[/tex]

Substitute [tex]y = \frac 12[/tex] in both equations

[tex]3x + ky = 8[/tex]

[tex]3x + k \times \frac 12 = 8[/tex]

[tex]3x + \frac k2 = 8[/tex]

[tex]x - 2ky = 5[/tex]

[tex]x - 2k \times \frac 12 = 5[/tex]

[tex]x - k = 5[/tex]

Make x the subject in [tex]x - k = 5[/tex]

[tex]x = 5 + k[/tex]

Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]

[tex]3(5 + k) + \frac k2 = 8[/tex]

Open bracket

[tex]15 + 3k + \frac k2 = 8[/tex]

Multiply through by 2

[tex]30 + 6k + k = 16[/tex]

[tex]30 + 7k = 16[/tex]

Collect like terms

[tex]7k = 16 - 30[/tex]

[tex]7k = - 14[/tex]

Divide both sides by 7

[tex]k = -2[/tex]

Hence, the value of constant k is -2.

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Given:

Amplitude = 21

Vertical shift = 19 units down

To find:

The maximum and the minimum value.

Solution:

The general form of sine function is:

[tex]y=A\sin (Bx+C)+D[/tex]

Where, |A| is amplitude, [tex]\dfrac{2\pi}{B}[/tex] is period, [tex]-\dfrac{C}{B}[/tex] is phase shift and D is the vertical shift.

Here,

[tex]Maximum=D+A[/tex]

[tex]Minimum=D-A[/tex]

We have,

Amplitude: [tex]A = 21[/tex]

Vertical shift: [tex]D=-19[/tex]

Negative sign means shifts downwards.

Now,

[tex]Maximum=D+A[/tex]

[tex]Maximum=-19+21[/tex]

[tex]Maximum=2[/tex]

And,

[tex]Minimum=D-A[/tex]

[tex]Minimum=-19-21[/tex]

[tex]Minimum=-40[/tex]

Therefore, the minimum value is -40 and the maximum value is 2.

Answer:

There are no like terms

Step-by-step explanation:

×^2+9

=ײ+9

Answer:

m <1 = 147

m <2 = 90

Step-by-step explanation:

In rhombus diagonals are perpendicular to each other so

m <2 = 90

m < 1 = 180- 33

= 147

Answered by Gauthmath

The required angle of the rhombus m∠1 = 57° and m∠2 = 90°.

Given that,
A figure of a rhombus is shown,
An angle of 33° is given,
m∠1 and m∠2 is to be determined.

The triangle is a geometric shape that includes 3 sides and sum of the interior angle should not greater than 180°.

The angle can be defined as the one line inclined over another line.

Here, the rhombus has been shown with an angle of 33° of the side with one of the diagonal.

Since the diagonal of the rhombus bisect each other at an angle of 90 so the angle m∠2 = 90  and the sum of the interior angle of a triangle is 180. So,
m∠1 + 33 + 90 = 180
m∠1 = 180 - 123
m∠1 = 57

Thus, the required angle of the rhombus m∠1 = 57° and m∠2 = 90°.

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The inequality that relates the number of hours to the weekly sales is:

[tex]450 + 0.20x \ge 35y[/tex]

The complete question implies that we define an inequality that represents the relationship between the number of hours worked in a week and the weekly sales

We make use of the following representation:

[tex]x \to[/tex] weekly sales from cars.

[tex]y \to[/tex] hours worked in a week

His weekly salary is then calculated as:

Salary (S) = Earnings per week + Commission * Sales from car

So, we have:

[tex]S = 450 + 20\% * x[/tex]

Express percentage as decimal

[tex]S = 450 + 0.20* x[/tex]

[tex]S = 450 + 0.20x[/tex]

Assume he works for y hours in a week.

His hourly rate is:

[tex]Hourly = \frac{S}{y}[/tex] --- i.e. weekly salary divided by number of hours

[tex]Hourly = \frac{450 + 0.20x}{y}[/tex]

For this rate to be at least [tex]\$35[/tex], the following condition must be true

[tex]Hourly \ge 35[/tex] --- i.e. is hourly rate must be greater than or equal 35

So, we have:

[tex]\frac{450 + 0.20x}{y} \ge 35[/tex]

Multiply both sides by y

[tex]450 + 0.20x \ge 35y[/tex]

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Answer:

Wdym? that is fraction form, but if you ment decimal form; it is .7777 repeating and .25

Step-by-step explanation:

Answer:

[tex]\frac{(x+3)}{9}[/tex]

Step-by-step explanation:

Answer:

6.82 cm

Step-by-step explanation:

1000=V=pi*r^2*h. 1000=pi*r^3, r=6.82 cm

Answer:

so thats 2/6 or 1/3

Step-by-step explanation:

A die has 6 sides your odds of getting 2 or lesser are 1/3 or 33%

Answer: (a): Good course, (b): Bad course

Step-by-step explanation:

Firstly, because the standard deviation of the good course results is lower, there is less variation so he performs more consistently there.

Secondly, the trick with the second question is that while the mean of the bad course is slightly less, the standard deviation is quite a lot higher than that of the good course, so it's more likely that the highest single test score belongs to the bad course.

Answer:

a = sqrt(7)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

a^2 +3^2 = 4^2

a^2 +9 = 16

a^2 = 16-9

a^2 = 7

Taking the square root

a = sqrt(7)

Answer:

Hello,

Step-by-step explanation:

3)

[tex]x^2-4x+3=0\\x^2-3x-x+3=0\\x(x-3)-(x-3)=0\\(x-3)(x-1)=0\\\\x-intercepts\ are\ x=3\ or\ x=1[/tex]

4)

[tex]-x^2-8x+12=0\\x^2+8x-12=0\\(x^2+2*4x+16)-16-12=0\\\\(x+4)^2-28=0\\\\\\(x+4-2\sqrt{7} )((x+4+2\sqrt{7} )=0\\\\x-intercepts\ are \ x=-4+2\sqrt{7}\ and\ x=-4-2\sqrt{7}\\\\[/tex]

5)

[tex]f(x)=-3(x-7)(x+4)\\=-3(x^2-3x-28)\\\\=-3(x^2-2*\dfrac{3}{2} *x+\dfrac{9}{4} )+\dfrac{27}{4} +84\\\\=-3(x-\dfrac{3}{2})^2+\dfrac{363}{4} \\\\\\Vertex\ is\ (\dfrac{3}{2},\dfrac{363}{4})[/tex]

Answer:

Yes.

Step-by-step explanation:

Minus and difference mean the same thing. To find the difference, you subtract or minus, so they are the same thing.

Answer:

you guess any value of x and then you substitute any three values for example for the first equation you can guess the value of x to be 1 or 2 or 3

Answer:

Does the answer help you?

Answer:

6/(x + 4)(x - 2)

Step-by-step explanation:

(12x - 96)/(x² - 4x - 32) ÷ (6x² - 6x - 12)/(3x + 3)

12x - 96 = 12(x - 8)

x² - 4x - 32 = (x - 8)(x + 4)

(12x - 96)/(x² - 4x - 32) = 12/(x + 4)

6x² - 6x - 12 = (3x + 3)(2x - 4)

(6x² - 6x - 12)/(3x + 3) = 2x - 4 = 2(x - 2)

(12x - 96)/(x² - 4x - 32) ÷ (6x² - 6x - 12)/(3x + 3) = 12/(x + 4) ÷ 2(x - 2) = 12/(x + 4) × 1/2(x - 2) = 6/(x+4)(x-2)

Step-by-step explanation:

The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.

Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are

±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).

Trying out a few roots until we get one that works using synthetic division, we can try

x+1 (the root is x=-1)

-1  |     1       1        -6         -14         -12

    |            -1          0          6           8

    __________________________

          1     0        -6            -8         -4

the remainder is -4, so this does not work

x+2 (the root is x=-2)

-2 |     1       1        -6         -14         -12

    |            -2          2          8          12

    __________________________

          1      -1       -4           -6         0

Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is

-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6

Using the rational roots theorem, the possible roots of x³-x²-4x-6 are

±(1,2,3,6)

Starting with

x-1 (root is x=1), we have

1 |     1       -1        -4         -6      

    |            1          0         -4        

    _____________________

          1      0       -4           -10

there is a remainder, so this is not a root

next, x-2 (root is x=2)

2 |     1       -1        -4         -6      

    |            2         2         -4        

    _____________________

          1      1       -2           -10      

there is a remainder, so this is not a root

next, x-3 (root is x=3)

3|     1       -1        -4         -6      

    |            3         6         6        

    _____________________

          1      2      2          0

x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2

Answer:

A = 120

Step-by-step explanation:

Angle A is a vertical angle to 120 and vertical angles are equal

A = 120

[tex]\Large\rm\underbrace{{\green{ \: Angle \: A \: = \: 120 \degree}}}[/tex]

Because vertically opposite angles are always equal.

Answer:

Is 11

Step-by-step explanation:

x+(-y)+z —> -5 +(+7)+9 = -5+7+9 = 11

Answer:

x ≈ 55.5°

Step-by-step explanation:

Using the Sine rule in the triangle

[tex]\frac{5}{sinx}[/tex] = [tex]\frac{5.7}{sin70}[/tex] ( cross- multiply )

5.7 sinx = 5 sin70° ( divide both sides by 5.7 )

sin x = [tex]\frac{5sin70}{5.7}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{5sin70}{5.7}[/tex] ) ≈ 55.5° ( to the nearest tenth )

Answer:

[tex]x =55[/tex]°

Step-by-step explanation:

An isosceles triangle is a triangle with two congruent sides. One can see that the given triangle is an isosceles triangle, as two sides have a side length of (5) units. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides of an isosceles triangle are congruent. In this situation, this means that two angles have a measure of (x) degrees. As a given, the sum of angles in any triangle is (180) degrees. Thus, one can form an equation, and solve for the unknown, (x):

[tex]x + x + 70 = 180[/tex]

Simplify,

[tex]2x + 70 =180[/tex]

Inverse operations,

[tex]2x + 70 =180[/tex]

[tex]2x = 110[/tex]

[tex]x =55[/tex]

Answer:

€520=£442.83

=£442.83-£260

=£182.83 into dollars=$251.52

Therefore he receives $251.52

Answer:

b:25

Step-by-step explanation:

77 degrees Fahrenheit is 25 degrees Celsius. So, the correct answer for the given equation is the second option.

An equation is a combination of two or more expressions separated by an equal sign(=), indicating that the expressions are equal to each other. The expressions, though, are a group of numbers, variables, mathematical operations, etcetera. An equation can be represented on the Cartesian plane.

The relation between Celsius and Fahrenheit is given by the following equation:

[tex]C =\dfrac{5}{9}(F-32)[/tex],

Substitute F = 77 to convert 77 degrees Fahrenheit to Celsius.

[tex]C =\dfrac{5}{9}(77-32)[/tex]

   [tex]=\dfrac{5}{9}(77-32)\\=\dfrac{5}{9}\times45\\= 25[/tex]

Thus, the second option is correct.

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Answer:

Y = 2x - 4

(2,-4)

gradient= 2

y-intersept = -4

Answer:

13

Step-by-step explanation:

We know that a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = c^2

25+144 = c^2

169 = c^2

Taking the square root of each side

sqrt(169) = sqrt(c^2)

13 =c

Answer:

I believe it's 12 in.

Step-by-step explanation:

hope this helps you!

Answer:

D

Step-by-step explanation:

The function you need to use is the Tan(39).

Tan(x) = opposite / adjacent.

The opposite side does not make up the reference angle.

In this case, the opposite side = x

The adjacent side is not the hypotenuse and does make up the reference angle (which is not the right angle).

opposite = x

adjacent = 68

Tan(39) = x / 68              Multiply by 68

68*Tan(39) = x               Divide by Tan(39)

Tan(39) = 0.9098

68*.9098 = x

x = 55.07

Answer:

all have "bases" less than one which is a decay...

only "C" is greater than 1 (1.01)

"C" is the answer

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

125 of 500 can be written as:  125 /500

To find a percentage, we need to find an equivalent fraction with the denominator 100. Multiply both numerator & denominator by 100.  

125 /500  ×  100 /100

= ( 125 × 100/ 500 ) ×  1 /100   =  25 /100

Answer:

25%

Step-by-step explanation:

Of means multiply and is means equals

P *500 = 125

Divide each side by 500

P = 125/500

P = .25

Change to percent form

P = 25%