Question 8
Select the solution to the following system of equations:
3x+2y=0
-x-y=1

         There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.

[1] using the quadratic formula

     When the equation is in the form of ax² + bx + c = 0.

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

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[2] factoring

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[3] completing the square

     To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c

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Answer: 29, 31, 37, 41, 43, 47, 53.

Step-by-step explanation:

Answer:

=> Apply law of cosine

[tex]c^2=a^2+b^2-2abcos\left(C\right)[/tex]

=> input value

[tex]z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)[/tex]

=> simplify

[tex]z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}[/tex]

=> calulcation

[tex]z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}[/tex]

=> apply rule: Distance must be greater than 0

which is about 14.51828

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{7\sqrt{65}}{65}[/tex]

Step-by-step explanation:

Cosine is the ratio of the side adjacent to the angle and the right triangle hypotenuse.

[tex]cos[/tex] B = [tex]\frac{7}{\sqrt{65}}[/tex] = [tex]\frac{7\sqrt{65}}{65}[/tex]

Answer:

$12

Step-by-step explanation:

x+2y=82........(1)

3x+y=96.........(2)

y=96-3x...........(3)

x+2y=82

x+2(96-3x)=82

x+192-6x=82

-5x=82-192

-5x=-110

x=-110÷-5

x=22

y=96-3x

y=96-3(22)

y=96-66

y=30

Therefore,x=22 and Y=30

so silver= x =22

gold= y = 30

y=30;x=22

=30-22

-12

Therefore $12

=================================================================

Explanation:

Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.

The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.

Multiply this floor area with the height of the room (22 m) to get the volume of the room.

volume = (floor area)*(height) = 84*22 = 1848 cubic meters

Answer:

O The value of f(2) is smaller than the value of f(1).

Step-by-step explanation:

First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)

The simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have an expression:

[tex]= 8 \dfrac{3}{8} + 3 \dfrac{3}{8} + 2 \dfrac{3}{8} + \dfrac{3}{8}[/tex]

After simplification:

[tex]= \dfrac{67}{8} + \dfrac{27}{8} + \dfrac{19}{8} + \dfrac{3}{8}[/tex]

[tex]= \dfrac{67+27+19+3}{8}[/tex]

= 116/8

= 29/2

[tex]= 14\dfrac{1}{2}[/tex]

Thus, the simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.

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Answer:

i dont understand your question

Step-by-step explanation:

A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x) and g(x) can be plotted as shown in the below image.

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Answer:

0.341

Step-by-step explanation:

Multiply the probabilities: 0.55 * 0.62 = 0.341

Answer:

the function is only increasing.

Step-by-step explanation:

Answer:

2 hours

Step-by-step explanation:

Mike has a six hour head start so he is    6 x 2 = 12 miles ahead

 their 'closing speed' is  8-2 = 6 m/hr

    it will take Kim   12 / 6  = two hours to catch Mike

From the question given above, the ratio of L : W in simplified form is given as: 6 : 5. See the explanation below.

A ratio, simply, can be defined as the quantitative relationship that exists between two values which is indicative of the number of times one value can be obtained from the other.

Let X be the width of one of the rectangles and let its height be Y.

It is clear from the image that:

4X = 3Y

Hence

(4/3)X  = Y

Therefore,

Lenght (L) = 3Y

= 3 (4/3)X

= 4X

Width (W) = Y + 2X

= (4/3)X + 2X

= (10/3)X

Therefore,

L : W =  4X: 10/3X

= 4:10/3

To remove the fraction, multiply both sides of the ratio by 3

= 12 : 10, furhter simplify by halving each value, and we have

= 6:5

Hence, the ratio L: W in simplified form is 6 : 5.

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These are expression written as a function of sine, cosine and tangent. The value of x from the given function is 4.29

Trigonometry expression

These are expression written as a function of sine, cosine and tangent.

Given

tanx² - 1/3 = 0

Add 1/3 to both sides

tanx² - 1/3 + 1/3 = 0 + 1/3

tanx² = 1/3

x² = arctan(1/3)

x² = 18.44

x =4.29

Hence the value of x from the given function is 4.29

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Answer:

[tex]\frac{1}{102}[/tex]

Step-by-step explanation:

1) Negative Power Rule: [tex]x}^{-a}=\frac{1}{{x}^{a}}[/tex].

[tex]\frac{1}{3}\div 34[/tex]

2) Use this rule: [tex]a\div \frac{b}{c}=a\times \frac{c}{b}[/tex].

[tex]\frac{1}{3}\times \frac{1}{34}[/tex]

3)  Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}[/tex].

[tex]\frac{1\times 1}{3\times 34}[/tex]

4) Simplify [tex]1\times 1[/tex] to [tex]1[/tex].

[tex]\frac{1}{3\times 34}[/tex]

5) Simplify  [tex]3\times 34[/tex] to [tex]102[/tex] .

[tex]\frac{1}{102}[/tex]

The computation of the index shows that the value of 9 × 10² will be 900.

From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:

= 9 × 10²

Note that 10² simply means that you've to multiply 10 twice. This will be:

= 10 × 10 = 100

Therefore, 9 × 10² will be:

= 9 × 100

= 900

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Answer:

1, 4, 5, 6

Step-by-step explanation:

to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).

you can also double check by plugging both into a calculator and see if they equal the same number.

The value of f(9) for the given function is 5

From the question, we are to determine the value of f(9)

The given function is

f(x) = -13 + 2x

To determine f(9), we will put x = 9 in the given function

That is,

f(x) = -13 + 2x becomes

f(9) = -13 + 2(9)

f(9) = -13 + 18

f(9) = 5

Hence, the value of f(9) for the given function is 5

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Answer:x ≤ 3

Step-by-step explanation:

(14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
14.5x - 5x-10 ≤ 4 + 16 - 1/2x Get rid of the parenthesis

9.5x-10 ≤ 20-1/2x Combine like terms

10x - 10 ≤ 20

10x/10 ≤ 30/10

x ≤ 3

Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

where:

Rewrite both equations into slope-intercept form:

a) 2x + 4y = 15

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

b) 6x + 12y = 45

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

New equations:

[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

No Solution: the same slope (both lines will be parallel)

One Solution: different slopes and different y-intercepts

Infinitely Many Solutions: the same slope and y-intercept

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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

Equation #1

Subtract 2x from both sides

Divide both sides by 4

Equation #2

Subtract 6x from both sides

Divide both sides by 12

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

Answer:

Step-by-step explanation:

The total cost when 881 minutes is used is $477.50.

a + 480b = 277 equation 1

a + 990b = 532 equation 2

Where:

Subtract equation 1 from equation 2

510b = 255

b = 255 / 510

b = $0.50

In order to determine the flat fee, substitute for b in equation 1

a + 480(0.5) = 277

a + 240 = 277

a = 277 - 240

a = $37

Total cost = flat fee + (variable cost x number of minutes spoken)

$37 + (881 x 0.5) = $477.50

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Answer:

A) x = 113°

Explanation:

Given three sides: 6.4 cm, 5.8 cm, 10.2 cm

Use the cosine rule:

c² = a² + b² - 2ab cos(C)

Insert/put variables:

[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]

[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]

[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]

[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]

[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex]   = 113.36°  ≈ 113°  (rounded to nearest degree)

Using the t-distribution, it is found that the 95% confidence interval for the population mean rating for Miami is (5.73, 6.95).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Considering the given sample, the other parameters are given as follows:

[tex]\overline{x} = 6.34, s = 2.16, n = 50[/tex]

Hence, the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6.34 - 2.0096\frac{2.16}{\sqrt{50}} = 5.73[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6.34 + 2.0096\frac{2.16}{\sqrt{50}} = 6.95[/tex]

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Answer:

24/5

Step-by-step explanation:

x is 4.8, improper simplified is 24/5

Answer:

if I am awake then it is 9 am.

Step-by-step explanation:

if p then q the converse is if q then p.