simultaneous equation -- 4x+3y=16 .. 5x-y=1

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

Explanation:

Draw a vertical number line. Let's say we start at 0 on the number line. Zero means no net change (he doesn't gain weight, nor does he lose weight either).

Losing 8 pounds means we go down 8 units. Think of it like being at the ground level and then going down 8 floors to the basement level of a large building (eg: parking garage maybe).

After this movement, we're at -8 on the number line. Then move up 9 units to arrive at +1 or just 1 on the number line. So Alex has gained those 8 pounds back to his original weight, plus an extra pound. So that's why -8+9 = 1.

Then move down 2 units to get to -1. Lastly, from -1 move 6 units down to get to -7.

So overall, Alex has lost 7 pounds when everything is said and done.

Refer to the diagram below. We start at point A, move to point B after losing 8 pounds, then to C when gaining 9 pounds, and so on until we get to point E. Point E is at -7 on the vertical number line to represent that he lost 7 pounds.

----------------

We can think of it in another way:

add up all the losses to get

loss of 8 + loss of 2 + loss of 6 = loss of 16

So he lost 16 pounds if we ignore the "gained 9 pounds", but we have to account for that. So we'll take 9 away from 16 to get 16-9 = 7.

Overall, Alex lost 7 pounds.

[tex] \boxed{ \boxed{ \cos {}^{2} ( \theta) = \dfrac{1}{4} }}[/tex]

According to a Trigonometric Identity :

[tex] \hookrightarrow \mathrm{\sin {}^{2} ( \theta) + \cos {}^{2} ( \theta) = 1}[/tex]

Now, let's solve for [tex] \cos²(\theta)[/tex]

[tex] \longrightarrow \dfrac{3}{4} + \cos {}^{2} ( \theta) = 1[/tex]

[tex] \longrightarrow \cos{}^{2}( \theta) = 1 - \dfrac{3}{4} [/tex]

[tex]\longrightarrow \cos {}^{2} ( \theta) = \dfrac{4 - 3}{4} [/tex]

[tex]\longrightarrow \cos {}^{2} ( \theta) = \dfrac{1}{4} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{hope \: \: it \: \: helps \: \: you.....}}{\orange{}}}}}[/tex]

97 decibel sound is 2.5 times more intense than a 93 decibel sound

Correct option is C.

Sound intensity also known as acoustic intensity, is defined as the power transmitted by a sound wave per unit area in a direction perpendicular to that area. Sound intensity is the sound power in watts divided by the area (in square meters) covered by the sound. Sound loudness relates the intensity of a particular sound to its strength at the threshold of hearing, measured in decibels (dB).

Given expression for loudness

L = 10 log(I/I₀)

Loudness of two different sounds are

L₁ = 97 decibel and L₂ = 93 decibel.

Let the intensity for the loudness L₁ and L₂ are I₁ and I₂

Then,

L₁ = 10log(I₁/I₀) = 97

⇒ log(I₁/I₀) = 9.7

taking antilog

I₁/I₀ = antilog (9.7)

I₁/I₀ = 5011872336.27271

L₂ = 10log(I₂/I₀) = 93

⇒ log(I₂/I₀) = 9.3

taking antilog

I₂/I₀ = antilog (9.3)

I₂/I₀ = 1995262314.96888

Then,

(I₁/I₀)/(I₂/I₀) = 5011872336.27271/1995262314.96888

I₁/I₂ = 2.51188643 ≈ 2.5

Hence, 2.5 times more intense is 97 decibel sound than 93 decibel sound.

Learn more about intensity here:

https://brainly.com/question/30101270

#SPJ2

Answer:

Converting velocity into m/s

72x5/18=20 m/s²

Distance = Velocity *Time

20*5=100m

Step-by-step explanation:

hope it's helpful

The polynomial, [tex]5x^3 - x^2 + 2[/tex], is a trinomial and the degree of the polynomial is 3.

A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

The given polynomial, [tex]5x^3 - x^2 + 2[/tex], has three terms separated by addition and subtraction symbols, making it a trinomial.

The highest exponent in the polynomial is 3, which determines its degree.

So, the degree of the polynomial is 3.

To learn more on Polynomial click here:

https://brainly.com/question/11536910

#SPJ4

Answer: 5 Seconds

Step-by-step explanation: Given the equation of the height expressed ad;

h(t) = - 16t^2 + initial height

Given that initial height = 400feet

h(t) = - 16t^2 + 400

The waste will hit the ground at when h(t) = 0

substitute

0 =  - 16t^2 + 400

16t^2 = 400

t² = 400/16

t² = 25

t = √25

t = 5secs

Answer:

90 Students.

Step-by-step explanation:

1/2 (Half) of 180 is 90.

Answer:

90 students will choose basketball

Step-by-step explanation:

half (1/2) choose basketball and half of 180 is 90

Answer:

Find the volume of this prism.

Theoretically, the probability of selecting one red marble from this bag is 0.20.

If a student does not return his or her marble to the bag before the next student selects his or her marble, the theoretical probability of selecting a blue marble may be different for the next student.

Probability determines how likely it is an event would happen. The chances of the event happening lie between 0 and 1.

The probability of selecting one red marble from this bag = number of red marbles / total number of marbles

16 / 80 = 0.20

To learn more about probability, please check: https://brainly.com/question/13234031

#SPJ2

Answer: Answer:

A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B  

= (0.51, 0.57)

This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)

B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

_________________________________________________________

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.

Critical value = 2.33

Standard error = σₓ = √[p(1-p)/n]

p = sample proportion = 0.54

n = sample size = 1500

σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287

98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.54 ± (2.33 × 0.01287)

CI = 0.54 ± 0.02998)

98% CI = (0.51, 0.57)

98% Confidence interval = (0.51, 0.57)

B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;

- The sample data must have been obtained using a random sampling technique.

- The sampling distribution must be normal or approximately normal.

- The variables of the sample data must be independent of each other.

On the second point, the condition for a binomial distribution to approximate a normal distribution is that

np ≥ 10

and n(1-p) ≥ 10

The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.

For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Step-by-step explanation:

Answer:

hii

Step-by-step explanation:

follow me please gugs

Answer:

D

Step-by-step explanation:

el cociente es 12 y el resto es 4, porque 12 por 5 es 60. 60 es el cociente. y 64-60 = 4 por lo tanto 4 es el resto

Answer:

[tex]\frac{3x+1}{x}, x\neq -1[/tex]

Step-by-step explanation:

We can start by combining the fractions in the numerator. We can multiply them by x/x and x + 1/x + 1 respectively to get a common denominator of x(x + 1).

[tex]\frac{4}{x+1}*\frac{x}{x} +\frac{2}{x} *\frac{x+1}{x+1}\\\\\frac{4x}{x(x+1)}+\frac{2x+2}{x(x+1)}\\\\\frac{6x+2}{x(x+1)}[/tex]

Now we can rewrite an simplify:

[tex]\frac{\frac{6x+2}{x(x+1)} }{\frac{2}{x+1} }\\\\\\\frac{6x+2}{x(x+1)}*\frac{x+1}{2} \\\\\frac{3x+1}{x}[/tex]

The domain would be x ≠ -1 because the starting domain is [tex]x\neq -1; x\neq 0[/tex] and it changed to [tex]x\neq 0[/tex], so for the two fractions to be equal, the domain would be [tex]x\neq -1[/tex].

Answer:

The smallest possible value of k is 656

Step-by-step explanation:

The given width of the Eiffel Tower, w₁ = 328 feet

The given height of the Eiffel Tower, h₁ = 984 feet

The width of the space Maria can use on the shirt, w₂ = 0.75 feet

The height of the space she can use on the shirt, h₂ = 1.5 feet

We get;

The ratio of height to width of the Eiffel Tower = h₁/w₁ = 984/328 = 3

The height to width ratio of the space on the shirt = h₂/w₂ = 1.5/0.75 = 2

Therefore, that the aspect ratio of the space on the T-shirt is wider than the Eiffel Tower, the height of the space on the T-shirt is the limiting dimension of the scaled picture of the Eiffel Tower

Therefore, the scale factor, k = The ratio of the actual height of the Eiffel Tower, to the height of the space on the T-shirt

Where 'k' represent the integer value to shrink the Eiffel Tower and fit it on the T-shirt, and 'k' is the smallest ratios of the dimensions of width or height of the tower to the dimensions of the width or height of the space available on the shirt, given that the height to width ratio of the area on the shirt is smaller than that of the Eiffel Tower

Mathematically

k = h₁/h₂

∴ k = 984/1.5 = 656

The scale factor of the height of the Eiffel Tower to the height of the space available on the T-shirt, k = The smallest possible value of k = 656.

Answer:

1/6

Explanation:

This is because if you were to take up the entire wall with these same proportions, you would need six colors.

Step-by-step explanation:

Can u upload image so that i can help u

By solving a system of equations, we will see that the rational function is:

[tex]f(x) = \frac{12}{(x + 2)} -3[/tex]

First, we need to see the x-value of the vertical asymptote, here we can see that the vertical asymptote happens at x = -2, then the denominator will be something like:

d = (x - (-2)) = (x + 2).

Then our rational function will be something like:

[tex]f(x) = \frac{a}{(x + 2)} + c[/tex]

In the graph we can see two things, first:

f(0) = 3

f(1) = 1

Replacing that in our function, we get:

[tex]\frac{a}{(0 + 2)} + c = 3\\\\ \frac{a}{(1 + 2)} + c = 1[/tex]

This is a system of equations, that can be rewritten as:

a/2 + c = 3

a/3 + c = 1

Isolathing c in both equations, we get:

a/2 - 3 = -c = a/3 - 1

Then we have:

a/2 - 3 = a/3 - 1

Now we can solve this for a:

a/2 - a/3 = 3 - 1

a/6 = 2

a = 2*6 = 12

And the value of c is given by:

-c = a/3 - 1 = 12/3 - 1 = 4 - 1 = 3

c = -3

Then the rational function is:

[tex]f(x) = \frac{12}{(x + 2)} - 3[/tex]

If you want to learn more about rational functions, you can read:

https://brainly.com/question/1851758

Answer:

B. 3(1/3)^x

Step-by-step explanation:

Edg 2022

Answer:

B

Step-by-step explanation:

edge 2021

Answer:

b

Step-by-step explanation:

Answer:

c. 60

Step-by-step explanation:

If we know that d is 90 degrees. We can make a conclusion that we have a 30, 60, 90 triangle. D is 90 and a triangle is 180 degrees. So we can automatically knock off 90 from the 180 giving us another 90. Now we know that we have a 30 and 60 to work with. F is an angle that is larger than E. So E is 30 and F is 60.

Answer:

5 months

Step-by-step explanation:

150 + 45x = 195 240 285 330 375 420

125 + 50x = 175 225 275 325 375 425

From the following compound inequalities, all the compound inequalities have a solution.

A compound inequality is a type of inequality that comprises two basic inequalities.

From the given information, we have:

To determine the compound inequality with no solution, we need to solve each of the inequalities.

1.

2x + 3  < 3x - 4 and 3x + 7 > 5x - 9

Collect like terms

= 2x - 3x < - 4 - 3  and 3x - 5x > - 9 - 7

= -x < -7 and -2x > -16

= x < 7 and x > 8    (has a solution)

2.

2(x -6) < 3(x+6) and 6(x+3) > 9(x-1)

Open brackets

= 2x - 12 < 3x + 18 and 6x + 18 > 9x - 9

Collect like terms

= 2x - 3x < 18 + 12 and 6x - 9x > - 9 - 18

= - x < 30 and - 3x > - 27

= x > -30 and x > 9   (has a solution)

3.

8x + 15 ≤ 4x - 5 and -7x + 2 < -6x + 3

Collect like terms

= 8x - 4x  ≤ - 5 - 15 and -7x - 6x < 3 - 2

= 4x ≤ - 20 and -13x < 1

= x  ≤ -5 and x < - 1/13   ( has a solution)

4.

-5x - 1 ≥ -7x + 9 and -4x - 7 < 5x + 11

= -5x + 7x ≥ 9 + 1 and -4x -5x < 11 + 7

= 2x ≥ 10 and -9x < 18

= x  ≥ 5 and x < -2 ( has a solution)

Learn more about compound inequality here:

https://brainly.com/question/7070563

#SPJ1

Answer:

bete a la her ha pir que yo no me use la reasouesta

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

Work Shown:

Multiply top and bottom by [tex]\sqrt{2}[/tex] to rationalize the denominator

[tex]\frac{10-\sqrt{18}}{\sqrt{2}}\\\\\frac{\sqrt{2}(10-\sqrt{18})}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{2}*10-\sqrt{2}*\sqrt{18}}{\sqrt{2*2}}\\\\\frac{\sqrt{2}*10-\sqrt{2*18}}{\sqrt{4}}\\\\\frac{10\sqrt{2}-\sqrt{36}}{2}\\\\\frac{10\sqrt{2}-6}{2}\\\\\frac{-6+10\sqrt{2}}{2}\\\\\frac{2(-3+5\sqrt{2})}{2}\\\\-3+5\sqrt{2}\\\\[/tex]

We end up with something in the form [tex]a+b\sqrt{2}[/tex] where a = -3 and b = 5

answer:B

got it right on edg

The function that represents the exponential graph is, [tex]y = 2^{x+2} + 3[/tex].

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

We know a function is called an exponential function when the exponent is the independent variable, For example, aˣ.

From the graph of the function, When x = 0, y = 7.

Observing the options we have,

[tex]y = 2^{x+2} + 3[/tex].

When x = 0.

[tex]y = 2^{0+2} + 3.[/tex]

[tex]y = 2^{2} + 3.[/tex]

y = 7.

learn more about graphs here :

https://brainly.com/question/2288321

#SPJ7

Answer:

See explanation below

Step-by-step explanation:

1. 10 students didn't talk on the phone because they've spent zero hours on the phone.

2. 3 hours is the largest number of hours

Answer:50

Step-by-step explanation:

3/5 = 3 ÷ 5 = 0.6

30 ÷ 0.6 = 50

otra explicacion:

30/1 ÷ 3/5= 30/1 x 5/3 = 150/3 = 50

Answer:

D. x = -5y^2

Step-by-step explanation:

I used a graphing calculator.

Answer:

PL, PQ

Step-by-step explanation:

a ray starts with a point and goes on for infinity (the arrow)

Answer:

you find the area of triangle by the formula

1/2×base×height

Answer:

Area of triangle = ½ × base × height

Step-by-step explanation:

(A = ½ × b × h)

This formula is mainly used to find the area of the triangle.

Answer:

26 m

Step-by-step explanation:

Find what length is needed for fencing by finding the perimeter of the land.

Use the perimeter formula, P = 2l + 2w

Plug in the length and width:

P = 2l + 2w

P = 2(8) + 2(5)

P = 16 + 10

= 26

So, the length of wire needed is 26 m