Which of the following is the equation for the graph shown

(You could do this shorter, but by the time i realized that it was too late.)

First, we need one of the variables (x or y) to have the same coefficient.
Lets use the variable y, since it uses smaller numbers.

Multiply the first equation by the denominator of y, which is 3. Then multiply the second equation by the denominator of y in the second equation, which is 4.

You get:
1st equation: [tex]\frac{3}{2} x+ y = 27[/tex]
2nd equation: [tex]\frac{12}{5}x - 3y=-12[/tex]
Now we need to multiply the first equation by 3, so we can have "3y" in both of the equations.
1st equation: 9/2x + 3y = 81
2nd equation: [tex]\frac{12}{5}x - 3y=-12[/tex]
Now we can subtract both of the equations.
12/5x + 9/2x = 69 We need to make the common denominator for x.
24/10x + 45/10x = 69
69/10x=69
x=10
Now we substitute x into the first equation (or the second, doesn't matter).
1/2 * 10 + 1/3y=9
5 + 1/3y = 9
1/3 y = 4
y = 12

Answer:

(10, 12 )

Step-by-step explanation:

let's begin by clearing the fractions from both equations

[tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{3}[/tex] y = 9 ( multiply through by 6 ( the LCM of 2 and 3 to clear ) )

3x + 2y = 54 → (1)

[tex]\frac{3}{5}[/tex] x - [tex]\frac{3}{4}[/tex] y = - 3 ( multiply through by 20 ( the LCM of 5 and 4 to clear ) )

12x - 15y = - 60 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x )

- 12x - 8y = - 216 → (3)

add (2) and (3) term by term to eliminate x

0 - 23y = - 276

- 23y = - 276 ( divide both sides by - 23 )

y = 12

substitute y - 12 into either of the 2 equations and solve for x

substituting into (1)

3x + 2(12) = 54

3x + 24 = 54 ( subtract 24 from both sides )

3x = 30 ( divide both sides by 3 )

x = 10

solution is (10, 12 )

The tenth term of the arithmetic sequence will be 15. Then the correct option is A.

Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as

[tex]\rm a_n = a_1 + (n - 1)d[/tex]

We have

a₇ = 6

d = 3

n = 7

Then the first term will be

a₇ = a₁ + (7 – 1)3

6 = a₁ + 18

a₁ = 6 – 18

a₁ = -12

Then the 10th term will be

a₁ = -12

d = 3

n =10

Then we have

a₁₀ = -12 + (10 – 1)3

a₁₀ = -12 + 27

a₁₀ = 15

Then the tenth term of the arithmetic sequence will be 15.

Then the correct option is A.

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The correct option is (A). The factored form of a-b is (5-3p⁴)(25+15p⁴+9p⁸).

Given that A and B are monomials where a = 125 and b = 27p¹².

Monomial expressions include only one non-zero term. Numbers, variables, or multiples of numbers and variables are all examples of monomials.

Firstly, substitute a=125 and b = 27p¹² into a-b, we get

a-b=125-27p¹²        ......(1)

As we know, 125=(5)³, 27p¹²=(3p⁴)

So, equation (1) can be rewritten as

a-b=(5)³-(3p⁴)

Now, apply a³-b³=(a-b)(a²+ab+b²).

a³-b³=(5-3p⁴)(5²+5(3p⁴)+(3p⁴)²)

Further, Simplify using exponent rule with the same exponent (ab)ⁿ=aⁿbⁿ.

a³-b³=(5-3p⁴)(5²+5×3p⁴+3²×(p⁴)²)

Furthermore, calculate the power, we get

a³-b³=(5-3p⁴)(5²+5×3p⁴+9(p⁴)²)

Then, Simplify using exponent power rule (aˣ)ⁿ=aˣⁿ, we get

a³-b³=(5-3p⁴)(5²+5×3p⁴+9p⁸)

Now, multiply the monomials, we get

a³-b³=(5-3p⁴)(5²+15p⁴+9p⁸)

Further, calculate the power, we get

a³-b³=(5-3p⁴)(25+15p⁴+9p⁸)

Finally, reorder the expressions, we get

a³-b³=(5-3p⁴)(9p⁸+15p⁴+25)

Hence, the factored form of a-b where a and b monomials and a = 125 and b = 27p¹² is (5-3p⁴)(9p⁸+15p⁴+25).

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Answer:a

Step-by-step explanation:

i just did it

Answer:

261.81818181

Step-by-step explanation:

400÷275=x

x×180

Answer:

If 275 gallon of oil tank costs $400 to fill.

Then 180 gallon of oil tank costs $261.8 to fill.

Step-by-step explanation:

Step 1 of 2

If 275  gallon of oil tank costs $400  to fill.

Then the cost to fill 180  gallon of oil tank can be found by forming a proportion.

Let the required cost be x.

[tex]$$\begin{aligned}\frac{\text { cost }}{\text { Gallons of Gas }} &=\frac{\text { cost }}{\text { Gallons of Gas }} \\\frac{\$ 400}{275} &=\frac{x}{180}\end{aligned}[/tex]

Multiplying both sides by 180 we get,

[tex]$$\begin{aligned}\frac{\$ 400}{275} \times 180 &=\frac{x}{180} \times 180 \\x &=\frac{\$ 400}{55} \times 36 \\x &=\$ 261.8\end{aligned}$$[/tex]

Step 2 of 2

To check if the answer is reasonable, we substitute it back in the formed proportion

[tex]$\frac{\$ 400}{275}=\frac{x}{180}$$[/tex]

We found x=$261.8 hence,

[tex]$\frac{\$ 400}{275}=\frac{\$ 261.8}{180}$$$\$ 1.45=\$ 1.45$$Here, $L H S=R H S$[/tex]

Hence, our answer is correct.

The translation function is T(x,y) = (x + 3, y - 2) and the reflection function is (-x, y)

The point is given as:

(x, y)

The translation is given as:

3 units to the right and 2 units down.

This is represented as:

(x + 3, y - 2)

Hence, the translation function is T(x,y) = (x + 3, y - 2)

The point is given as:

(x, y)

The reflection is given as:

Reflection across the y-axis

This is represented as:

(-x, y)

Hence, the  reflection function is (-x, y)

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The equation represented by the model is 3x²-4x+1=(3x-1)(x-1).

Given model represents a polynomial of the form ax²+bx and model is in figure.

Consider the given table.

The first row in the table represents first term of the polynomial.

In first row first three terms are variables and last term are constant.

Write all the terms of the first row in the form of sum.

+x+x+x-1=3x-1

The first column in the table represents second term of the polynomial.

In first column first term are variable and last term are constant.

Write all the terms of the first column in the form of sum.

+x-1=x-1

The product of first term of polynomial (3x-1) and second term of polynomial (x-1) is equal to the sum of all remaining terms in this table.

+x²+x²+x²-x-x-x-x+1=3x²-4x+1.

We can also check this by multiplying (3x-1) and (x-1) as

(3x-1)(x-1)=3x(x-1)-1(x-1)

(3x-1)(x-1)=3x(x)-3x(1)-1(x)+1(1)

(3x-1)(x-1)=3x²-3x-x+1

(3x-1)(x-1)=3x²-4x+1

Hence, the equation represented by the given model in the form of polynomial ax²+bx is (3x-1)(x-1)=3x²-4x+1.

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The fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]

To find the fourth root of ⁴√(81x³y⁴z⁸) with rational exponents, we use the root rule of indices which states that [tex]\sqrt[n]{a} = a^{\frac{1}{n} }[/tex]

So, ⁴√(81x³y⁴z⁸) = ⁴√(81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸)

We now apply the

So, ⁴√(81x³y⁴z⁸) = ⁴√81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸

[tex]= 3 X x^{\frac{3}{4} } X y^{\frac{4}{4} } X z^{\frac{8}{4} } \\= 3 X x^{\frac{3}{4} } X y^{1} X z^{2} \\= 3x^{\frac{3}{4} }yz^{2}[/tex]

So, the fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]

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See below for the calculations of the slopes of the graphs

The slope of a line is calculated using:

m= (y2 - y1)/(x2 - x1)

Using the above formula, we have:

Line 1: (-2, 0) and (3, 2)

Slope, m= (2 - 0)/(3 + 2)

m= 2/5

Hence, the slope is 2/5

Line 2: (2, -3) and (-2, 4)

Slope, m= (4 + 3)/(-2 - 2)

m= -7/4

Hence, the slope is -7/4

Line 3: (-4, -2) and (1, 3)

Slope, m= (3 + 2)/(1 + 4)

m= 1

Hence, the slope is 1

Line 4: (0, 0) and (-3, -4)

Slope, m= (-4 - 0)/(-3 - 0)

m= 4/3

Hence, the slope is 4/3

Line 5: (0, 0) and (-1, -4)

Slope, m= (-4 - 0)/(-1 - 0)

m= 4

Hence, the slope is 4

Line 6: (-2, 1) and (3, 2)

Slope, m= (2 - 1)/(3 + 2)

m= 1/5

Hence, the slope is 1/5

Line 7: (-2, -1) and (2, -4)

Slope, m= (-4 + 1)/(2 + 2)

m= -3/4

Hence, the slope is -3/4

Line 8: (-2, -3) and (-1, -4)

Slope, m= (-4 + 3)/(-1 + 2)

m= -1

Hence, the slope is -1

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Using proportions, it is found that the value of x is of x = 5, hence option A is correct.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Since the triangles are similar, the lengths are proportional. Researching the problem on the internet, we have that the proportions are given as follows:

Hence:

[tex]\frac{x}{25} = \frac{5}{25}[/tex]

Simplifying the denominators:

x = 5.

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Answer:

see explanation

Step-by-step explanation:

(a)

x² - 36 = 0 ← is a difference of squares and factors as

(x - 6)(x + 6) = 0

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 6 = 0 ⇒ x = 6

(b)

x² - 5x + 4 = 0

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

the factors are - 1 and - 4 , since

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

(x - 1)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

(c)

x² - 2x = 3 ( subtract 3 from both sides )

x² - 2x - 3 = 0 ← in standard form

consider the product of the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)

the factors are + 1 and - 3 , since

1 × - 3 = - 3 and 1 - 3 = - 2 , then

(x + 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

(d)

6x² - 11x - 10 = 0

consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 10 = - 60 and sum = - 11

the factors are + 4 and - 15

use these factors to split the x- term

6x² + 4x - 15x - 10 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 2) - 5(3x + 2) = 0 ← factor out (3x + 2) from each term

(3x + 2)(2x - 5) = 0

equate each factor to zero and solve for x

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]

The equation of the line in the graph given is: y = -3x - 1.

Find the slope of the line, which is: m = rise/run.

Rise of the line = 3 units

Run = 1

Slope (m) = -3/1 = -3

Y-intercept (b) = -1 (at this point, x equals zero)

Substitute m = -3 and b = -1 into y = mx + b

y = -3x + (-1)

y = -3x - 1

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What would be the effect of this change is: a). both area rate and flow rate would increase.

Assuming a driver shift into third gear in which there was reduction in the engine speed while on the other hand the tractor speed increase.

The effect of the change will result in the increase in area rate as well as the  flow rate.

Therefore the correct option  is A.

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Answer:

Step-by-step explanation:

2.5 miles = 12 fishes

Therefore,

8 miles = 12*8/2.5=96/2.5= 960/25=38.4 fishes

Answer:

HI: 17.9

GH: 22.1

Step-by-step explanation:

1) There are three trigonometric ratios for right-angled triangles.

Sin = opposite/hypotenuse

Cos = adjacent/hypotenuse

Tan = opposite/adjacent.

2) Opposite to the 90° lies the hypotenuse. Opposite to the given angle lies the opposite.

Beside the given angle lies the adjacent.

3) The value of G given to us is 54°. The length of GI is 13. We are asked to find the lengths of HI and GH. We cannot find GH (we can, but I prefer the current method) without the length of HI. Let's find HI.

Tan(54) = x/13

Tan(54) × 13 = x

x = 17.89

4) We can use the Pythagorean theorem to find the length of GH. His theorem is c² = a² + b².

c² = a² + b²

c² = 13² + 17.89²

c² = 489.0521

c = √489.0521

c = 22.11

5) Round off the answers to the nearest tenth.

HI = 17.9

GH = 22.1

The correct statement about the earthquake in the state is option c. State A had approximately 3,362 more earthquakes than State B.

we have x/y = 0.00299

y = 163696

To solve for x we have

163696 * 0.00299

= 4895 earthquakes

x = 0.1402 x 10931

= 1533

Next we have to find the difference

4895 - 1533 = 3362 earthquakes.

We have to conclude that state A has 3362 earthquakes more than B. Hence the answer is c.

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Complete question

The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density.

Which statement about the number of earthquakes the states had for the given time span is true?

State A had approximately 1,533 more earthquakes than State B.

State B had approximately 1,533 more earthquakes than State A.

State A had approximately 3,362 more earthquakes than State B.

State B had approximately 3,362 more earthquakes than State A.

Answer:

1?

Step-by-step explanation:

The minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.

The standard deviation is given as (σ) = 1.69.

The mean number of dresses given (μ) = 7.6.

Margin of error given (M.E.) = 0.14.

Confidence level given = 98%.

Z-Score corresponding to 98% confidence interval (Z) = 2.33.

We are asked to find the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval.

We assume the size of the sample to be n.

By the formula of Margin of Error:

M.E. = Z*(σ/√n).

Substituting the values, we get:

0.14 = 2.33*(1.69/√n),

or, √n = 2.33*1.69/0.14 = 28.126429,

or, n = 791.096 ≈ 791 (As sample size needs to be a whole number).

Thus, the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.

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Answer: 8.2 mm

Step-by-step explanation:

[tex]\sin 60^{\circ}=\frac{v}{9.5}\\\\v=9.5 \sin 60^{\circ} \approx \boxed{8.2 \text{ mm}}[/tex]

The domain of the function f(x) is: -6 < x ≤ 4, and the value that is in the domain of the function f(x) is 4

The function is given as:

f(x) = 2x + 5,   -6 < x ≤ 0

f(x) = 2x + 3,   0 < x ≤ 4

The above means that the domain of the function f(x) is:

-6 < x ≤ 0 and 0 < x ≤ 4

When combined, we have:

-6 < x ≤ 4

This means that x is greater than -6 but does not exceed 4

Hence, the value that is in the domain of the function f(x) is 4

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Answer:

4

Step-by-step explanation:

got it right on edge

A table can be represented with a linear function equation as y = mx + b, where m is the slope and b is the y-intercept.

Assuming we have a table of values as shown in the image attached below, to write an equation of linear function for the table, do the following:

Pick two pairs of values, say, (1, 5) and (2, 25) and find the slope (m):

Slope (m) = change in y / change in x = (25 - 5)/(2 - 1)

Slope (m) = 20

Find the y-intercept (b) by substituting (x, y) = (1, 5) and m = 20 into y = mx + b:

5 = 20(1) + b

5 = 20 + b

5 - 20 = b

-15 = b

b = -15

Write the equation of the linear function by substituting m = 20 and b = -15 into y = mx + b:

y = 20x - 15

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Answer:

x = 6 cm

Step-by-step explanation:

• in the parallelogram, if we consider the side of length 12

  as the base then the corresponding height is 5.

In this case the area of our parallelogram = 5 × 12 = 60 cm²

………………………………………………

• in the parallelogram, if we consider the side of length 10

  as the base then the corresponding height is x.

In this case the area of our parallelogram = 10 × x = 10x cm²

………………………………………………

In order to determine x ,we equate the two different results

that we got for the same area .

In other words ,we have to solve the equation 10x = 60.

10x = 60

⇔ x = 60/10 = 6

Answer:

Step-by-step explanation:

the 2 triangles are similar, we can solve with an equation

12 : 10 = x : 5

x = 12 * 5 : 10

x = 60 : 10

x = 6 cm

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: ED = 5 \:\: units[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \:FE + ED = FD[/tex]

[tex]\qquad \tt \rightarrow \:5 + x = 10[/tex]

[tex]\qquad \tt \rightarrow \:x = 10 - 5[/tex]

[tex]\qquad \tt \rightarrow \:x = 5[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The value of ED is 5 units, which is determined by using the concept of midpoint.

The figure given below shows a line segment FD, where the length of line segment FD refers to the distance between its endpoints, F and D.

Given that E is the midpoint of FD.

FE = 5 units

FD = 10 units

Since M is the midpoint of FD, So FE = ED

⇒ FD = FE + ED

Substitute the values of FE = 5 and  FD = 10, in the above equation,

⇒10 = 5 +ED

⇒ ED = 10 - 5

⇒ ED = 5

Therefore, the value of ED is 5 units.

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The geometry illustrates that the value of DB is 34°

AB = 87°

ED = 37°

BCD will be:

= (360° - 87° - 32°)/2

= 118°

FA will be:

= 118°/2

= 59°

DC = 118/2 = 59°

HB = GA = 17°

DB = 2 × 17° = 34°

EG = GA = 17°

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Answer: 70%

Step-by-step explanation:

A basket contains:

5 yellow balls

3 blue balls

2 white balls

What would be the probability of randomly picking a ball and the ball not being blue?

So, we can find the probability of picking up a blue ball. Let's do that first.

To calculate the probability of getting a blue ball, we need to divide the number of blue balls by the number of possible balls.

The number of blue balls = 3

The total number of balls = 2 + 3 + 5 = 10 balls

3 blue balls divided by 10 balls = 0.3.

If you multiply 0.3 by 100%, it will give you a probability of finding a blue ball equal to 30%

Now, we just need to find the probability of NOT finding a blue ball. Because we have 30% of finding a blue ball, we just need to subtract 30% from 100%.

100 - 30$ = 70%

The probability of not getting a blue ball is equal to 70%.

Hope I Helped!

[tex]|\Omega|=5+3+2=10\\|A|=5+2=7\\\\P(A)=\dfrac{7}{10}=70\%[/tex]

If the function is vertically compressed, the resulting function will be g(x) = 3/4x^2

Quadratic functions are functions that has a leading degree of 2. Given the parent function f(x) = ax^2

where

2 is the exponent/degree

If the function is vertically compressed, the value of a must be less than 1, hence the possible expression when vertically compressed is g(x) = 3/4x^2

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Answer:

Hence, 0.026 can be expressed as [tex]$2.6 \times 10^{-2}$[/tex].

Step-by-step explanation:

- Given 0.026

- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .

- Then count n and write in scientific notation.

Step 1 of 1

Consider 0.026

[tex]$$\Rightarrow 2.6$$[/tex]

Decimal has moved 2 places to right.

The power will be negative as original no. is less than 1 .

[tex]$$\begin{aligned}&2.6 \times 10^{-2} \\&0.026=2.6 \times 10^{-2} .\end{aligned}$$[/tex]

Answer:

4!

Step-by-step explanation:

using the slope formula and the points (-1, 0) and (-2, -4) on the line:

-4 - 0 / -2 - -1 = -4 - 0 / -2 + 1 = -4 / -1, and since both the top and bottom are negative, they make a positive, giving you a positive 4

the slope formula is rise/run, or y2 - y1 / x2 - x1!

The features of the function g(x) = 4log(x) + 4 are

The function is given as;

g(x) = 4log(x) + 4

The intercept

A logarithmic function has no y-intercept.

Set g(x) to 0, to determine the x-intercept

4log(x) + 4 = 0

Divide through by 4

log(x) + 1 = 0

This gives

log(x) = -1

Take the inverse of both sides

x = 10^-1

Evaluate

x = 0.1

The x-intercept is (0.1, 0)

The vertical asymptote

Recall that:

A logarithmic function has no y-intercept.

This is so because it is undefined at x = 0

So, the vertical asymptote is x = 0

The domain and the range

A logarithmic function cannot take a negative input or 0 input

So, the domain is x > 0

However, the range is all set of real numbers i.e (-∞, ∞)

Hence, the features of g(x) are (b), (d) and (e)

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The image of G when A IMG is rotated 180 around the origin is (-2,-4).

To rotate a figure 180 degrees around the origin, we reverse the signs of both the x-coordinate and the y-coordinate. In the image, the point G has coordinates (2,4). Reversing the signs of these coordinates gives us (-2,-4).

Rotate the figure 180 degrees around the origin. This means that we imagine the figure being flipped over the origin.

Reverse the signs of both the x-coordinate and the y-coordinate of the point G. This is because when we rotate a figure 180 degrees around the origin, the signs of both the x-coordinate and the y-coordinate are reversed.

The new coordinates of G are the coordinates of the point that is the result of rotating the figure 180 degrees around the origin and reversing the signs of the coordinates of point G. In this case, the new coordinates of G are (-2,-4).

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