Solve the system of equations using substitution. 6x=−6y−30−3x−3y=15

The fill up of the missing points are:

Using the image attached, one can see that m<1 and m<2 creates a kind of  linear pair hence one can say they are both supplementary using the law of LINEAR POSTULATE THEOREM.

Based on the fact that the supplementary angles add up to 180 degrees, therefore:

m<1 + m<2 = 180   - will be equation 1

Since the interior angles m<2 and m<3 are known to be equal based on the CONGRUENCE POSTULATE THEOREM. Therefore

m<2 = m<3 ---  will be equation 2

Then place eqn. 2 into eqn. 2

m <1 + m <3 = 180

This connote that m<1 and m<3 are supplementary.

Hence, The fill up of the missing points are:

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Answer:

v =L× b×h

=5× 4×3

=60 cubic centimeter

Answer:

[tex]\sqrt{60}[/tex]

Step-by-step explanation:

Use the Pythagorean theorem a^2 + b^2 = c^2

In this case you are given a and c, so set the equation up like

2^2 + b^2 = 8^2

b^2 = 8^2 - 2^2

b =[tex]\sqrt{8^{2} -2^{2} }[/tex]

b =[tex]\sqrt{60}[/tex]

30 pounds of coffee A and 60 pounds of coffee B used.

According to statement

Type A coffee costs Charmaine $4.25 per pound

Type B coffee costs $5.40 per pound.

Total cost of month on coffee is $451.50

AND

B=2A -(1)

Let's form the equation

4.25A + 5.40B = 451.50

Put equation 1 in it then

4.25A + 5.40*2A = 451.50

15.05A = 451.50

A = 30 pounds then

B = 60 pounds.

So, 30 pounds of coffee A and 60 pounds of coffee B used.

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Answer: A

Step-by-step explanation:

Let c(y)=x.

[tex]\implies x=y^3 -5\\\\x+5=y^3\\\\y=\sqrt[3]{x+5}\\\\c^{-1}(x)=\sqrt[3]{x+5}[/tex]

Answers:

i) [tex]\sf (x + 2)(x+ 3)[/tex]

ii) [tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]

Factorize expression's:

i.

[tex]\sf (x + 1)^2 + 3(x + 1) + 2[/tex]

apply perfect square and distributive method

[tex]\sf (x^2 + 2(x)(1) + 1^2) + 3x + 3 + 2[/tex]

expand

[tex]\sf x^2 + 2x + 1 + 3x + 3 + 2[/tex]

collect like terms

[tex]\sf x^2 + 2x + 3x + 3 + 2 + 1[/tex]

add/subtract like terms

[tex]\sf x^2 + 5x + 6[/tex]

breakdown

[tex]\sf x^2 + 3x + 2x+ 6[/tex]

factor common term

[tex]\sf x(x + 3) + 2(x+ 3)[/tex]

collect into groups

[tex]\sf (x + 2)(x+ 3)[/tex]

ii.

[tex]\sf (9x^2 + 9x - 4)(9x^2 + 9x - 10) - 72[/tex]

breakdown

[tex]\sf (9x^2 + 12x - 3x - 4)(9x^2 + 15x - 6x - 10) - 72[/tex]

factor common term

[tex]\sf (3x(3x + 4) -1( 3x + 4)) ( (3x(3x + 5)- 2(3x +5) )- 72[/tex]

collect like terms

[tex]\sf (3x -1)( 3x + 4) (3x- 2)(3x +5) - 72[/tex]

expand

[tex]\sf 81x^4+162x^3-45x^2-126x-32[/tex]

factor

[tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]

Answer:

[tex]\textsf{1.} \quad (x+3)(x+2)[/tex]

[tex]\textsf{2.} \quad (3x+1)(3x+2)(9x^2+9x-16)[/tex]

Step-by-step explanation:

Question 1

[tex]\textsf{Given expression}: \quad(x+1)^2+3(x+1)+2[/tex]

[tex]\textsf{Let }u=(x+1) \implies u^2+3u+2[/tex]

[tex]\textsf{To factor }\:\:u^2+3u+2:[/tex]

Rewrite the middle term as u + 2u:

[tex]\implies u^2+u+2u+2[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies u(u+1)+2(u+1)[/tex]

Factor out the common term (u+1):

[tex]\implies (u+2)(u+1)[/tex]

Replace [tex]u[/tex] with [tex](x+1)[/tex] :

[tex]\implies (x+1+2)(x+1+1)[/tex]

Simplify:

[tex]\implies (x+3)(x+2)[/tex]

Question 2

[tex]\textsf{Given expression}: \quad (9x^2+9x-4)(9x^2+9x-10)-72[/tex]

Expand:

[tex]\implies 9x^2(9x^2+9x-10)+9x(9x^2+9x-10)-4(9x^2+9x-10)-72[/tex]

[tex]\implies 81x^4+81x^3-90x^2+81x^3+81x^2-90x-36x^2-36x+40-72[/tex]

Collect like terms:

[tex]\implies 81x^4+81x^3+81x^3-90x^2+81x^2-36x^2-90x-36x+40-72[/tex]

Combine like terms:

[tex]\implies 81x^4+162x^3-45x^2-126x-32[/tex]

Use the Factor Theorem:

If f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x).

[tex]\begin{aligned}\implies f \left(-\dfrac{1}{3}\right) & =81\left(-\dfrac{1}{3}\right)^4+162\left(-\dfrac{1}{3}\right)^3-45\left(-\dfrac{1}{3}\right)^2-126\left(-\dfrac{1}{3}\right)-32\\ & = 1-6-5+42-32\\ & = 0\end{alilgned}[/tex]

Therefore (3x + 1) is a factor.

[tex]\begin{aligned}\implies f \left(-\dfrac{2}{3}\right) & =81\left(-\dfrac{2}{3}\right)^4+162\left(-\dfrac{2}{3}\right)^3-45\left(-\dfrac{2}{3}\right)^2-126\left(-\dfrac{2}{3}\right)-32\\ & = 16-48-20+84-32\\ & = 0\end{alilgned}[/tex]

Therefore (3x + 2) is a factor.

Therefore:

[tex]\implies f(x)=(3x+1)(3x+2)(ax^2+bx+c)[/tex]

Compare the coefficient of x⁴ and the constant to find a and c:

[tex]\implies 3 \cdot 3 \cdot a=81 \implies a=9[/tex]

[tex]\implies 2c=-32 \implies c=-16[/tex]

Therefore:

[tex]\implies f(x)=(3x+1)(3x+2)(9x^2+bx-16)[/tex]

Expand:

[tex]\implies f(x)=81x^4+(81+9b)x^3-(126-9b)x^2-(144-2b)x-32[/tex]

Compare the coefficient of x³ to find b:

[tex]\implies 81+9b=162 \implies b=9[/tex]

Therefore, the fully factorized expression is:

[tex]\implies (3x+1)(3x+2)(9x^2+9x-16)[/tex]

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The equation which expresses the number of bacteria, P, present at any time, t is P(t) = 4(2)^t

Check all options

When t = 1

P(t) = 8(4)^t

= 8(4)¹

= 8(4)

P(t) = 32

Not true

P(t) = 4(2)^t

= 4(2)¹

= 4(2)

= 8

True

P(t) = (2)^t

= (2)¹

= 2

Not true

P(t) = 8(2)^t

= 8(2)¹

= 8(2)

= 16

Not true

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Answer:

49

Step-by-step explanation:

[tex]3^{2} *5+4[/tex]

= [tex]9*5+4[/tex]        Simplify the exponents.

= [tex]45+4[/tex]           Multiplication.

= 49                Addition.

Answer:

49

Step-by-step explanation:

1. Whenever there is an exponent, we solve that first. 3^2 is 9.

2. In an equation, multiplication, and division is first, and since there is no division in the equation, we do the multiplication first. 9 x 5 is 45.

3. We finish by adding 4 to 45, which is 49.

The justification used is multiplicative property of equality because both sides are multiplied by the same value

Given the expression below

-1/3(4x^2 - 3) - 3 = 5x^2 - 2

We are to determine the justification by Anne to get the step 2 as shown

(4x^2 - 3) - 3 = -3(5x^2 - 2)

Expand

(4x^2 - 3) - 3 = -15x^2 + 6

Hence the justification used is multiplicative property of equality because both sides are multiplied by the same value

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Hi

arithmetic serie mean that to change from a rank to an other, you add "r"

So :  if 6 is  S1, and  2 is  pace,    

then you need 8 hops to go from S1 to S9.

so you 'r going to add the reason 8 times.

so :  S9 = 6 + 8 * 2   =   6 + 16 = 22

conclusion :  S9 = 22

The length of the measure of YZ is 80cm

Perpendicular lines are lines that are at angle 90 degrees to each other. From the given diagram;

WX = 82cm

Required

Length. of YZ

Using the pythagoras theorem

YV = VZ = √41²-9²

YV = VZ = √1600

YV = VZ = 40

Since YZ = YV + VZ

YZ = 40cm + 40cm

YZ= 80cm

Hence the length of the measure of YZ is 80cm

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The best description on measurement of the center of this data is; C. The Rome data center is best described by the mean. The New York data center is best described by the median.

If we make the box and whisker plot of the Rome and New York data, we will see that there will clearly be an outlier in the New York data.

Thus;

Due to the fact that the data set for New York has an outlier and the mean is skewed, it means that we would use the median.

Finally, we see that the Rome data set is symmetrical because it has no outlier,  and as such we can use the mean.

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Answer:

Greetings !

check the attachment above☝️ but i haven't done the second question wait a moment. thx

Due to length restrictions, we cannot summarize the results of the three parts about the quadratic equations of the form x² + b · x + c = 0. We kindly invite to check the explanation for further details.

In this question we have several exercises with quadratic equations of the form x² + b · x + c = 0 and, to be more exactly, quadratic equations with the following characteristics:

x² - (r₁ + r₂) · x + r₁ · r₂ = 0      (1)

Please notice that the first grade coefficient is equal to the inverse of the sum of the two roots and the zero grade coefficient is the product of the two coefficients.

Now we proceed to resolve all the points:

Part I

a) (x + 17) · (x + 1) = x² + 18 · x + 18, r₁ = - 17, r₂ = - 1

b) (x + 5) · (x + 4) = x² + 9 · x + 20, r₁ = - 5, r₂ = - 4

c) (x - 11) · (x - 1) = x² - 12 · x + 11, r₁ = 11, r₂ = 1

d) (x - 18) · (x - 2) = x² - 20 · x + 36, r₁ = 18, r₂ = 2

Part II

a) x² - 12 · x + 27

b) (x + 4) · (x + 8)

c) (x - 5) · (x - 7)

d) (x - 4) · (x - 5)

Part III

a) (x - 18) · (x + 3) = x² - 15 · x - 54

b) (x + 18) · (x + 3) = x² + 21 · x + 54

c) (x + 18) · (x - 3) = x² + 15 · x - 54

d) (x - 18) · (x - 3) = x² - 21 · x + 54

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The function that models the independent variable, x, in terms of y, is:

[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]

Here we have the relation:

[tex]y = 2.56*(1.04)^x[/tex]

We want to write x in terms of y, so we just need to isolate x.

We have:

[tex]\frac{y}{2.56} = (1.04)^x[/tex]

Now we can apply the natural logarithm in both sides, so we get:

[tex]ln(\frac{y}{2.56}) = ln((1.04)^x)\\\\ln(\frac{y}{2.56}) = ln((1.04))*x[/tex]

Now we can just isolate x.

[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]

That is the function that models the independent variable, x, in terms of y.

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Step-by-step explanation:

[tex]algenbraic[/tex]

Answer:

x = 157/60

Step-by-step explanation:

x + 2/3 - x + 1/5 = x - 3/4 - 1

x - x - x = -2/3 - 1/5 - 3/4 - 1

-60x/60 = -40/60 - 12/60 - 45/60 - 60/0

-60x = -40 - 12 - 45 - 60

-60x = -157

x = -157/-60

x = 157/60

157/60 + 2/3 - 157/60 + 1/5 = 157/60 - 3/4 - 1

2/3 + 1/5 = 157/60 - 3/4 - 1

40/60 + 12/60 = 157-60 - 45/60 - 60/60

40 + 12 = 157 - 45 - 60

52 = 157 - 105

The way to use the distance formula to classify quadrilateral include:

The steps to calculate the perimeter and area of a polygon:

Step 1: Plot the given points on the graph.

Step 2: Connect the points and identify the figure.

Step 3: Determine lengths by counting the grid lines.

Step 4: Use a formula to calculate the perimeter and area if one exists.

Step 5: If there are no formulas for a figure, the perimeter can be calculated by summing the lengths of the sides. We might estimate the area without an area formula by counting the number of small squares enclosed.

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The value of f(-2) is 0

The graph of the function is added as an attachment

The graph is given as:

y = f(x)

When x =-2. we have

y = f(-2)

From the graph, we have:

x = -2 and y = 0

So, we have

f(-2) = 0

Hence, the value of f(-2) is 0

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3 is the square root of nine.

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } ​square root of, end square root . Finding the square root of a number is the opposite of squaring a number.

To find the fraction square root, first, find the square root of the numerator and then find the square root of denominator. After finding the square root values, simplify the fraction. For example, √(4/16), can be written as √4/√16.

(3)^2 = 9

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Answer:

D

Step-by-step explanation:

The red line starts with a filled in circle that mean that the number -12 is included.  The graph is saying that x can be -12 or any number above -12.  The line under the > is telling you that 12 is included.

Answer:

first option x = 7

Step-by-step explanation:

"x" is the cathetus opposite the angle of 30°

14 is the hypotenuse

use the sine function

[tex]sin30^{0} =\frac{x}{14}[/tex]

[tex]x=14sen30^{0} =14(0.5)=7[/tex]

Hope this helps

Answer: Circle lines

Step-by-step explanation:

Hopefully the attached image helps, it is a diagram of all the labeled lines on a circle excluding the radius (BG or GE)

Loc and Reza together will finish the entire mowing process on the lawn at 1:14 p.m.

Loc mow the total area in 20 mins.

So, his pace is 1 lawn / 20 minutes or 1/20th of a lawn each minute.

Reza's pace is 1 lawn / 30 minutes, or 1/30th of a lawn each minute because he can mow the grass in that amount of time.

Reza joins Loc after he has been mowing for 5 minutes. He can mow 1/20th of the grass in these 5 minutes, which is 5/20th of the lawn =1/4th lawn

There is currently just

1-1/4=3/4 of the lawn left to complete.

We may construct the following equation by assuming that they mow together for x mins:

1/20x + 1/30x = 3/4 [amount done by Loc + Reza = total amount]

⇒(3x+2x)/60x = 3/4

⇒5x/60 = 3/4

⇒x/12= 3/4

⇒4x=36

⇒x= 9 mins

So, when they collaborate, they can complete the lawn in 9 minutes.

Hence, Loc mows alone for 9+5 mins = 14 mins

Therefore, it is concluded that starting at 1 p.m they finish the mowing at 1:14 p.m.

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The CPT code that is used here is CPT code 11755.

This is the code that is used as the biopsy of the nail bed. The CPT code is used to report this procedure.

Then it would be determined if it is a case of melanoma or lesion that is causing the issues with the individuals nails.

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he correct code for biopsy of the nail bed or nail plate.

Answer:

Step-by-step explanation:

1a+1b(a+b-c)+1b+1c(b=c-a)+ 1a+1c(c+a-b)

1a+1b-c+1b +1c-a+1a+1c-b

1a+2b-c+a+1c-b

2a+1b+c this is the answer I think lol

Let the missing number x

So, ATQ

[tex] \frac{3}{14} \times x = 6[/tex]

[tex] \frac{14}{3} \times \frac{3}{14} x = 6 \times \frac{14}{3} [/tex]

[tex] \frac{1}{3} \times 3x = \frac{14}{3} \times 6[/tex]

[tex]x = \frac{14}{3} \times 6[/tex]

[tex]x = 14 \times 2[/tex]

[tex]x = 28[/tex]

Therefore, 3/14 of 28 is 6...

Answer:

28

Step-by-step explanation:

Let the number we are looking for = [tex]x[/tex]

∴ [tex]\frac{3}{14}[/tex] of [tex]x[/tex] is 6

⇒  [tex]\frac{3}{14}[/tex]   ×  [tex]x = 6[/tex]

• Divide both sides of equation by  [tex]\frac{3}{14}[/tex] :

⇒  [tex]x = 6 \div \frac{3}{14}[/tex]

⇒ [tex]x = 28[/tex]

∴ The missing part is 28.

The true statements are :

the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.

The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.

A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers. The whiskers represents the minimum and maximum scores.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median.  The third line on the box represents the upper (third) quartile.

Range for New Orleans = 85 - 50 = 35

Range for Indianapolis = 75 - 25 = 50

Median for New Orleans = 70

Upper quartile for  Indianapolis = 70

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Answer:

1 +10=11 (since 0 is neither negative or positive the first and second positive integerswith 1 or 0