Which construction is illustrated above ?

Multiply by the inverse of 3/4 which is 4/3. -6 times 4/3 (or 1 1/3) which is -8 because 1/3 of -6 is -2 and -2 plus -6 is -8.

x=-8

Answer:

Multiply by 4/3

Step-by-step explanation:

To solve for x, we need to isolate x.

We can isolate x in one step by multiplying by the reciprocal of 3/4, which is 4/3

3/4x = -6

Multiplying by 4/3

4/3* 3/4 x = -6 * 4/3

x = -8

The point-slope form of line:

[tex]y-y_1=m(x-x_1)[/tex]

The fomula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the coordinates of the points:

[tex]m=\dfrac{-4-2}{1-(-2)}=\dfrac{-6}{1+2}=\dfrac{-6}{3}=-2[/tex]

[tex]y-(-4)=-2(x-1)[/tex]       use distributive property

[tex]y+4=-2x+2[/tex]      subtract 4 from both sides

[tex]\boxed{y=-2x-2}[/tex]

Answer:

y = -2x-2

Step-by-step explanation:

The line passes through the points (-2, 2) and (1, -4).

The slope of the line is given by

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-4-2}{1+2}\\\\m=\frac{-6}{3}\\\\m=-2[/tex]

The slope intercept form of a line is given by

y = mx +b, where m is the slope and b is the y-intercept.

We have, m = -2. Hence, the equation is

y = -2x + b

Now, use the point (-2,2) to find b

2 = -2(-2) + b

2 = 4 +b

b = -2

Hence, the equation of the line is y = -2x-2

Third option is correct.

Answer:

8

Step-by-step explanation:

Substitute the equation and values into the average rate of change formula.

Answer:

x^3 +2x^2 -4x -8

Step-by-step explanation:

The factors of x^2 +4x +4 are (x +2)^2.

The factors of 4 -x^2 are -1(x -2)(x +2).

The least common denominator is the least common multiple of these, excluding the -1 multiplier. That multiple is ...

... (x +2)^2 × (x -2) = x^3 +2x^2 -4x -8

_____

Comment on the minus sign

When the given fractions are expressed using the denominator above, the second one will need to have its numerator sign adjusted. The two fractions are ...

The LCD or Least Common Denominator for the fractions 7/(x^2 + 4x + 4) and 5/(4 - x^2) is the product of the distinct denominators after factoring, which is (x+2)^2(4 - x^2), given they have no common factors.

The acronym LCD refers to the Least Common Denominator, which in mathematics, is the least common multiple of the denominators of a set of fractions. It is used to find a common denominator so that the fractions can be combined or compared. For the fractions 7/x^2 + 4x + 4 and 5/4 - x^2, the LCD would be the product of the distinct denominators assuming they cannot be factored into common factors. In this case, assuming x^2 + 4x + 4 cannot be further factored (it is a perfect square: (x+2)^2), the denominators are x^2 + 4x + 4 and 4 - x^2 (since we consider x^2 to have a negative coefficient here). Consequently, if there are no common factors, the LCD is (x^2 + 4x + 4)(4 - x^2) or (x+2)^2(4 - x^2).

Answer:

Add your entire question here to receive help from users and Brainly teachers. Pictures are great when things are difficult to type.

Step-by-step explanation:

Type your complete question or upload a picture to receive help on those tough questions. Your question is difficult to read or decipher. Try adding a picture next time to make it clearer to understand.

Answer:

221.0001

Step-by-step explanation:

Attempt to look at the number of 0s behind the decimal point, which you add those 0s and the digit number (1) into place

221

  0.0001

221.0001

Answer:

Boys : girls

5:6

Step-by-step explanation:

Boys : girls

20:24

We can divide each  of these numbers by 4

20/4 =5

24/4 =6

Boys : girls

5:6

Answer:

For every 5 boys there are 6 girls

Step-by-step explanation:

because 20 and 24 both go into the same number and thats four.

20 divided by 4 = 5

24 divided by 4= 6

so for every 5 boys there are 6 girls

Answer:

5f

Step-by-step explanation:

-5+x=0

Add 5 to both sides of the equation.

x=5

Answer:

We need to add 5F to make the sum 0

Step-by-step explanation:

-5 +  temperature = 0

Add 5 to each side

-5 + 5 +  temperature=0 + 5

temperature = 5

We need to add 5F to make the sum 0

Answer:

A. 8x - 9y = -23

Step-by-step explanation:

(-4,-1) and (1/2,3)

We write the equation in slope intercept form y=mx+b

then we convert it into standard form

m is the slope and b is the y intercept

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

(-4,-1) and (1/2,3)

[tex]slope = \frac{3-(-1)}{\frac{1}{2}-(-4)}[/tex]

[tex]slope = \frac{4}{\frac{1}{2}+4}[/tex]

[tex]slope = \frac{4}{\frac{9}{2}}[/tex]

[tex]slope = 4*\frac{2}{9}[/tex]

[tex]slope m =\frac{8}{9}[/tex]

To find out b we plug in (-4,-1)  and slope m value in y = mx+b

-1 = (8/9) (-4) + b

[tex]-1 = -\frac{32}{9} +b[/tex]

Add 32/9 on both sides

[tex]-1+\frac{32}{9} = b[/tex]

Take common denominator 9

[tex]\frac{-9+32}{9} = b[/tex]

[tex]\frac{23}{9} = b[/tex]

So equation y = mx + b becomes

[tex]y= \frac{8x}{9} + \frac{23}{9}[/tex]

Standard form is Ax + By = C

To get standard form , multiply the whole equation by 9

9y = 8x + 23

Subtract 8x on both sides

-8x + 9y = 23

Multiply the whole equation by -1

8x - 9y = -23

Answer:

9. x=10

10. x=8

11. x=9/4=2.25

12. x=28

13. x=14

14. x=35

15. x=66

16. x=77/6

Step-by-step explanation:

9. x/20=18/36

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 18:

x/20=(18/18) / (36/18)

x/20=1/2

Solving for x: Multiplying both sides of the equation by 20:

20(x/20)=20(1/2)

x=10

10. x/12=6/9

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 3:

x/12=(6/3) / (9/3)

x/12=2/3

Solving for x: Multiplying both sides of the equation by 12:

12(x/12)=12(2/3)

x=4(2)

x=8

11. x/3=3/4

Solving for x: Multiplying both sides of the equation by 3:

3(x/3)=3(3/4)

x=9/4=2.25

12. x/42=30/45

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 15:

x/42=(30/15) / (45/15)

x/42=2/3

Solving for x: Multiplying both sides of the equation by 42:

42(x/42)=42(2/3)

x=14(2)

x=28

13. x/12=14/12

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 2:

x/12=(14/2) / (12/2)

x/12=7/6

Solving for x: Multiplying both sides of the equation by 12:

12(x/12)=12(7/6)

x=2(7)

x=14

14. x/25=28/20

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 4:

x/25=(28/4) / (20/4)

x/25=7/5

Solving for x: Multiplying both sides of the equation by 25:

25(x/25)=25(7/5)

x=5(7)

x=35

15. x/110=(160-100)/100

x/110=60/100

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 20:

x/110=(60/20) / (100/20)

x/110=3/5

Solving for x: Multiplying both sides of the equation by 110:

110(x/110)=110(3/5)

x=22(3)

x=66

16. x/11=(x+7)/17

Solving for x: Cross Multiplication:

17x=11(x+7)

Eliminating the parentheses on the right side of the equation:

17x=11(x)+11(7)

Multiplying:

17x=11x+77

Grouping the x's on the left side of the equation: Subtracting 11x both sides of the equation:

17x-11x=11x+77-11x

Subtracting:

6x=77

Dividing both sides of the equation by 6:

6x/6=77/6

Dividing:

x=77/6

Look at the picture.

Use the Pythagorean theorem to solve h:

[tex]h^2+5^2=7^2[/tex]

[tex]h^2+25=49[/tex]            subtract 25 from both sides

[tex]h^2=24\to h=\sqrt{24}[/tex]

ΔADC and ΔCDB are similar. Therefore the sides are in proportion:

[tex]\dfrac{h}{5}=\dfrac{x}{h}[/tex]       cross multiply

[tex]5x=h^2[/tex]      put the value of h

[tex]5x=(\sqrt{24})^2[/tex]

[tex]5x=24[/tex]       divide both sides by 5

[tex]x=4.8[/tex]

y = 5 + x → y = 5 + 4.8 = 9.8

Or other method. ΔADC and ΔACB are similar. Therefore the sides are in proportion:

[tex]\dfrac{y}{7}=\dfrac{7}{5}[/tex]        multiply both sides by 7

[tex]y=\dfrac{49}{5}\\\\\boxed{y=9.8}[/tex]

Answer:

0.0064 is your answer

Step-by-step explanation:

because 4÷25 = 0.16 and 4÷100=0.04 and of course 4÷4=1

When the 0.16 and 0.04 that gets 0.0064

The pair of points on the inverse function g, given that (-3,4) and (5,-2) are on function f, are (4,-3) and (-2,5), obtained by swapping the x and y coordinates of the original points.

To determine which pair of points are on function g, which is the inverse of function f, we swap the x and y coordinates of the given points on function f. The points (-3,4) and (5,-2) are on function f, so the corresponding points on the inverse function g would be (4,-3) and (-2,5), respectively. In the context of functions and their inverses, the dependence of y on x in one function becomes the dependence of x on y in the inverse function. This flipping of coordinates is an essential property of inverse functions and can be visualized by reflecting across the line y = x on a graph.

Answer:

31

Step-by-step explanation:

(24/3)+(7x2)-(15/5)+(6*2)

8+(7x2)-(15/5)+(6*2)

8+14-(15/5)+(6*2)

8+14-3+(6*2)

8+14-3+12

22-3+12

19+12

31

Sorry if I did my math wrong :)

Answer:

y = 3x - 18

Step-by-step explanation:

The given line, y = -3x + 9, has slope -3.  Any new line perpendicular to this has slope +3/1, or just 3.

Start with the general slope-intercept form of the equation of a straight line:

y = mx + b.  Now substitute 9 for y, 9 for x and 3 for m:

9 = 3(9) + b.  Then b = -18, and the desired equation is y = 3x - 18.

The equation of the line perpendicular to y = -3x + 9 that passes through the point (9,9) is y = ([tex]\frac{1}{3}[/tex])x + 6.

The question is asking to find the equation of a line in slope-intercept form that is perpendicular to the given line y = -3x + 9 and passes through the point (9,9). To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the new line. The slope of any line perpendicular to a line with a slope of m is [tex]-\frac{1}{m}[/tex]. Since the given line has a slope of -3, the slope of the perpendicular line will be [tex]\frac{1}{3}[/tex]. Now using the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope, we can write the equation of the new line through the point (9,9) as y - 9 = ([tex]\frac{1}{3}[/tex])(x - 9). Simplifying this equation gives us y = ([tex]\frac{1}{3}[/tex])x + 6, which is in slope-intercept form y = mx + b where m is the slope and b is the y-intercept of the line.

Answer:

YES

Step-by-step explanation:

First, let's find the total number of seats int he airplane.

14 + 64 + 4 * 108 = 510

The airplane has a total or 510 seats.

Half of the number of seats is 510/2 = 255.

Now let's calculate the number of seats being used and compare with 255.

5/7 * 14 + 5/16 * 64 + 5/9 * 4 * 108 =

= 2 * 5 + 4 * 5 + 12 * 4 * 5

= 10 + 20 + 240

= 270

270 seats are being used.

270 is greater than 255, so more than half of the seats are being used.

Answer: YES

Answer:

Step-by-step explanation:

Y=cos(x+r/2)

Answer:

[tex]y=cos(x+\pi )[/tex]

Step-by-step explanation:

From the graph, we can see that y = -1 when x  = 0.

So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.

1. y = cos(x + pi/2) = cos(0 + pi/2) = 0

2. y = cos(x+2pi) = cos(0+2pi) = 1

3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5

4. y = cos(x+pi) = cos(0+pi) = -1

Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.

Answer:

y = 4.5 x

Step-by-step explanation:

If this is a proportional relationship, we can find the slope

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

m = (27-0)/(6-0)

m = 27/6

m=9/2

The slope is 9/2

The y intercept, where it crosses the y axis is 0

Using the slope intercept form of the equation y=mx+b

y = 9/2 x+0

y =9/2x

It wants the decimal form

y = 4.5 x

multiply. your answer is 11894.217.

this could be a cross multiply problem, so [tex]\frac{25.7}{x} =\frac{1}{462.81} =11894.217[/tex]

Answer:

Her average was 86%

Answer:

86%

Step-by-step explanation:

Final answer:

A formula to determine Seth's weekly lunch expense is Weekly Spending = n × 5, where n represents the new price of lunch and the multiplication by 5 accounts for each day of the school week.

Explanation:

To help Seth determine how much he'll now spend on lunch every week, we need to create a formula that takes into account the new price of a lunch and the frequency of his purchases. Let's assume the new price of a lunch is represented by the variable n. Since Seth buys lunch 5 days a week, the formula to calculate his weekly spending will be Weekly Spending = n × 5. This formula can be used to multiply the new price of a lunch (n) by 5, giving Seth the total amount he will spend each week on school lunches.

Answer:

2/3

Step-by-step explanation:

You flip the second fraction and multiply the fractions.

When we divide (1/2) by (3/4) we have 2/3.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The fraction (1/2) is divided by another fraction (3/4).

Now, we know (a/b)/(c/d) = (a/b)×(d/c).

Therefore, (1/2) is divided by (3/4) is,

= (1/2)×(4/3).

= 4/6.

= 2/3.

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Look at the picture.

∠2 and ∠3 are Corresponding Angles. j || k, thereofre m∠2 = m∠3.

∠1 and ∠3 are supplementary angles, therefore m∠1 + m∠3 = 108°.

m∠1 = 10x + 4, m∠2 = m∠3 = 4x - 6. Therefore we have the equation:

(10x + 4) + (4x - 6) = 180

(10x + 4x) + (4 - 6) = 180

14x - 2 = 180     add 2 to both sides

14x = 182     divide both sides by 14

x = 13

10x + 4 = 10(13) + 4 = 130 + 4 = 134

4x - 6 = 4(13) - 6 = 52 - 6 = 46

Answer: x=2 or x=-12

Step-by-step explanation: Subtract 12 to both sides of the equation: x² + 10x = 24. Subtract 24 to both sides of the equation: x² + 10x -24. Next, find out which two numbers multiply to -24 and add up to 10: 12 and -2.

X² + 12x + -2x -24.

X(x - 2) and 12(x - 2)

Solve for x: (x+12) and (x-2) = 0

X = -12 or x=2

Answer:  The correct option is

(A) x = -12 or x = 2.

Step-by-step explanation:  We are given to solve the following quadratic equation for x :

[tex]x^2+10x+12=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

From equation (i), we have

[tex]x^2+10x+12=36\\\\\Rightarrow x^2+10x+12-36=0\\\\\Rightarrow x^2+10x-24=0\\\\\Rightarrow x^2+12x-2x-24=0~~~~~~~[\textup{the sum of 12 and -2 is 10 and product is -24}]\\\\\Rightarrow x(x+12)-2(x+12)=0\\\\\Rightarrow (x+12)(x-2)=0\\\\\Rightarrow x+12=0,~~~~x-2=0\\\\\Rightarrow x=-12,2.[/tex]

Thus, the required solution of the given equation is x = -12 or x = 2.

Option (A) is CORRECT.

Answer:

31 and 28

Step-by-step explanation:

Let x represent the first number.

Let y represent the second number.

x + y = 59

x - y = 3

Use substitution method to solve.

x = y + 3

y + 3 + y = 59

2y + 3 = 59

Subtract both sides by 3.

2y = 56

Divide both sides by 2.

y = 28

Let's find the second number.

59 - 28 = 31

Check

31 -28 = 3

Answer The two numbers are 28 and 31.

The numbers are 31 and 28.

To find the two numbers where the sum is 59 and the difference is 3, we can set up two equations based on the information given.

Let the two numbers be x and y, where x > y. The equations would be:

Adding these two equations eliminates y, giving us:

2x = 62

Divide both sides by 2 to find x:

x = 31

Now substitute x back into one of the original equations to find y:

31 + y = 59

Subtract 31 from both sides:

y = 59 - 31

y = 28

Therefore, the two numbers are 31 and 28.

Answer:

Carr University has 1000 times more students than Whitestone College

Step-by-step explanation:

Whitestone College has a student population of 4 x 10 students

Carr University has a student population of 40,000 students.

To find out how big the number of students at Carr is compared to Whitestone College students.

Students of Carr University / Students of Whitestone.

40,000 / 4 x 10 = 1000

Carr University has 1000 times more students than Whitestone College

Answer:$7.50

Step-by-step explanation: make 4 boxes on a paper and put two lines in each box and you see that it is 8 in the boxes all to heather so that equals $8.00 so you can’t put a dollar in each box because if you do it will equal twelve dollars and you have to make ten dollars so you put $0.50 in each box so in each box it will be $2.50 in each box so you have to add $2.50 for times so it equals $10.00 so I added it it does  add up to ten dollars  so to see how much 3 bottles of water count you have to add up $2.50 3 timer and it equal $7.50

3 bottles of water costs $ 7.50

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to the problem,

4 bottles of water costs $ 10

1 bottle of water costs $ (10 / 4) = $ 2.50

3 bottles of water costs $ (2.50 x 3) = $ 7.50

∴Cost of 3 bottles is $7.50

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